8902334
A PCA-Based Change Detection Framework for Multidimensional Data Streams: Change Detection in Multidimensional Data Streams
Detecting changes in multidimensional data streams is an important and challenging task. In unsupervised change detection, changes are usually detected by comparing the distribution in a current (test) window with a reference window. It is thus essential to design divergence metrics and density estimators for comparing the data distributions, which are mostly done for univariate data. Detecting changes in multidimensional data streams brings difficulties to the density estimation and comparisons. In this paper, we propose a framework for detecting changes in multidimensional data streams based on principal component analysis, which is used for projecting data into a lower dimensional space, thus facilitating density estimation and change-score calculations. The proposed framework also has advantages over existing approaches by reducing computational costs with an efficient density estimator, promoting the change-score calculation by introducing effective divergence metrics, and by minimizing the efforts required from users on the threshold parameter setting by using the Page-Hinkley test. The evaluation results on synthetic and real data show that our framework outperforms two baseline methods in terms of both detection accuracy and computational costs.
8578310
On-Line Unsupervised Outlier Detection Using Finite Mixtures with Discounting Learning Algorithms
Outlier detection is a fundamental issue in data mining, specifically in fraud detection, network intrusion detection, network monitoring, etc. SmartSifter is an outlier detection engine addressing this problem from the viewpoint of statistical learning theory. This paper provides a theoretical basis for SmartSifter and empirically demonstrates its effectiveness. SmartSifter detects outliers in an on-line process through the on-line unsupervised learning of a probabilistic model (using a finite mixture model) of the information source. Each time a datum is input SmartSifter employs an on-line discounting learning algorithm to learn the probabilistic model. A score is given to the datum based on the learned model with a high score indicating a high possibility of being a statistical outlier. The novel features of SmartSifter are: (1) it is adaptive to non-stationary sources of data; (2) a score has a clear statistical/information-theoretic meaning; (3) it is computationally inexpensive; and (4) it can handle both categorical and continuous variables. An experimental application to network intrusion detection shows that SmartSifter was able to identify data with high scores that corresponded to attacks, with low computational costs. Further experimental application has identified a number of meaningful rare cases in actual health insurance pathology data from Australia's Health Insurance Commission.
17144146
Event Detection in Crowded Videos
Real-world actions occur often in crowded, dynamic environments. This poses a difficult challenge for current approaches to video event detection because it is difficult to segment the actor from the background due to distracting motion from other objects in the scene. We propose a technique for event recognition in crowded videos that reliably identifies actions in the presence of partial occlusion and background clutter. Our approach is based on three key ideas: (1) we efficiently match the volumetric representation of an event against oversegmented spatio-temporal video volumes; (2) we augment our shape-based features using flow; (3) rather than treating an event template as an atomic entity, we separately match by parts (both in space and time), enabling robustness against occlusions and actor variability. Our experiments on human actions, such as picking up a dropped object or waving in a crowd show reliable detection with few false positives.
52800392
Detecting Change in Data Streams
Detecting changes in a data stream is an important area of research with many applications. In this paper, we present a novel method for the detection and estimation of change. In addition to providing statistical guarantees on the reliability of detected changes, our method also provides meaningful descriptions and quantification of these changes. Our approach assumes that the points in the stream are independently generated, but otherwise makes no assumptions on the nature of the generating distribution. Thus our techniques work for both continuous and discrete data. In an experimental study we demonstrate the power of our techniques.
5453116
Event detection from time series data
In the past few years there has been increased interest in using data-mining techniques to extract interesting patterns from time series data generated by sensors monitoring temporally varying phenomenon. Most work has assumed that raw data is somehow processed to generate a sequence of events, which is then mined for interesting episodes. In some cases the rule for determining when a sensor reading should generate an event is well known. However, if the phenomenon is ill-understood, stating such a rule is difficult. Detection of events in such an environment is the focus of this paper. Consider a dynamic phenomenon whose behavior changes enough over time to be considered a qualitatively significant change. The problem we investigate is of identifying the time points at which the behavior change occurs. In the statistics literature this has been called the change-point detection problem. The standard approach has been to (a) upriori determine the number of change-points that are to be discovered, and (b) decide the function that will be used for curve fitting in the interval between successive change-points. In this paper we generalize along both these dimensions. We propose an iterative algorithm that fits a model to a time segment, and uses a likelihood criterion to determine if the segment should be partitioned further, i.e. if it contains a new changepoint. In this paper we present algorithms for both the batch and incremental versions of the problem, and evaluate their behavior with synthetic and real data. Finally, we present initial results comparing the change-points detected by the batch algorithm with those detected by people using visual inspection.
