These are a couple of little purchases. The New Workbox took my fancy. It is from a set of school reading cards. Such lovely simple hand drawn graphics which are screenprinted using a limited palette.
In a word NO. Some mischievous people love to start and pass on a rumor! but please it is always a good idea to check out facts from the source before passing on false information.
As I said in my last post for the year I have decided to put the business up for sale. (look back for details)
Patchwork on Central is a Great business and fabrics are my passion. As anyone who has been in lately can see it is business as usual, with as much new fabric as ever. I have just signed a 3 x 3 x 3 year lease so am not in any great hurry.
I will be sending out my intentions to everyone on my email list after the end of this financial year as well as advertise, as I have done no more about selling than put it on my blog and tell a few customers.
Don't you just love a gift that keeps coming! I received a subscription to the gorgeous British magazine Selvedge for Christmas last year and get such a surprise when I get home and find it sitting on the bench.
It takes me two seconds to rip the envelope open flick through and then many days to devour every word and image in it.
When seeing the ad in the mag, I did feel a bit jealous of Adrienne and Carolyn from the shop, who will soon be on their way to London to see the wonderful Quilt Exhibition at the V&A.
This is a quick project that I have made using a half metre pack (8x16th's from the shop) You will get quite a few scarves from this pack.
This gives me a bit of space to re arrange the pieces if I feel inclined. With this quilt after first placing the yellow's I decided that they were a little light. The white background that was coming through made them stand out too much. So out came my old skills of tea dying (from my country phase)
This is really good for that fabric that just does not go with anything. Test fabric first with a small piece, less tea if you just want to take the brightness out. Don't go too dark as it just goes ugly.
After many requests I have decided to run a few Saturday classes dedicated to making and designing your own contemporary quilt using the ripped method. I have had many students achieve great results in past classes, I am told it helps get any frustrations out of your system at the same time.
Anyone interested just call into the shop, phone or email. I run a casual basics class every second week with a max of 6 students. This class will concentrate on design and how to achieve a balanced quilt.
The photo's are of my current project using a variety of Kaffe fabrics and Japanese fabrics currently in stock. (yet to be sewn) It will be in the shop later this week for anyone who would like a look.
Tram Destination rolls seem to be everywhere at the moment, but quite expensive. I had these destinations printed over 18 months ago and it is a cheap way of getting the look on a budget.
We sell the panels, for $10 each on the lightweight linen, or $30 a panel on the heavier French linen. (really nice for cushions.)
I used the lightweight one to make the door curtain and put a piece of calico between them and top and bottom. I think is very appropriate for the shop at last stop tram 5.
You often read of the supposed rivalry between Melbourne and Sydney. I have always thought is a media beat up.
What a beautiful building. We all get so busy with our day to day goings on that we don't stop to admire the beauty we all have in our own cities.
As usual I have been pretty ruthless. All bags and quite a few clothes etc in the store are all 50% OFF.
As I am no longer Australian Distributor of the French products Place des Lices I am clearing out the warehouse!
A great opportunity to stockpile presents for Mothers Day and birthdays. Anyone who knows the product knows how lovely it is.
I have always been fond of a bit of kitsch! So when I saw these at Camberwell Market this morning I knew they needed to come home with me.
I have had my cousin staying with me this week and like many older baby boomers she is doing our family tree.
I tell you what, fact is more bizarre than fiction! After looking at her tree it turned out I was second cousin to a close friends, sisters husband, even though he came from SA and I came from WA his mother and my father were cousins.
In light of the much awaited Tim Burton film Alice in Wonderland, I thought I would give you a sneak peek of Effie's latest quilt. She is appliqueing images off the gorgeous, Japanese double sided muslin that is in the shop. If you are interested in the class book early as her class fills quickly.
I found this so cute bag in one of my Vintage magazines, thought I would share it. Someone may like to make it. The heading is a great example of how our language has changed and words have different meanings now.
Please join us, as we hope to inspire you through this blog and don't be shy to let us know your thoughts by email as we would love to hear from you.
I hope you enjoy reading this blog, as much as Lynn and staff enjoy posting all the happenings in the shop and around Melbourne, Australia.
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A visualization device includes: an evaluation index calculation unit 11 which calculates the value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; and a visualization processing unit 12 which generates image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion.
International Search Report for PCT Application No. PCT/JP2013/007078, dated Mar. 11, 2014. cited by applicant .
Japanese Office Action for JP Application No. 2014-551875 dated Oct. 10, 2017 with English Translation. cited by applicant.
1. A visualization device comprising: an evaluation index calculation unit which is implemented by a processor and which calculates a value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; a visualization processing unit which is implemented by the processor and which generates image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion; and an output device which depicts the high-dimensional data using the image information generated by the visualization processing unit.
2. The visualization device according to claim 1, wherein the evaluation index calculation unit uses a binary tree as the criterion for conditioning the second attribute group with the first attribute group.
3. The visualization device according to claim 1, wherein the evaluation index calculation unit uses a multi-branch tree as the criterion for conditioning the second attribute group with the first attribute group.
4. The visualization device according to claim 1, wherein the evaluation index calculation unit uses a correlation coefficient as the evaluation index representing the feature degree.
5. The visualization device according to claim 1, wherein when class information on data to be visualized is given, the evaluation index calculation unit uses an accuracy rate of class classification as the evaluation index representing the feature degree.
7. The visualization device according to claim 1, wherein the visualization processing unit outputs image information in which two-dimensional scatter plots corresponding to combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values, are arranged in a tree view format.
8. The visualization device according to claim 1, wherein the visualization processing unit outputs image information in which parallel coordinate plots corresponding to combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values, are arranged in a tree view format.
9. A visualization method comprising: calculating a value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; generating image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion; and depicting, by an output device, the high-dimensional data using the generated image information.
10. A non-transitory computer readable information recording medium storing a visualization program, when executed by a processor, that performs a method for calculating a value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; generating image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion; and depicting, by an output device, the high-dimensional data using the image information.
This application is a National Stage Entry of PCT/JP2013/007078 filed on Dec. 3, 2013, which claims priority from Japanese Patent Application 2012-272413 filed on Dec. 13, 2012, the contents of all of which are incorporated herein by reference, in their entirety.
