Subspace Clustering of High Dimensional Data

Computers in Biology and Medicine, 2006

The development of microarray technologies gives scientists the ability to examine, discover and monitor the mRNA transcript levels of thousands of genes in a single experiment. Nonetheless, the tremendous amount of data that can be obtained from microarray studies presents a challenge for data analysis. The most commonly used computational approach for analyzing microarray data is cluster analysis, since the number of genes is usually very high compared to the number of samples. In this paper, we investigate the application of the recently proposed k-windows clustering algorithm on gene expression microarray data. This algorithm apart from identifying the clusters present in a data set also calculates their number and thus requires no special knowledge about the data.

2007

Clustering suffers from the curse of dimensionality, and similarity functions that use all input features with equal relevance may not be effective. We introduce an algorithm that discovers clusters in subspaces spanned by different combinations of dimensions via local weightings of features. This approach avoids the risk of loss of information encountered in global dimensionality reduction techniques, and does not assume any data distribution model. Our method associates to each cluster a weight vector, whose values capture the relevance of features within the corresponding cluster. We experimentally demonstrate the gain in perfomance our method achieves with respect to competitive methods, using both synthetic and real datasets. In particular, our results show the feasibility of the proposed technique to perform simultaneous clustering of genes and conditions in gene expression data, and clustering of very high-dimensional data such as text data.

Journal of Biomedical Informatics, 2004

In microarray gene expression data, clusters may hide in subspaces. Traditional clustering algorithms that make use of similarity measurements in the full input space may fail to detect the clusters. In recent years a number of algo- rithms have been proposed to identify this kind of projected clusters, but many of them rely on some critical parame- ters whose proper

Proceedings of the 8th ACM SIGMOD workshop on Research issues in data mining and knowledge discovery - DMKD '03, 2003

Pattern Recognition, 2012

This paper proposes a new method to weight subspaces in feature groups and individual features for clustering high-dimensional data. In this method, the features of high-dimensional data are divided into feature groups, based on their natural characteristics. Two types of weights are introduced to the clustering process to simultaneously identify the importance of feature groups and individual features in each cluster. A new optimization model is given to define the optimization process and a new clustering algorithm FG-k-means is proposed to optimize the optimization model. The new algorithm is an extension to k-means by adding two additional steps to automatically calculate the two types of subspace weights. A new data generation method is presented to generate high-dimensional data with clusters in subspaces of both feature groups and individual features. Experimental results on synthetic and real-life data have shown that the FG-k-means algorithm significantly outperformed four k-means type algorithms, i.e., k-means, W-k-means, LAC and EWKM in almost all experiments. The new algorithm is robust to noise and missing values which commonly exist in high-dimensional data.

Genome biology, 2002

We focus on microarray data where experiments monitor gene expression in different tissues and where each experiment is equipped with an additional response variable such as a cancer type. Although the number of measured genes is in the thousands, it is assumed that only a few marker components of gene subsets determine the type of a tissue. Here we present a new method for finding such groups of genes by directly incorporating the response variables into the grouping process, yielding a supervised clustering algorithm for genes. An empirical study on eight publicly available microarray datasets shows that our algorithm identifies gene clusters with excellent predictive potential, often superior to classification with state-of-the-art methods based on single genes. Permutation tests and bootstrapping provide evidence that the output is reasonably stable and more than a noise artifact. In contrast to other methods such as hierarchical clustering, our algorithm identifies several gene...

Global Trends in Intelligent Computing Research and Development

A need has long been identified for a more effective methodology to understand, prevent, and cure cancer. Microarray technology provides a basis of achieving this goal, with cluster analysis of gene expression data leading to the discrimination of patients, identification of possible tumor subtypes, and individualized treatment. Recently, soft subspace clustering was introduced as an accurate alternative to conventional techniques. This practice has proven effective for high dimensional data, especially for microarray gene expressions. In this review, the basis of weighted dimensional space and different approaches to soft subspace clustering are described. Since most of the models are parameterized, the application of consensus clustering has been identified as a new research direction that is capable of turning the difficulty with parameter selection to an advantage of increasing diversity within an ensemble.

2010 IEEE International Conference on Bioinformatics and Biomedicine (BIBM), 2010

Clustering is a common step in the analysis of microarray data. Microarrays enable simultaneous highthroughput measurement of the expression level of genes. These data can be used to explore relationships between genes and can guide development of drugs and further research. A typical first step in the analysis of these data is to use an agglomerative hierarchical clustering algorithm on the correlation between all gene pairs. While this simple approach has been successful it fails to identify many genetic interactions that may be important for drug design and other important applications.

