38902380
Construction Algorithm of Principal Curves in the Sense of Limit
Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.
15790608
Clustering High-Dimensional Data with Low-Order Neighbors
Density-based and grid-based clustering are two main clustering approaches. The former is famous for its capability of discovering clusters of various shapes and eliminating noises, while the latter is well known for its high speed. Combination of the two approaches seems to provide better clustering results. To the best of our knowledge, however, all existing algorithms that combine density-based clustering and grid-based clustering take cells as atomic units, in the sense that either all objects in a cell belong to a cluster or no object in the cell belong to any cluster. This requires the cells to be small enough to ensure the fine resolution of results. In high-dimensional spaces, however, the number of cells can be very large when cells are small, which would make the clustering process extremely costly. On the other hand, the number of neighbors of a cell grows exponentially with the dimensionality of datasets, which makes the complexity increase further. In this paper, we present a new approach that takes objects (or points) as the atomic units, so that the restriction of cell size can be relaxed without degrading the resolution of clustering results. In addition, a concept of ith-order neighbors is introduced to avoid considering the exponential number of neighboring cells. By considering only low-order neighbors, our algorithm is very efficient while losing only a little bit of accuracy. Experiments on synthetic and public data show that our algorithm can cluster high-dimensional data effectively and efficiently.
7425380
Enhancing DWT for Recent-Biased Dimension Reduction of Time Series Data
In many applications, old data in time series become less important as time elapses, which is a big challenge to traditional techniques for dimension reduction. To improve Discrete Wavelet Transform (DWT) for effective dimension reduction in this kind of applications, a new method, largest-latest-DWT, is designed by keeping the largest k coefficients out of the latest w coefficients at each level of DWT transform. Its efficiency and effectiveness is demonstrated by our experiments.
29045473
On Reduct Construction Algorithms
This paper critically analyzes reduct construction methods at two levels. At a high level, one can abstract commonalities from the existing algorithms, and classify them into three basic groups based on the underlying control structures. At a low level, by adopting different heuristics or fitness functions for attribute selection, one is able to derive most of the existing algorithms. The analysis brings new insights into the problem of reduct construction, and provides guidelines for the design of new algorithms
1206474
Interactive classification using a granule network
Classification is one of the main tasks in machine learning, data mining and pattern recognition. Compared with the extensively studied data-driven approaches, the interactively user-driven approaches are less explored. A granular computing model is suggested for re-examining the classification problems. An interactive classification method using the granule network is proposed, which allows multi-strategies for granule tree construction and enhances the understanding and interpretation of the classification process. This method is complementary to the existing classification methods.
6467988
Empirical and Theoretical Comparisons of Selected Criterion Functions for Document Clustering
This paper evaluates the performance of different criterion functions in the context of partitional clustering algorithms for document datasets. Our study involves a total of seven different criterion functions, three of which are introduced in this paper and four that have been proposed in the past. We present a comprehensive experimental evaluation involving 15 different datasets, as well as an analysis of the characteristics of the various criterion functions and their effect on the clusters they produce. Our experimental results show that there are a set of criterion functions that consistently outperform the rest, and that some of the newly proposed criterion functions lead to the best overall results. Our theoretical analysis shows that the relative performance of the criterion functions depends on (i) the degree to which they can correctly operate when the clusters are of different tightness, and (ii) the degree to which they can lead to reasonably balanced clusters.
1134220
The design of an interactive online help desk in the Alexandria Digital Library
In large software systems such as digital libraries, electronic commerce applications, and customer support systems, the user interface and system are often complex and difficult to navigate. It is necessary to provide users with interactive online support to help users learn how to effectively use these applications. Such online help facilities can include providing tutorials and animated demonstrations, synchronized activities between users and system supporting staff for real time instruction and guidance, multimedia communication with support staff such as chat, voice, and shared whiteboards, and tools for quick identification of user problems. In this paper, we investigate how such interactive online help support can be developed and provided in the context of a working system, the Alexandria Digital Library (ADL) for geospatially-referenced data. We developed an online help system, AlexHelp!. AlexHelp! supports collaborative sessions between the user and the librarian (support staff) that include activities such as map browsing and region selection, recorded demonstration sessions for the user, primitive tools for analyzing user sessions, and channels for voice and text based communications. The design of AlexHelp! is based on user activity logs, and the system is a light-weight software component that can be easily integrated into the ADL user interface client. A prototype of AlexHelp! is developed and integrated into the ADL client; both the ADL client and AlexHelp! are written in Java.
37471711
Coarsening Classification Rules on Basis of Granular Computing
The task of classification, as a well-studied field of machine learning and data mining, has two main purposes: describing the classification rules in the training dataset and predicting the unseen new instances in the testing dataset. Normally, one expects a high accuracy for precisely descriptive use. However, a higher accuracy is intended to generate longer rules, which are not easy to understand, and may overfit the training instances. This motivates us to propose the approach of coarsening the classification rules, namely, reasonably sacrifice the accuracy of description in a controlled level in order to improve the comprehensibility and predictability. The framework of granular computing provides us a formal and systematic methodology for doing this. In this paper, a modified PRISM classification algorithm is presented based on the framework of granular computing.