The present invention relates to a visualization device, a visualization method, and a visualization program, which make a data structure, especially an overview of data distribution, graspable to examine preprocessing and an analytical method to be applied in performing data analysis on high-dimensional data.
A data visualization technique is a technique essential for advancing work efficiently in data analysis work. With the development of sensing technology and information management technology, the necessity has increased in recent years where data have become enormous and complicated.
The following scenes are considered as typical scenes of application of the data visualization technique in the area of data analysis: (1) A scene where a data structure is overviewed as a stage prior to analysis, (2) a scene where learning results are interpreted when the data structure is learned as a model by a machine learning technique or the like, and (3) a scene where prediction results are considered when a prediction is made using the learned model.
In the scene (1), there is a method as typical visualization means used to overview the data structure, where after high-dimensional data are compressed into lower dimensions using a multivariate analysis technique such as principal component analysis or multidimensional scaling, the compressed data are displayed on a two-dimensional scatter plots. There is also a visualization technique, called Scatter Plot Matrix (hereinafter referred to as SPM), for arranging, in a matrix form, two-dimensional scatter plots for all combinations of two-dimensional data obtained from the original high-dimensional data. Further, there is a visualization technique, called Parallel Coordinate Plot (hereinafter referred to as PCP or parallel coordinate plot), for arranging axes corresponding to respective dimensions longitudinally in parallel with one another, plotting observed values so that the minimum value will appear at the lower end and the maximum value will appear at the upper end in all the dimensions, and connecting observed values on adjacent axes with line segments.
The principal component analysis and the multidimensional scaling are useful to visualize information indicative of scattering of data points in a multidimensional space while storing the information as much as possible. Further, the SPM and the PCP are useful to visualize a relationship between specific minor dimensions existing in high dimensional space by one diagram as a whole.
Patent Literature (PTL) 1 describes a method of classifying learning data with continuous-valued attributes using a decision tree based on the data distribution feature to make a decision of or change in a model structure easy. In the method described in PTL 1, each node in a generated decision tree is displayed as a scatter plot of an objective function as a data group concerning certain one attribute and an explanatory function as a data group concerning the multiple remaining attributes to make the data distribution feature understandable.
In the principal component analysis, for example, there is a problem that it is difficult to interpret a visualized content depending on the data even in a relatively low dimension. Further, in the multidimensional scaling, for example, there is a problem that the plot itself becomes complicated as the number of data and the number of dimensions increase. Thus, these visualization techniques are not necessarily versatile.
Further, in the method described in PTL 1, attributes displayed as scatter plots are fixed to objective variables and certain one explanatory variable. Therefore, an attribute to be displayed cannot be set for each node. As a result, for example, when data structures existing in high-dimensional data are to be analyzed, the data structures capable of being overviewed by a user (analyst) are limited to some of the data structures.
Therefore, it is an object of the present invention to provide a visualization device, a visualization method, and a visualization program, capable of overviewing more data structures as characteristic data structures existing in high-dimensional data to be analyzed when a user analyzes the high-dimensional data.
A visualization device according to the present invention includes: an evaluation index calculation unit which calculates the value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; and a visualization processing unit which generates image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion.
Specifically, the visualization device according to the present invention narrows down data having characteristic structures in the high-dimensional data before performing visualization processing. Here, it is assumed that data are given in a matrix form of [sample.times.attribute]. Hereinafter, the attribute is synonymous with the dimension. Next, the visualization device applies visualization processing itself to the data narrowed down. As the method of narrowing down data having characteristic structures, consider paying attention to data on some attributes (second attribute group) conditioned with other some attributes (first attribute group). Here, the presence of multiple combinations of the first attribute group and the second attribute group is assumed. Therefore, it is desired to be able to extract as many combinations as possible from the standpoint of visualization to enable the analyst to overview as many data structures as possible. As the method of enabling the analyst to overview as many data structures as possible, for example, there is a method of defining some sort of evaluation index representing the feature degree of a data structure, calculating a value of the evaluation index for each combination of the first attribute group and the second attribute group, and applying an appropriate visualization technique to a combination of the first attribute group and the second attribute group having a particularly large value. Here, as the evaluation index, for example, a correlation coefficient or a quantity such as degree-of-separation/mutual information when class information is given is considered. The class information is an attribute representing a quantity to be predicted in data analysis. For example, for marketing in CRM (Customer Relationship Management), an attribute representing the purchase behavior of customers corresponds to the class information. Specifically, the degree of separation is the accuracy rate of class classification. When multiple combinations of attribute groups large in evaluation index exist, the visualization device provides an interface to enable the analyst to overview all the combinations as much as possible at a time. As an example of the method for enabling overviewing of all the combinations of attribute groups at a time, there is a method of arranging graphs in a tree view format to be described later.
A visualization method according to the present invention includes: calculating the value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; and generating image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion.
A visualization program according to the present invention causes a computer to execute: a process of calculating the value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; and a process of generating image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion.
According to the present invention, when analyzing high-dimensional data, a user can overview more data structures as characteristic data structures existing in high-dimensional data to be analyzed.
FIG. 2 It depicts an explanatory diagram depicting an example of a decision tree created based on the five-dimensional data depicted in FIG. 1.
FIG. 3 It depicts an explanatory diagram depicting an example of the output results of a visualization device for the five-dimensional data depicted in FIG. 1.
FIG. 4 It depicts a block diagram depicting the configuration of a first exemplary embodiment of a visualization device according to the present invention.
FIG. 5 It depicts a flowchart depicting the operation of the first exemplary embodiment of the visualization device according to the present invention.
FIG. 6 It depicts a block diagram depicting a minimum configuration of a visualization device according to the present invention.
A first exemplary embodiment of the present invention will be described below with reference to the accompanying drawings.
FIG. 1 is an explanatory diagram depicting an example of the results of visualizing five-dimensional data using SPM. Here, a problem of classifying "o" indicative of one sample and "x" indicative of the other sample for the five-dimensional data using SPM depicted in FIG. 1 is considered. When class information is purchase behavior, the sample represents each individual customer. In FIG. 1, scatter plots for any two-dimensional combinations in five dimensions are depicted.