32557980
Change-Point Detection in Time-Series Data by Direct Density-Ratio Estimation
Change-point detection is the problem of discovering time points at which properties of time-series data change. This covers a broad range of real-world problems and has been actively discussed in the community of statistics and data mining. In this paper, we present a novel non-parametric approach to detecting the change of probability distributions of sequence data. Our key idea is to estimate the ratio of probability densities, not the probability densities themselves. This formulation allows us to avoid non-parametric density estimation, which is known to be a difficult problem. We provide a change-point detection algorithm based on direct density-ratio estimation that can be computed very efficiently in an online manner. The usefulness of the proposed method is demonstrated through experiments using artificial and real datasets. keywords: change-point detection, direct density-ratio estimation, kernel methods, time-series data
2279539
Learning from Time-Changing Data with Adaptive Windowing
We present a new approach for dealing with distribution change and concept drift when learning from data sequences that may vary with time. We use sliding windows whose size, instead of being fixed a priori, is recomputed online according to the rate of change observed from the data in the window itself: The window will grow automatically when the data is stationary, for greater accuracy, and will shrink automatically when change is taking place, to discard stale data. This delivers the user or programmer from having to guess a time-scale for change. Contrary to many related works, we provide rigorous guarantees of performance, as bounds on the rates of false positives and false negatives. In fact, for some change structures, we can formally show that the algorithm automatically adjusts the window to a statistically optimal length. Using ideas from data stream algorithmics, we develop a time- and memory-ecient version of this algorithm, called ADWIN2. We show how to incorporate this strategy easily into
10591316
An Information-Theoretic Approach to Detecting Changes in Multi-Dimensional Data Streams
An important problem in processing large data streams is detecting changes in the underlying distribution that generates the data. The challenge in designing change detection schemes is making them general, scalable, and statistically sound. In this paper, we take a general, information-theoretic approach to the change detection problem, which works for multidimensional as well as categorical data. We use relative entropy, also called the Kullback-Leibler distance, to measure the difference between two given distributions. The KL-distance is known to be related to the optimal error in determining whether the two distributions are the same and draws on fundamental results in hypothesis testing. The KL-distance also generalizes traditional distance measures in statistics, and has invariance properties that make it ideally suited for comparing distributions. Our scheme is general; it is nonparametric and requires no assumptions on the underlying distributions. It employs a statistical inference procedure based on the theory of bootstrapping, which allows us to determine whether our measurements are statistically significant. The scheme is also quite flexible from a practical perspective; it can be implemented using any spatial partitioning scheme that scales well with dimensionality. In addition to providing change detections, our method generalizes Kulldorff’s spatial scan statistic, allowing us to quantitatively identify specific regions in space where large changes have occurred. We provide a detailed experimental study that demonstrates the generality and efficiency of our approach with different kinds of multidimensional datasets, both synthetic and real.
10651142
PCA Feature Extraction for Change Detection in Multidimensional Unlabeled Data
When classifiers are deployed in real-world applications, it is assumed that the distribution of the incoming data matches the distribution of the data used to train the classifier. This assumption is often incorrect, which necessitates some form of change detection or adaptive classification. While there has been a lot of work on change detection based on the classification error monitored over the course of the operation of the classifier, finding changes in multidimensional unlabeled data is still a challenge. Here, we propose to apply principal component analysis (PCA) for feature extraction prior to the change detection. Supported by a theoretical example, we argue that the components with the lowest variance should be retained as the extracted features because they are more likely to be affected by a change. We chose a recently proposed semiparametric log-likelihood change detection criterion that is sensitive to changes in both mean and variance of the multidimensional distribution. An experiment with 35 datasets and an illustration with a simple video segmentation demonstrate the advantage of using extracted features compared to raw data. Further analysis shows that feature extraction through PCA is beneficial, specifically for data with multiple balanced classes.
