In this paper, we identify two issues involved in developing an automated feature subset selection algorithm for unlabeled data: the need for finding the number of clusters in conjunction with feature selection, and the need for normalizing the bias of feature selection criteria with respect to dimension. We explore the feature selection problem and these issues through FSSEM (Feature Subset Selection using Expectation-Maximization (EM) clustering) and through two different performance criteria for evaluating candidate feature subsets: scatter separability and maximum likelihood. We present proofs on the dimensionality biases of these feature criteria, and present a cross-projection normalization scheme that can be applied to any criterion to ameliorate these biases. Our experiments show the need for feature selection, the need for addressing these two issues, and the effectiveness of our proposed solutions.

Semi-supervised clustering uses a small amount of supervised data to aid unsupervised learning. One typical approach specifies a limited number of must-link and cannotlink constraints between pairs of examples. This paper presents a pairwise constrained clustering framework and a new method for actively selecting informative pairwise constraints to get improved clustering performance. The clustering and active learning methods are both easily scalable to large datasets, and can handle very high dimensional data. Experimental and theoretical results confirm that this active querying of pairwise constraints significantly improves the accuracy of clustering when given a relatively small amount of supervision. 1

In recent years, we have seen a tremendous growth in the volume of text documents available on the Internet, digital libraries, news sources, and company-wide intranets. This has led to an increased interest in developing meth-ods that can efficiently categorize and retrieve relevant information. Retrieval techniques based on dimensionality reduction, such as Latent Semantic Indexing (LSI), have been shown to improve the quality of the information being retrieved by capturing the latent meaning of the words present in the documents. Unfortunately, the high computa-tional requirements of LSI and its inability to compute an effective dimensionality reduction in a supervised setting limits its applicability. In this paper we present a fast dimensionality reduction algorithm, called concept indexing (CI) that is equally effective for unsupervised and supervised dimensionality reduction. CI computes a k-dimensional representation of a collection of documents by first clustering the documents into k groups, and then using the centroid vectors of the clusters to derive the axes of the reduced k-dimensional space. Experimental results show that the dimensionality reduction computed by CI achieves comparable retrieval performance to that obtained using LSI, while requiring an order of magnitude less time. Moreover, when CI is used to compute the dimensionality reduction in a supervised setting, it greatly improves the performance of traditional classification algorithms such as C4.5 and kNN.

This paper explores the problem of feature subset selection for unsupervised learning within the wrapper framework. In particular, we examine feature subset selection wrapped around expectation-maximization (EM) clustering with order identification (identifying the number of clusters in the data). We investigate two di erent performance criteria for evaluating candidate feature subsets: scatter separability and maximum likelihood. When the "true" number of clusters k is unknown, our experiments on simulated Gaussian data and real data sets show that incorporating the search for k within the feature selection procedure obtains better "class" accuracy than fixing k to be the number of classes. There are two reasons: 1) the "true" number of Gaussian components is not necessarily equal to the number of classes and 2) clustering with different feature subsets can result in di erent numbers of "true" clusters. Our empirical evaluation shows that feature selection reduces the number of features and improves clustering performance with respect to the chosen performance criteria.

Data mining in large data sets often requires a sampling or summarization step to form an in-core representation of the data that can be processed more efficiently. Uniform random sampling is frequently used in practice and also frequently criticized because it will miss small clusters. Many natural phenomena are known to follow Zipf 's distribution and the inability of uniform sampling to find small clusters is of practical concern. Density Biased Sampling is proposed to probabilistically under-sample dense regions and oversample light regions. A weighted sample is used to preserve the densities of the original data. Density biased sampling naturally includes uniform sampling as a special case. A memory efficient algorithm is proposed that approximates density biased sampling using only a single scan of the data. We empirically evaluate density biased sampling using synthetic data sets that exhibit varying cluster size distributions finding up to a factor of six improvement over uniform s...