An analyst can overview a distribution of data in any two-dimensional space through the scatter plots depicted in FIG. 1. For example, the analyst can read from FIG. 1 that "o" is concentratedly distributed as relatively large values and "x" is concentratedly distributed as relatively small values in a first dimension (attribute V1). However, it is difficult to read, form the scatter plots depicted in FIG. 1, further information regarding classification information on "o" and "x" at a time.
In the exemplary embodiment, a decision tree is used as a method of narrowing down data. Further, since the classification problem is considered here, a degree of separation between "o" and "x" as an index representing a feature degree is considered.
FIG. 2 is an explanatory diagram depicting an example of the decision tree created based on the five-dimensional data depicted in FIG. 1. The inequalities in the decision tree depicted in FIG. 2 represent branch conditions, and the numbers of leaves represent "the number of o pieces" or "the number of x pieces."
In the exemplary embodiment, a visualization device extracts a dimension in which "o" and "x" are separated best as a node closest to the root of the tree, i.e., as a node closest to the upper part of FIG. 2 in creating the decision tree. Therefore, for example, it can be read from the decision tree depicted in FIG. 2 that the attribute V1 best separates "o" and "x" like the scatter plots depicted in FIG. 1. It can also be read that attribute V2 best separates "o" and "x" in terms of data with values of attribute V1 being 0.02335 or more. Further, it can be read that attribute V3 best separates "o" and "x" in terms of data with values of attribute V1 being less than 0.02335.
Further, in the exemplary embodiment, the visualization device provides an interface as depicted in FIG. 3 as output results to enable these pieces of information on the classification between "o" and "x" to be overviewed at a time. FIG. 3 is an explanatory diagram depicting an example of the output results of the visualization device for the five-dimensional data depicted in FIG. 1. In FIG. 3, three scatter plots are arranged to correspond to the structure of the decision tree depicted in FIG. 2. Each dashed line in each scatter plot depicted in FIG. 3 is drawn in a position corresponding to the left side value of the inequality at each node depicted in FIG. 2.
Scatter plot A depicted in FIG. 3 corresponds to a node with the branch condition being "0.02335<=V1," a node with "-1.227<=V2," and a node with "-0.2746<=V3" depicted in FIG. 2.
Scatter plot B depicted in FIG. 3 corresponds to a node with the branch condition being "-0.2746<=V3," a node with "0.1117<=V5," and a node with "-3.464<=V4" depicted in FIG. 2. In other words, scatter plot B represents data regarding attribute V3, attribute V5, and attribute V4, limited to samples small in the values of attribute V1, i.e., conditioned by attribute V1. In the case of scatter plot B, attribute V1 corresponds to a first attribute group, and attribute V3, attribute V5, and attribute V4 correspond to a second attribute group.
Scatter plot C depicted in FIG. 3 corresponds to a node with the branch condition being "-1.227<=V2," a node with "-1.098<=V4," and a node with "1.868<=V5" depicted in FIG. 2. In other words, scatter plot C represents data regarding attribute V2, attribute V4, and attribute V5, limited to samples large in the values of attribute V1, i.e., conditioned by attribute V1. In the case of scatter plot C, attribute V1 corresponds to the first attribute group, and attribute V2, attribute V4, and attribute V5 correspond to the second attribute group.
Although three scatter plots are contained in FIG. 3, any number of scatter plots may be contained in the output results. For example, the number of scatter plots may be changed according to the depth of the tree, or only scatter plots corresponding to nodes separating "o" and "x" well, i.e., nodes having particularly large evaluation index values may be contained in the output results. Note that the determination as to whether a node separates "o" and "x" well may be made, for example, by determining whether the evaluation index value is larger than a predetermined criterion.
From scatter plot A depicted in FIG. 3, when data are narrowed down to samples taking on large values in terms of attribute V1, the analyst can read that "o" is distributed as relatively large values and "x" is distributed as relatively small values in terms of attribute V2 disproportionately. On the other hand, when data are narrowed down to samples taking on small values in terms of attribute V1, the analyst can read that "o" is distributed as relatively large values and "x" is distributed as relatively small values in terms of attribute V3 disproportionately.
Similarly, from scatter plot B, when data are narrowed down to samples taking on small values in terms of attribute V1 and further large values in terms of attribute V3, the analyst can read that "o" and "x" are relatively separated in terms of attribute V5.
Similarly, from scatter plot C, when data are narrowed down to samples taking on large values in terms of attribute V1 and further large values in terms of attribute V2, the analyst can read that "x" is concentratedly distributed as small values in terms of attribute V4 compared with "o."
Information on the above data structure that can be read from each scatter plot depicted in FIG. 3 cannot be found by the typical visualization means mentioned above. Further, the results depicted in FIG. 3 can be combined with the background knowledge of the analyst regarding data to enable the analyst to develop an analysis policy, such as to exclude some data from the analysis or apply another analytical method to some data.
FIG. 4 is a block diagram depicting the configuration of the first exemplary embodiment of the visualization device according to the present invention.
The decision tree creation unit 102 takes input of data to be visualized and the decision tree parameters from the data/parameter input unit 101. The decision tree creation unit 102 creates the decision tree for the input data as depicted in FIG. 2 according to information on the input decision tree parameters. The numerical values such as "0.02335," "-1.227," and the like in the inequalities depicted in FIG. 2 are an example of numerical values calculated by the decision tree creation unit 102. The decision tree creation unit 102 outputs information on the created decision tree to the decision tree storage unit 103.
The decision tree storage unit 103 stores the information on the decision tree input from the decision tree creation unit 102.
The data/parameter input unit 101, the decision tree creation unit 102, and the tree view-formatted scatter plot creating unit 104 are, for example, implemented by a computer operating according to a visualization program. In this case, a CPU has only to read the visualization program and operate as the data/parameter input unit 101, the decision tree creation unit 102, and the tree view-formatted scatter plot creating unit 104 according to the program. Each of the data/parameter input unit 101, the decision tree creation unit 102, and the tree view-formatted scatter plot creating unit 104 may also be realized by separate hardware.