ACM SIGKDD Explorations Newsletter, 2004

Subspace clustering is an extension of traditional clustering that seeks to find clusters in different subspaces within a dataset. Often in high dimensional data, many dimensions are irrelevant and can mask existing clusters in noisy data. Feature selection removes irrelevant and redundant dimensions by analyzing the entire dataset. Subspace clustering algorithms localize the search for relevant dimensions allowing them to find clusters that exist in multiple, possibly overlapping subspaces. There are two major ...

2016

We consider a clustering problem where we observe feature vectors Xi ∈ Rp, i = 1, 2,..., n, from K possible classes. The class labels are unknown and the main interest is to estimate them. We are primarily interested in the modern regime of p n, where classical clustering methods face challenges. We propose Important Features PCA (IF-PCA) as a new clustering procedure. In IF-PCA, we select a small fraction of features with the largest Kolmogorov-Smirnov (KS) scores, where the threshold is chosen by adapting the recent notion of Higher Criticism, obtain the first (K − 1) left singular vectors of the post-selection normalized data matrix, and then estimate the labels by applying the classical k-means to these singular vectors. It can be seen that IF-PCA is a tuning free clustering method. We apply IF-PCA to 10 gene microarray data sets. The method has competitive perfor-mance in clustering. Especially, in three of the data sets, the error rates of IF-PCA are only 29 % or less of the e...

INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY, 2007

When clustering high dimensional data, traditional clustering methods are found to be lacking since they consider all of the dimensions of the dataset in discovering clusters whereas only some of the dimensions are relevant. This may give rise to subspaces within the dataset where clusters may be found. Using feature selection, we can remove irrelevant and redundant dimensions by analyzing the entire dataset. The problem of automatically identifying clusters that exist in multiple and maybe overlapping subspaces of high dimensional data, allowing better clustering of the data points, is known as Subspace Clustering. There are two major approaches to subspace clustering based on search strategy. Top-down algorithms find an initial clustering in the full set of dimensions and evaluate the subspaces of each cluster, iteratively improving the results. Bottom-up approaches start from finding low dimensional dense regions, and then use them to form clusters. Based on a survey on subspace ...

2004

The development of microarray technologies gives scientists the ability to examine, discover and monitor the mRNA transcript levels of thousands of genes in a single experiment. Nevertheless, the tremendous amount of data that can be obtained from microarray studies presents a challenge for data analysis. The most commonly used computational approach for analyzing microarray data is cluster analysis. In this paper, we investigate the application of an unsupervised extension of the recently proposed k-windows clustering algorithm on gene expression microarray data. This algorithm apart from identifying the clusters present in a dataset also calculates their number thus no special knowledge about the data is required. To improve the quality of the clustering, we selected the most highly correlated genes with respect to the class distinction of the genes. The results obtained by the application of the algorithm exhibit high classification success.

Bioinformatics, 2003

Motivation: This paper introduces the application of a novel clustering method to microarray expression data. Its first stage involves compression of dimensions that can be achieved by applying SVD to the gene-sample matrix in microarray problems. Thus the data (samples or genes) can be represented by vectors in a truncated space of low dimensionality, 4 and 5 in the examples studied here. We find it preferable to project all vectors onto the unit sphere before applying a clustering algorithm. The clustering algorithm used here is the quantum clustering method that has one free scale parameter. Although the method is not hierarchical, it can be modified to allow hierarchy in terms of this scale parameter. Results: We apply our method to three data sets. The results are very promising. On cancer cell data we obtain a dendrogram that reflects correct groupings of cells. In an AML/ALL data set we obtain very good clustering of samples into four classes of the data. Finally, in clustering of genes in yeast cell cycle data we obtain four groups in a problem that is estimated to contain five families.

2004

In this paper, we investigate the application of an unsupervised extension of the recently proposed k-windows clustering algorithm on gene expression microarray data. The k-windows algorithm is used both to identify sets of genes according to their expression in a set of samples, and to cluster samples into homogeneous groups. Experimental results and comparisons indicate that this is a promising approach.

2010

Clustering algorithms break down when the data points fall in huge-dimensional spaces. To tackle this problem, many subspace clustering methods were proposed to build up a subspace where data points cluster efficiently. The bottom-up approach is used widely to select a set of candidate features, and then to use a portion of this set to build up the hidden subspace step by step. The complexity depends exponentially or cubically on the number of the selected features. In this paper, we present SEGCLU, a SEGregation-based subspace CLUstering method which significantly reduces the size of the candidate features' set and has a cubic complexity. This algorithm was applied at noise-free data of DNA copy numbers of two groups of autistic and typically developing children to extract a potential bio-marker for autism. 85% of the individuals were classified correctly in a 13-dimensional subspace.