11015660
Statistical change detection for multi-dimensional data
This paper deals with detecting change of distribution in multi-dimensional data sets. For a given baseline data set and a set of newly observed data points, we define a statistical test called the density test for deciding if the observed data points are sampled from the underlying distribution that produced the baseline data set. We define a test statistic that is strictly distribution-free under the null hypothesis. Our experimental results show that the density test has substantially more power than the two existing methods for multi-dimensional change detection.
15054959
A unifying framework for detecting outliers and change points from time series
We are concerned with the issue of detecting outliers and change points from time series. In the area of data mining, there have been increased interest in these issues since outlier detection is related to fraud detection, rare event discovery, etc., while change-point detection is related to event/trend change detection, activity monitoring, etc. Although, in most previous work, outlier detection and change point detection have not been related explicitly, this paper presents a unifying framework for dealing with both of them. In this framework, a probabilistic model of time series is incrementally learned using an online discounting learning algorithm, which can track a drifting data source adaptively by forgetting out-of-date statistics gradually. A score for any given data is calculated in terms of its deviation from the learned model, with a higher score indicating a high possibility of being an outlier. By taking an average of the scores over a window of a fixed length and sliding the window, we may obtain a new time series consisting of moving-averaged scores. Change point detection is then reduced to the issue of detecting outliers in that time series. We compare the performance of our framework with those of conventional methods to demonstrate its validity through simulation and experimental applications to incidents detection in network security.
16602555
Efficient estimation of dynamic density functions with an application to outlier detection
In this paper, we propose a new method to estimate the dynamic density over data streams, named KDE-Track as it is based on a conventional and widely used Kernel Density Estimation (KDE) method. KDE-Track can efficiently estimate the density with linear complexity by using interpolation on a kernel model, which is incrementally updated upon the arrival of streaming data. Both theoretical analysis and experimental validation show that KDE-Track outperforms traditional KDE and a baseline method Cluster-Kernels on estimation accuracy of the complex density structures in data streams, computing time and memory usage. KDE-Track is also demonstrated on timely catching the dynamic density of synthetic and real-world data. In addition, KDE-Track is used to accurately detect outliers in sensor data and compared with two existing methods developed for detecting outliers and cleaning sensor data.
44112860
Direct importance estimation for covariate shift adaptation
A situation where training and test samples follow different input distributions is called covariate shift. Under covariate shift, standard learning methods such as maximum likelihood estimation are no longer consistent—weighted variants according to the ratio of test and training input densities are consistent. Therefore, accurately estimating the density ratio, called the importance, is one of the key issues in covariate shift adaptation. A naive approach to this task is to first estimate training and test input densities separately and then estimate the importance by taking the ratio of the estimated densities. However, this naive approach tends to perform poorly since density estimation is a hard task particularly in high dimensional cases. In this paper, we propose a direct importance estimation method that does not involve density estimation. Our method is equipped with a natural cross validation procedure and hence tuning parameters such as the kernel width can be objectively optimized. Furthermore, we give rigorous mathematical proofs for the convergence of the proposed algorithm. Simulations illustrate the usefulness of our approach.
45704793
Change-point detection in time-series data by relative density-ratio estimation
The objective of change-point detection is to discover abrupt property changes lying behind time-series data. In this paper, we present a novel statistical change-point detection algorithm that is based on non-parametric divergence estimation between two retrospective segments. Our method uses the relative Pearson divergence as a divergence measure, and it is accurately and efficiently estimated by a method of direct density-ratio estimation. Through experiments on real-world human-activity sensing, speech, and Twitter datasets, we demonstrate the usefulness of the proposed method.