The decision tree storage unit 103 is realized by a storage device such as a memory provided in the visualization device.
FIG. 5 is a flowchart depicting the operation of the first exemplary embodiment of the visualization device according to the present invention.
As described above, in the exemplary embodiment, data having characteristic structures in the high-dimensional data are narrowed down before the visualization processing itself is performed. Further, in the exemplary embodiment, the tree view-formatted scatter plots created based on the information on the decision tree used to narrow down the data are output so that more characteristic data structures existing in the high-dimensional data can be overviewed at a time. Therefore, when analyzing the high-dimensional data, the analyst can grasp multiple characteristic data structures existing in the data. This enables the analyst to develop a policy as to what preprocessing and analytical method are to be applied.
Further, since the exemplary embodiment focuses on the extraction of conditioned data structures, samples having characteristic data structures can be extracted beforehand as preprocessing in analyzing the high-dimensional data and analyzed separately. In addition, it is possible to provide information used to decide on the number of mixtures and a model in each component when a multipeak model like a contaminated normal distribution as analysis means is applied to data.
In the exemplary embodiment, the case where the visualization device includes the image output unit is described, but the image output unit may not be included in the visualization device. In this case, the tree view-formatted scatter plot creating unit 104 has only to output image information to an external display, printer, or the like communicable with the visualization device. According to such a configuration, the configuration of the visualization device can be more simplified.
Further, in the exemplary embodiment, the case where the degree of separation is used as the evaluation index representing the feature degree is described, but a correlation coefficient may be used. Further, when class information on the data to be visualized is given, entropy may be used as the evaluation index representing the feature degree.
Further, in the exemplary embodiment, the case where the scatter plots are arranged in a tree view format and displayed is described, but the PCP may be arranged in a tree view format and displayed. Further, in the exemplary embodiment, the case where the decision tree creation unit 102 uses a binary tree to create the decision tree is described, but the decision tree creation unit 102 may use a multi-branch tree other than the binary tree to create the decision tree. In this case, the tree view-formatted scatter plot creating unit 104 has only to create tree view-formatted scatter plots according to the structure of the decision tree.
The present invention is applicable to general scenes for discovery of knowledge from high-dimensional data. For example, when a reason for the failure of an industrial product such as a car or a home electrical appliance is identified using machine learning technology from information on the values of many sensors incorporated in the industrial product, the visualization device according to the present invention can be used. In this case, it can be preliminarily overviewed whether there is a characteristic structure between data on the kind of specific reason for a failure and data on the kind of sensor at the stage of examining the analytical method. As another example, when a relationship between personal information on customers and purchase behavior is examined for marketing in CRM, the visualization device according to the present invention can also be used in the same way.
FIG. 6 is a block diagram depicting a minimum configuration of a visualization device according to the present invention. As depicted in FIG. 6, the visualization device includes: an evaluation index calculation unit 11 (corresponding to the decision tree creation unit 102 depicted in FIG. 4) which calculates the value of an evaluation index representing a feature degree for each of combinations of a first attribute group and a second attribute group in terms of data on the second attribute group including one or more attributes and conditioned with the first attribute group including one or more attributes among high-dimensional data to be visualized; and a visualization processing unit 12 (corresponding to the tree view-formatted scatter plot creating unit 104 depicted in FIG. 4) which generates image information for presenting combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values based on a predetermined criterion.
According to this configuration, information on combinations of attribute groups having particularly large evaluation index values can be presented to a user. Therefore, when high-dimensional data are to be analyzed, the analyst can grasp multiple characteristic data structures existing in the data. This enables the analyst to develop a policy as to what preprocessing and analytical method are to be applied.
According to this configuration, an interface including tree view-formatted scatter plots as depicted in FIG. 3 can be presented to the analyst.
According to this configuration, tree view-formatted scatter plots on high-dimensional data can be created based on information on a multi-branch tree created based on the high-dimensional data. This can deal with more complicated conditioning in creating a decision tree.
According to such configurations, since the evaluation index representing the feature degree of a data structure can be expressed as a numerical value, a comparison of evaluation indexes for each of the combinations of the first attribute group and the second attribute group can be made more accurately.
(6) A visualization device wherein the visualization processing unit 12 outputs image information in which two-dimensional scatter plots corresponding to combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values, are arranged in a tree view format.
(7) A visualization device wherein the visualization processing unit 12 outputs image information in which parallel coordinate plots corresponding to combinations of the first attribute group and the second attribute group, which are determined to have large evaluation index values, are arranged in a tree view format.
According to such configurations, the analyst can overview more characteristic data structures existing in the high-dimensional data to be visualized at a time. Further, since a combination of attribute groups having a larger evaluation index value is displayed in a position closer to the upper part of the tree view, the analyst can readily interpret the visualized content. In addition, since only scatter plots corresponding to combinations of attribute groups having particularly large evaluation index values can be presented to the user, even when the number of data and number of dimensions of high-dimensional data to be visualized become large, the plots themselves do not become complicated.
While the present invention has been described with reference to the exemplary embodiment and examples, the present invention is not limited to the aforementioned exemplary embodiment and examples. Various changes that can be understood by those skilled in the art within the scope of the present invention can be made to the configurations and details of the present invention.
This application is based upon and claims the benefit of priority from Japanese patent application No. 2012-272413, filed on Dec. 13, 2012, the disclosure of which is incorporated herein in its entirety by reference.
A method for ascertaining a parking area of at least one street section includes providing information indicating a usable width of the street section, the usable width representing a drivable width of the street section between spaces for parked vehicles at the two lateral sides of a driving vehicle; the driving vehicle driving the street section and ascertaining lateral distances from objects using an ascertainment device situated in the driving vehicle; comparing the ascertained lateral distances to the usable width; and ascertaining the parking area by way of the comparison.
The present application is a continuation of and claims priority to U.S. patent application Ser. No. 14/852,089, filed Sep. 11, 2015, the content of which is hereby incorporated herein by reference in its entirety.
1. A method for ascertaining a parking area of a street section, the method comprising: comparing, by processing circuitry, ascertained lateral distances from objects to a predetermined usable width of the street section; and ascertaining, by the processing circuitry, the parking area based on the comparison.
