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Abstract

Techniques for multidimensional scaling visualize objects as points in a low-dimensional metric map. As a result, the visualizations are subject to the fundamental limitations of metric spaces. These limitations prevent multidimensional scaling from faithfully representing non-metric similarity data such as word associations or event co-occurrences. In particular, multidimensional scaling cannot faithfully represent intransitive pairwise similarities in a visualization, and it cannot faithfully visualize "central" objects. In this paper, we present an extension of a recently proposed multidimensional scaling technique called t-SNE. The extension aims to address the problems of traditional multidimensional scaling techniques when these techniques are used to visualize non-metric similarities. The new technique, called multiple maps t-SNE, alleviates these problems by constructing a collection of maps that reveal complementary structure in the similarity data. We apply multiple maps t-SNE to a large data set of word association data and to a data set of NIPS co-authorships, demonstrating its ability to successfully visualize non-metric similarities.

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Abstract

The paper investigates the acceleration of t-SNE-an embedding technique that is commonly used for the visualization of high-dimensional data in scatter plots-using two tree-based algorithms. In particular, the paper develops variants of the Barnes-Hut algorithm and of the dual-tree algorithm that approximate the gradient used for learning t-SNE embeddings in O(N*logN). Our experiments show that the resulting algorithms substantially accelerate t-SNE, and that they make it possible to learn embeddings of data sets with millions of objects. Somewhat counterintuitively, the Barnes-Hut variant of t-SNE appears to outperform the dual-tree variant.

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Abstract

We present a new technique called "t-SNE" that visualizes high-dimensional data by giving each datapoint a location in a two or three-dimensional map. The technique is a variation of Stochastic Neighbor Embedding (Hinton and Roweis, 2002) that is much easier to optimize, and produces significantly better visualizations by reducing the tendency to crowd points together in the center of the map. t-SNE is better than existing techniques at creating a single map that reveals structure at many different scales. This is particularly important for high-dimensional data that lie on several different, but related, low-dimensional manifolds, such as images of objects from multiple classes seen from multiple viewpoints. For visualizing the structure of very large data sets, we show how t-SNE can use random walks on neighborhood graphs to allow the implicit structure of all of the data to influence the way in which a subset of the data is displayed. We illustrate the performance of t-SNE on a wide variety of data sets and compare it with many other non-parametric visualization techniques, including Sammon mapping, Isomap, and Locally Linear Embedding. The visualizations produced by t-SNE are significantly better than those produced by the other techniques on almost all of the data sets.

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Date

23. 3.2008 19:10:22

Footnote

In 13 chapters, Part Two provides an introduction to KDD, an overview of data mining techniques, and examples of the usefulness of data model visualizations. The importance of visualization throughout the KDD process is stressed in many of the chapters. In particular, the need for measures of visualization effectiveness, benchmarking for identifying best practices, and the use of standardized sample data sets is convincingly presented. Many of the important data mining approaches are discussed in this complementary context. Cluster and outlier detection, classification techniques, and rule discovery algorithms are presented as the basic techniques common to the KDD process. The potential effectiveness of using visualization in the data modeling process are illustrated in chapters focused an using visualization for helping users understand the KDD process, ask questions and form hypotheses about their data, and evaluate the accuracy and veracity of their results. The 11 chapters of Part Three provide an overview of the KDD process and successful approaches to integrating KDD, data mining, and visualization in complementary domains. Rhodes (Chapter 21) begins this section with an excellent overview of the relation between the KDD process and data mining techniques. He states that the "primary goals of data mining are to describe the existing data and to predict the behavior or characteristics of future data of the same type" (p. 281). These goals are met by data mining tasks such as classification, regression, clustering, summarization, dependency modeling, and change or deviation detection. Subsequent chapters demonstrate how visualization can aid users in the interactive process of knowledge discovery by graphically representing the results from these iterative tasks. Finally, examples of the usefulness of integrating visualization and data mining tools in the domain of business, imagery and text mining, and massive data sets are provided. This text concludes with a thorough and useful 17-page index and lengthy yet integrating 17-page summary of the academic and industrial backgrounds of the contributing authors. A 16-page set of color inserts provide a better representation of the visualizations discussed, and a URL provided suggests that readers may view all the book's figures in color on-line, although as of this submission date it only provides access to a summary of the book and its contents. The overall contribution of this work is its focus an bridging two distinct areas of research, making it a valuable addition to the Morgan Kaufmann Series in Database Management Systems. The editors of this text have met their main goal of providing the first textbook integrating knowledge discovery, data mining, and visualization. Although it contributes greatly to our under- standing of the development and current state of the field, a major weakness of this text is that there is no concluding chapter to discuss the contributions of the sum of these contributed papers or give direction to possible future areas of research. "Integration of expertise between two different disciplines is a difficult process of communication and reeducation. Integrating data mining and visualization is particularly complex because each of these fields in itself must draw an a wide range of research experience" (p. 300). Although this work contributes to the crossdisciplinary communication needed to advance visualization in KDD, a more formal call for an interdisciplinary research agenda in a concluding chapter would have provided a more satisfying conclusion to a very good introductory text.