5949718
Feature selection for fusion of speaker verification via Maximum Kullback-Leibler distance
This paper proposes an optimal scheme of feature selection for the fusion technique of speaker verification by Maximum Kullback-Leibler Distance. Through the investigations of bi-feature fusion schemes by six acoustic features, the information content of each fusion scheme via the Maximum Kullback-Leibler distance are computed in turn. The advantage of this distance is to overcome the shortcoming of the asymmetry of conventional Kullback-Leibler distance. This can keep the stability and correctness of the computation of the information content. In the experimental section, NIST 2001 corpus is used for evaluation. From the computation results by a variety of fusion schemes, it is found that the fusion between MFCC and residual phase hold the most information content. It indicates this scheme is able to yield an excellent performance. To verify its correctness, the EER evaluations are conducted. From the evaluation results, the EER of the fusion between MFCC and residual phase outperforms other fusion schemes. Therefore, the Maximum Kullback-Leibler distance can be considered as an effective metric for the feature selection in the fusion of speaker verification.
15506682
Comprehensive Survey on Distance/Similarity Measures between Probability Density Functions
Distance or similarity measures are essential to solve many pattern recognition problems such as classification, clustering, and retrieval problems. Various distance/similarity measures that are applicable to compare two probability density functions, pdf in short, are reviewed and categorized in both syntactic and semantic relationships. A correlation coefficient and a hierarchical clustering technique are adopted to reveal similarities among numerous distance/similarity measures.
3348287
Activity recognition using cell phone accelerometers
Mobile devices are becoming increasingly sophisticated and the latest generation of smart cell phones now incorporates many diverse and powerful sensors. These sensors include GPS sensors, vision sensors (i.e., cameras), audio sensors (i.e., microphones), light sensors, temperature sensors, direction sensors (i.e., magnetic compasses), and acceleration sensors (i.e., accelerometers). The availability of these sensors in mass-marketed communication devices creates exciting new opportunities for data mining and data mining applications. In this paper we describe and evaluate a system that uses phone-based accelerometers to perform activity recognition, a task which involves identifying the physical activity a user is performing. To implement our system we collected labeled accelerometer data from twenty-nine users as they performed daily activities such as walking, jogging, climbing stairs, sitting, and standing, and then aggregated this time series data into examples that summarize the user activity over 10- second intervals. We then used the resulting training data to induce a predictive model for activity recognition. This work is significant because the activity recognition model permits us to gain useful knowledge about the habits of millions of users passively---just by having them carry cell phones in their pockets. Our work has a wide range of applications, including automatic customization of the mobile device's behavior based upon a user's activity (e.g., sending calls directly to voicemail if a user is jogging) and generating a daily/weekly activity profile to determine if a user (perhaps an obese child) is performing a healthy amount of exercise.
1431210
A martingale framework for concept change detection in time-varying data streams
In a data streaming setting, data points are observed one by one. The concepts to be learned from the data points may change infinitely often as the data is streaming. In this paper, we extend the idea of testing exchangeability online (Vovk et al., 2003) to a martingale framework to detect concept changes in time-varying data streams. Two martingale tests are developed to detect concept changes using: (i) martingale values, a direct consequence of the Doob's Maximal Inequality, and (ii) the martingale difference, justified using the Hoeffding-Azuma Inequality. Under some assumptions, the second test theoretically has a lower probability than the first test of rejecting the null hypothesis, "no concept change in the data stream", when it is in fact correct. Experiments show that both martingale tests are effective in detecting concept changes in time-varying data streams simulated using two synthetic data sets and three benchmark data sets.
2270026
Data Stream Clustering With Affinity Propagation
Data stream clustering provides insights into the underlying patterns of data flows. This paper focuses on selecting the best representatives from clusters of streaming data. There are two main challenges: how to cluster with the best representatives and how to handle the evolving patterns that are important characteristics of streaming data with dynamic distributions. We employ the Affinity Propagation (AP) algorithm presented in 2007 by Frey and Dueck for the first challenge, as it offers good guarantees of clustering optimality for selecting exemplars. The second challenging problem is solved by change detection. The presented StrAP algorithm combines AP with a statistical change point detection test; the clustering model is rebuilt whenever the test detects a change in the underlying data distribution. Besides the validation on two benchmark data sets, the presented algorithm is validated on a real-world application, monitoring the data flow of jobs submitted to the EGEE grid.