2. The method of claim 1, wherein the method is performed according to an algorithm by which an apparent parking area ascertained on the basis of a double-parked vehicle is discarded, based on a deviation in a predefined manner of the ascertained lateral distances from the usable width.
3. The method of claim 1, wherein the method is performed according to an algorithm by which an apparent parking area ascertained on the basis of an on-coming vehicle is discarded, based on a deviation in a predefined manner of the ascertained lateral distances from the usable width.
6. The method of claim 1, wherein the processing circuitry is at least partly located in an ascertaining vehicle driving on the street section.
7. The method of claim 1, wherein the processing circuitry is at least partly located in a server remote from an ascertaining vehicle for which the parking area is ascertained.
8. The method of claim 1, wherein the ascertaining of the parking area is carried out in real time while the street section is being driven, the ascertained lateral distances being ascertained while the street section is being driven.
9. The method of claim 1, wherein the ascertaining of the parking area is carried in an evaluation phase after the ascertained lateral distances are ascertained from a driving on the street section.
10. The method of claim 1, wherein the lateral distances are ascertained by an ascertaining vehicle based on detections of a sensor of the ascertaining vehicle while the ascertaining vehicle is driving on the street section.
11. The method of claim 10, wherein a maximum range of a total of the lateral distances which the ascertaining vehicle can ascertain is 2* a maximum range of the sensor +a width of the ascertaining vehicle.
12. The method of claim 11, wherein the method further comprises, in an event that the maximum range does not cover the entire usable width, detecting a position of the ascertaining vehicle, and using the detected position.
13. The method of claim 1, wherein the lateral distances are ascertained by an ascertaining vehicle.
14. The method of claim 1, wherein the predetermined width is a drivable width of the street section between parked vehicles.
15. The method of claim 1, wherein the parking area is ascertained in response to satisfaction of a condition that one or more of the ascertained lateral distances is greater than the predetermined usable width.
16. The method of claim 1, further comprising ascertaining the lateral distances based on a correlation between sensed distances obtained by one or more sensors traveling in opposite directions.
17. The method of claim 1, further comprising ascertaining the lateral distances, wherein the ascertaining of the lateral distances includes averaging a plurality of distance measurements of a corresponding plurality of locations.
18. The method of claim 1, further comprising ascertaining the lateral distances, wherein the ascertaining of the lateral distances includes averaging a plurality of distance measurements of a particular location.
19. The method of claim 18, wherein the plurality of distance measurements are obtained during a corresponding plurality of drives by the particular location.
20. An ascertaining vehicle comprising: an ascertainment device that includes: a sensor for ascertaining lateral distances from objects; and circuitry using which: the ascertained lateral distances are compared to a predetermined usable width of a street section; and a parking area of the street section is ascertained based on the comparison.
21. The ascertaining vehicle of claim 20, further comprising a communication device for transmitting data of the ascertainment device to a server facility.
23. A non-transitory computer-readable medium on which are stored instructions that are executable by a computer processor and that, when executed by the processor, cause the processor to perform a method for ascertaining a parking area of a street section, the method comprising: obtaining lateral distances from objects; comparing the ascertained lateral distances to a predetermined usable width of the street section; and ascertaining the parking area based on the comparison.
24. A server comprising: an interface to a communication network; and processing circuitry, wherein the processing circuitry is configured to: obtain, from a vehicle, over the communication network, and via the interface, lateral distances from objects; compare the obtained lateral distances to a predetermined usable width of a street section; and ascertain, based on the comparison, a parking area of the street section.
The present invention relates to a method for ascertaining a parking area of at least one street section. The present invention further relates to a device for ascertaining a parking area of at least one street section.
Various methods are known in the related art for ascertaining distances of a vehicle from objects with the aid of distance-based sensors (e.g., ultrasonic sensors, radar sensors, video sensors, lidar sensors).
An objective of the present invention is to provide an improved method for ascertaining a parking area of a street section.
According to an example embodiment, the objective is attained by a method for ascertaining a parking area of at least one street section including the steps of: providing a usable width of a street section, the usable width representing a drivable width of the street section between parked vehicles; driving the street section using an ascertaining vehicle and ascertaining lateral distances from objects using an ascertainment device situated in the ascertaining vehicle; comparing the ascertained lateral distances to the usable width; and ascertaining the parking area by way of the comparison.
The method may be used advantageously especially for completing incomplete parking space maps. If the measured usable width (between vehicles at both sides of the driving vehicle) coincides with the known, i.e., expected, usable width, an inference is made that the parking area is occupied. Ultimately, this makes it possible to use parked vehicles to detect parking areas, whereby known methods based exclusively on detecting parking spaces are significantly improved.
On account of the information regarding the usable width of the street section, it is possible advantageously to ascertain parking areas and to provide these for example in the form of a parking space map. This allows for parking areas to be learned quickly, as a result of which it becomes possible to prepare a complete and current parking space map using a relatively small number of passes.
In an example, the method is further characterized by that, in the event of a defined deviation of the ascertained lateral distances from the usable width, which initially indicates an apparent parking area, but which apparent parking area is determined because of a vehicle parked in a second row of the street section (within the usable width), the apparent parking area is discarded. It is thus possible to filter out detected "false" parking areas so that these do not enter the parking space map.
In an example, the method is further characterized by that, in the event of a defined deviation of the ascertained lateral distances from the usable width, an apparent parking area ascertained on the basis of a vehicle of oncoming traffic is discarded. Even in the event of oncoming traffic, it is thus possible to filter out a "false" parking area detected on the basis of the detection mechanism, which is therefore not entered in the parking space map. Ultimately, a type of "deplausibilization of parking space" is thus provided, which is advantageously functional even when the usable width is not represented between vehicles parked on the edges of the street.
In an example, the method further provides for a maximum usable width of the street section to have the following value: 2.times.the maximum range of the ascertainment device+width of the ascertaining vehicle. This makes it possible to take the ranges of different sensor technologies into account such as e.g., ultrasound, radar, laser, etc. In the event that the sensor technology used does not reach the mentioned range, additional localization methods may be used, e.g., using GPS data.