This paper is intended to serve as an overview of a rapidly emerging research and applications area. In addition to providing a general overview, motivating the importance of data mining problems within the area of knowledge discovery in databases, our aim is to list some of the pressing research challenges, and outline opportunities for contributions by the optimization research communities. Towards these goals, we include formulations of the basic categories of data mining methods as optimization problems. We also provide examples of successful mathematical programming approaches to some data mining problems. keywords: data analysis, data mining, mathematical programming methods, challenges for massive data sets, classification, clustering, prediction, optimization. To appear: INFORMS: Journal of Compting, special issue on Data Mining, A. Basu and B. Golden (guest editors). Also appears as Mathematical Programming Technical Report 98-01, Computer Sciences Department, University of Wi...

We present a framework for clustering distributed data in unsupervised and semi-supervised scenarios, taking into account privacy requirements and communication costs. Rather than sharing parts of the original or perturbed data, we instead transmit the parameters of suitable generative models built at each local data site to a central location. We mathematically show that the best representative of all the data is a certain " mean" model, and empirically show that this model can be approximated quite well by generating artificial samples from the underlying distributions using Markov Chain Monte Carlo techniques, and then fitting a combined global model with a chosen parametric form to these samples. We also propose a new measure that quantifies privacy based on information theoretic concepts, and show that decreasing privacy leads to a higher quality of the combined model and vice versa. We provide empirical results on different data types to highlight the generality of our framework. The results show that high quality distributed clustering can be achieved with little privacy loss and low communication cost.

Abstract. Clustering is an important data mining task. Data mining often concerns large and high-dimensional data but unfortunately most of the clustering algorithms in the literature are sensitive to largeness or high-dimensionality or both. Di erent features a ect clusters di erently, some are important for clusters while others may hinder the clustering task. An e cient wayof handling it is by selecting a subset of important features. It helps in nding clusters e ciently, understanding the data better and reducing data size for e cient storage, collection and processing. The task of nding original important features for unsupervised data is largely untouched. Traditional feature selection algorithms work only for supervised data where class information is available. For unsupervised data, without class information, often principal components (PCs) are used, but PCs still require all features and they may be di cult to understand. Our approach: rst features are ranked according to their importance on clustering and then a subset of important features are selected. For large data we use a scalable method using sampling. Empirical evaluation shows the e ectiveness and scalability of our approach for benchmark and synthetic data sets. 1

Abstract—This paper describes a new hierarchical approach to content-based image retrieval called the “customized-queries ” approach (CQA). Contrary to the single feature vector approach which tries to classify the query and retrieve similar images in one step, CQA uses multiple feature sets and a two-step approach to retrieval. The first step classifies the query according to the class labels of the images using the features that best discriminate the classes. The second step then retrieves the most similar images within the predicted class using the features customized to distinguish “subclasses ” within that class. Needing to find the customized feature subset for each class led us to investigate feature selection for unsupervised learning. As a result, we developed a new algorithm called FSSEM (feature subset selection using expectation-maximization clustering). We applied our approach to a database of high resolution computed tomography lung images and show that CQA radically improves the retrieval precision over the single feature vector approach. To determine whether our CBIR system is helpful to physicians, we conducted an evaluation trial with eight radiologists. The results show that our system using CQA retrieval doubled the doctors ’ diagnostic accuracy. Index Terms—Image retrieval, feature selection, clustering, expectationmaximization, unsupervised learning. 1

this paper, we propose a novel clustering technique, which is based on a supervised learning technique called decision tree construction. The new technique is able to overcome many of these shortcomings. The key idea is to use a decision tree to partition the data space into cluster and empty (sparse) regions at different levels of details. The technique is able to find "natural" clusters in large high dimensional spaces efficiently. It is suitable for clustering in the full dimensional space as well as in subspaces. It also provides comprehensible descriptions of clusters. Experiment results on both synthetic data and real-life data show that the technique is effective and also scales well for large high dimensional datasets.