In an example, the method further provides for a position of the vehicle to be detected in the event that a range of the ascertainment device does not cover the entire usable width, the detected position being compared to the ascertained lateral distances. In this manner, the proper functionality of the method is ensured even when the usable width of the street section exceeds the sensor range.
In an example, the method further provides for ascertaining objects, in particular vehicles, from the ascertained distance values. Objects, in particular vehicles, are thereby detected from the ascertained distances, which are determined from defined echoes of the ascertainment device. Other objects, e.g., advertisement pillars, garbage containers etc., may also be detected, which do not enter the parking space map.
In an example, the method further provides for the method to be carried out at least partly locally in the ascertaining vehicle and/or at least partly in a server facility. In this manner, an existing processing capacity may be distributed or utilized in the best way possible.
In an example, the method further provides for the ascertained distance data to be transmitted to the server facility in an automated fashion. This makes it possible to aggregate in the long term a great quantity of historical data, which represent the conditions in a very current and accurate fashion.
In an example, the method further provides for the method to be carried out in real time while the street section is driven or just after the street section is driven in an evaluation phase. This makes it possible advantageously to implement different evaluation strategies.
In an example, the method further provides for the street section to be driven in different directions of travel, the ascertainment data of the drives in the different directions of travel being correlated. Driving the street section in opposite directions advantageously allows for an even more precise ascertainment of the parking area.
In an example, the method is further characterized by that parking areas are ascertained for a defined length of the street section. This makes it possible to produce parking space maps for selectively chosen areas.
According to an example embodiment, the objective is attained by a device for ascertaining a parking area of a street section, the device including an ascertaining vehicle equipped with an ascertainment device, it being possible to ascertain lateral distances using the ascertainment device, a usable width of the street section being known to the device, and a parking area being ascertainable from a comparison of the ascertained lateral distances with the usable width.
The present invention is described below in detail with additional features and advantages, with reference to several figures. For this purpose, each and every of the features presented in any of the specification, drawings, and claims form the subject matter of the present invention. The figures are specifically intended to illustrate the principles that are essential to an understanding of the present invention.
FIG. 1 is a diagrammatic sketch for explaining a functional principle of the method, according to an example embodiment of the present invention.
FIG. 2 is a diagrammatic sketch for explaining an advantageous development of the method, according to an example embodiment of the present invention.
FIG. 3 is a diagrammatic sketch for explaining a deplausibilization of an apparent parking area due to a vehicle in the second lane, according to an example embodiment of the present invention.
FIGS. 4 and 5 are diagrammatic sketches for explaining a deplausibilization of an apparent parking area as a result of oncoming traffic, according to an example embodiment of the present invention.
FIG. 6 is a diagrammatic sketch for explaining a recognition of a parking area, according to an example embodiment of the present invention.
FIGS. 7 and 8 are diagrammatic sketches for explaining a sensor range, according to an example embodiment of the present invention.
In the sense of the present invention, a so-called "usable width" or "drivable driving width" or "drivable driving lane" or "real street width" of a street or a section of a street defines a physical width of the street from curb to curb minus a respective width of a parked vehicle on each edge of the street. It is thus assumed that the usable width is defined only in those areas of the street that are bounded by parking areas. For this purpose, the usable width is ascertained by a pre-filtering process, in which e.g., the walls of buildings are not taken into account as limiting elements of the street section for ascertaining the usable width.
Conventionally, to ascertain the usable width, specific reflection patterns of alternating vehicles and parking spaces are normally used. The ascertainment of the mentioned parking spaces is in this instance bound up with a detection of characteristic echo images, it being necessary, e.g., for there to exist respectively a sequence of [parked vehicle--parking space] or [parking space--parked vehicle] in order to detect the parking space. This requires an extensive number of drives through the street section, it being very difficult to ascertain or verify areas, which are subject to great parking pressure and which are consequently very seldom or never free, as a parking area.
FIG. 1 shows a fundamental functional principle of method for ascertaining a parking area of a street section, according to an example embodiment of the present invention. An ascertaining vehicle 10 is shown, which drives along a street section 1 in the direction of the arrow. On both edges of street section 1, parked vehicles are shown, which occupy parking areas 13 (covered by vehicles 11) of street section 1. Ascertaining vehicle 10 includes an ascertainment device 12 for detecting a distance from objects situated laterally with respect to the direction of travel, ascertainment device 12 including an ultrasonic sensor, a radar sensor or another suitable sensor.
As already mentioned, ascertainment device 12 has advance information regarding a usable width 3 of the street section 1, a manner of ascertaining the usable width 3 and a manner of providing the usable width 3 being ultimately of secondary importance for ascertainment device 12. Ascertainment device 12 furthermore has information regarding that street section 1 has parking areas 13 at least on one side.
When street section 1 is driven, an example embodiment of the present invention provides for the detection of distances from objects, preferably vehicles 11, situated laterally from ascertaining vehicle 10, and for comparing these with known usable width 3. In this manner, as many lateral distances as possible are detected between ascertaining vehicle 10 and parked vehicles 11, at least one measurement being performed laterally essentially at a right angle on the left and on the right of ascertaining vehicle 10. The mentioned ascertainments are ultimately available in the form of limit points 2 of usable width 3, which thus represent "scanning points" of usable width 3. Because of tolerance thresholds, usable width 3 is represented by an arithmetic average value of distances between limit points 2.
In the event that, as shown in FIG. 1, the measured distance within the scope of a defined tolerance threshold (due to measurement or parking inaccuracies) essentially agrees with the previously known usable width 3, an inference is made to the effect that parking areas 13 along street section 1 are occupied. In this manner, it is possible to prepare a complete parking space map within a short time, since, unlike in the related art, it is not necessary that there be unoccupied parking areas 13 ("parking spaces") in order to detect parking areas 13.
FIG. 2 shows a principle of an advantageous development of the method. In this instance, objects, preferably in the form of vehicles 11, are ascertained or modeled from the measured lateral distance values by way of a processing step, which is indicated by tangential limit lines 2a on those vehicles 11 which ascertaining vehicle 10 has already passed. In this case as well, usable width 3 is compared to the distances between ascertained vehicles 11, and from this it is possible to infer parking areas 13.
FIG. 3 indicates a principle of a deplausibilization of a "false parking area" 13a, which is detected in a space behind a vehicle 11a that is parked in a second row and which is discarded for the purpose of preparing the parking space map. To detect a free parking area 13, ascertainment device 12 requires at least one object before or after free parking space 13 in order to generate a signal transition. This can be achieved when there is a clear difference between a currently measured usable width 3a between vehicle 11a parked in the second row and the opposite vehicle 11 and the previously known usable width 3. In this instance as well, there is thus a comparison between the currently measured usable width 3a and the previously known usable width 3, whereby a false parking space is discarded, tagged or otherwise marked as invalid and is thus not taken up into the parking space map.
As indicated in FIG. 4, this may be done analogously also in the case of an individual vehicle of oncoming traffic, the individual vehicle of oncoming traffic and the ascertaining vehicle 10 driving past each other at a defined low relative speed (e.g., approximately 45 km/h). The mentioned relative speed can be determined or adapted in a simple manner using suitable software algorithms. In this case too, there is no detection of a false parking area 13a, which is thus discarded and does not enter into the parking space map.
FIG. 5 essentially corresponds to FIG. 4, a scenario being represented in this case with moving oncoming traffic, in which a larger space occurs between two individual vehicles of the oncoming traffic, which is recognized as a false parking area 13a and is discarded or deplausibilized for the purpose of producing the parking space map.
FIG. 6 shows a "positive comparison" between known usable width 3 and the currently measured usable width 3a, the currently measured usable width 3a being greater than the known usable width 3, and for this reason a parking area 13 being recognized or validated.
FIG. 7 shows a scenario, in which a range of ascertainment device 12 on the left side of ascertaining vehicle 10 is not sufficient for ascertaining the distances from vehicles 11. Using ascertainment device 12, it is thus possible to ascertain only the limit points 2 to the right of ascertaining vehicle 10. In this case, it is possible to use additionally a position detection device (e.g., a GPS position detection device) in order to determine a position of ascertaining vehicle 10 that is accurate to within the centimeter range, and to ascertain in this manner distances from the laterally situated vehicles 11. The following equation applies for the maximum setpoint range d.sub.max of ascertainment device 12: d.sub.max=2.times.maximum sensor range+width of the ascertaining vehicle
If ascertainment device 12 is unable to reach the stated setpoint range d.sub.max, then no comparison can be performed with the previously known usable width 3, and the mentioned position detection device must be used additionally.
FIG. 8 indicates that a range of ascertainment device 12 is increased with the aid of another sensor technology in order thereby to be able to perform the lateral measurements. In this manner, as provided, it is possible to ascertain the limit points 2 on both sides of ascertaining vehicle 10. Depending on the sensor technology utilized in ascertainment device 12, a different sensor range of ascertainment device 12 may be utilized, whereby different usable widths 3 may be ascertained depending on the utilized technology.
The mentioned ascertainments of the lateral distances with the ascertainment of parking areas 13 and the deplausibilization of false parking areas 13a can be performed locally in ascertainment device 12 and/or in a decentralized server facility (not shown). Real-time processing can be provided or processing can be performed subsequent to drives along the street section. A communication device required for processing in the server facility for wired or wireless communication of ascertainment device 12 with the server facility is not shown.
The accuracy and reliability of the ascertainment of parking areas 13 increases with the number of drives through the respective street section 1 since averaging is then performed with an increased number of measured values.
Advantageously, the ascertainment of parking area 13 can already be performed in ascertaining vehicle 10 itself, for example by ascertainment device 12 or a control unit provided for this purpose. Alternatively or additionally, it is also conceivable that all acquired data are transmitted via a radio-based communication device (e.g., based on GSM, EDGE, UMTS, LTE, WLAN etc.) of the ascertaining vehicle 10 to a server facility, the ascertainment of parking area 13 in this case being performed by the server facility, which is normally significantly more powerful.
Preferably, there can also be a provision to perform the described measurements also in a second direction of travel of street section 1 and to correlate or compare them with the measured values of the drive through street section 1 performed in the first direction of travel (not shown). In this manner, it is possible to improve further a data quality of parking areas 13 or an accuracy of the parking space map produced from these.
The method can be implemented advantageously using different sensor technologies, e.g., ultrasonic sensors or radar sensors, which makes it possible to take economic aspects into account.
The method is preferably implemented as software, which facilitates adapting and updating the method.
FIG. 9 shows a basic flowchart of an example embodiment of the method of the present invention. In a step 20, a usable width 3 of street section 1 is provided, the usable width 3 representing a drivable width of street section 1 between parked vehicles 11. In a step 21, street section 1 is driven by an ascertaining vehicle 10 and lateral distances from objects are ascertained by an ascertainment device 12 situated in ascertaining vehicle 10. In a step 22, the ascertained lateral distances are compared to usable width 3. Parking area 13 is ascertained by way of the comparison in a step 23.
In summary, the present invention provides a method and a device for ascertaining a parking area of a street section. A type of "data mining" is performed for this purpose, which while driving carries out a continual comparison of an ascertained usable width with a previously known usable width. Ultimately, this makes it possible to produce parking space maps of high quality in an efficient manner. Advantageously, for recognizing the parking areas, it is possible to use also parking areas that are in an occupied state, and it is not necessary for parking areas to be unoccupied in order to be detected.
Although the present invention was described above with reference to specific example embodiments, one skilled in the art is also able to implement specific embodiments that were not disclosed above or that were disclosed above only partially, without deviating from the essence of the invention.
All Scripture is God-breathed and is useful for teaching, rebuking, correcting and training in righteousness, so that the servant of God may be thoroughly equipped for every good work. 2 Timothy 3.16-17
My good friend, Pastor Simon Mawdsley and I have just finished our 2nd workshop here in Lusaka, Zambia. We worked this week with a great group of 16 pastors who believe the Scriptures are God’s Words and useful in all of life. However, most of them have had little access or opportunity to be trained how to study God’s Word.
During the training, one of our young pastors, Alick Tembo, took me aside and told me with tears, ‘I’ve been a pastor for over 10 years but no one has ever come alongside me and taught me how to study and understand the scriptures. I honestly feel like I am dreaming because I never thought I would have training like this.’
What a joy and high privilege to be able to come alongside brothers like Alick, Charles, Jeremiah and others, growing in how to dig deeply into God’s Word, carefully observing what is there, not adding what is not there, fighting against the temptation to tickle ears and bending God’s Word.
Pastor Alick Tembo pastors the Vision Bible Church International, a church that he planted in a poor area of Lusaka six years ago. Beyond the good teaching and encouragement of his former pastor, Alick has had no access to bible training. He was thrilled to be chosen as one of the 16 pastors for our PathwaysAfrica workshop in Lusaka.
His church has already noticed the difference the Pathways workshop is having on Alick’s preaching – new power and clarity as he is preaching right from the text of God’s word, keeping his finger in the text. And he’s been sharing what he has learned with other pastors in his community — pastors training pastors!
Alick is married to Dorothy and they have two daughters, Jennifah (14) and Gloria (9). As is typical with most of our pastors, Alick’s church is able to pay him very little. As a result, Alick is a ‘tent-maker,’ working a second job to make ends meet. In his case, Alick sets up a table several days each week on a sidewalk in the busy city center, selling inexpensive cell phones and accessories.
Consider the financial sacrifice Alick and his family and the other pastors are making to faithfully participate three weeks each year in our PathwaysAfrica workshops! And think of how their tent-making impacts their time to study God’s Word to feed their people each week. Pray that local churches will be able to financially support their pastors to free them up full time to shepherd the flock.
Since ‘International’ is in his church’s name, I asked Alick, ‘Does your church reach beyond the borders of Zambia?’ He responded with a smile, ‘Not yet but we will take the Good News of Jesus to the ends of the earth!’ What a vision God has given Pastor Alick.
Pastor Corey Kugle (on the right) and I are on our way to the capital of Zambia, Lusaka, to begin our Pathway training of a group of sixteen Zambian pastors in nine, week-long workshops over the next three years. In growing relationships around God’s Word, we will be coaching them how to better observe, understand, interpret, accurately apply and teach God’s Word. Between each of our nine workshops, each of these pastors will be training other pastors in these same bible study skills and tools. Please pray for Corey and me (and my future teammate, Simon Mawdsley, on the left) as we meet, connect with, and work together Monday May 28 through Friday June 1.
On Saturday, June 2, I’ll travel with my Zambian brother Teddy Kamfwa to the town of Livingstone, Zambia where I will be leading a Pathways pre-training of about 50 local pastors. Our hope is to begin a second Pathways training workshop in Livingstone with a second group of 16 pastors who will then train other pastors. Please pray God will challenge and raise up His group of pastors in Livingstone.
The Sunday after I return from Zambia I’ll be sharing about God’s workings through PathwaysAfrica at Paseo del Rey Church. You’re welcome to join us Sunday, June 10, 9am and 10.35am.
I am so thankful and encouraged by many of you who have joined me with your financial partnership. I’m currently about one third of the way to my goal of $2800 per month. Your partnership will pay rich dividends in these pastors and their families and churches’ lives, and the pastors they train, for all of eternity.
I’d like to invite others of you to invest prayers and finances with me in PathwaysAfrica. Would you prayerfully consider partnering in training pastors who train pastors by committing to $25, $50, $80, $150 a month, or a special annual gift?
If you would like to join my team, go to pathwaysafrica.org and click Support Pathways. Or you can send your gifts directly to Paseo del Rey Church, memo “Pathways”, 900 Paseo del Rey, Chula Vista, CA 91910. All gifts are fully tax-deductible and you will receive a year-end receipt from the church.
Pastor Jean Berchamas invited us to open our bibles to Colossians. As he began to unfold God’s Word, tears came to my eyes. In our first few Pathways workshops in Rwanda, Pastor Jean and the other 15 pastors would open their bibles, read a verse, and then launch into stories and exhortations which had little to do with the passage they said they were preaching.
But now, several Pathways workshops later, Pastor Jean (second from left) and the other pastors were handling more accurately God’s Living Word, faithfully keeping their finger in the text. Stories from their churches told of new joy and obedience as God’s Word was preached faithfully, with clarity and relevance. And these 16 pastors were actively passing on what they were learning to other pastors in Rwanda!
These pastors had not lacked love or passion for Jesus. Rather, like so many other pastors around the world, they lacked access to training in how to study and teach God’s Word.
On July 29, I will transition from Lead Pastor of Paseo del Rey Church and become a missionary from Paseo del Rey. It has been a joy and a privilege to shepherd these wonderful people of Paseo del Rey Church for the past 38 years.
Now, God has opened a new door, and I will be focusing my time and attention on training more pastors who will train pastors in Africa. April and I will continue to live in Chula Vista, but I’ll be in Africa more, 3-4 times a year, 3-4 weeks at a time (April will join me on one journey each year).
I will be leading two different Pathways Training Networks. Each Pathways Training Network consists of 16 pastors who prepare for and participate in 9 one-week workshops that span three years. Being together over the three years provides time to nurture trusting relationships that are the bridge for meaningful and lasting discipleship, growth and training. We are launching our first Pathways group in Zambia in May, even before my transition actually occurs.
Paseo del Rey Church is committed to training pastors in Africa with me, and is generously providing a portion of my support for Pathways Africa.
I’d like to invite you to join my Pathways Africa Partnership team, investing in training pastors, like Jean in Africa. I am asking God for a group of partners like you who will pray regularly and financially support my work each month, or with an annual gift, over and above what you are giving your local church.
You can respond by clicking here. Join me in investing in training pastors who train pastors in Africa. Paseo del Rey Church will receive and administer your financial gifts—there are no administrative fees, and as your gifts are given directly to Paseo del Rey Church they are fully tax deductible.
Your partnership will bring a feast of God’s Word to many as together we team to train pastors who train pastors to study and preach God’s Living Word.
I hope and plan to talk personally with many of you individually over the next few months to share more about investing with me in Pathways Africa.
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