Adapting K-Means Algorithm for Discovering Clusters in Subspaces

2007

Traditional similarity or distance measurements usually become meaningless when the dimensions of the datasets increase, which has detrimental effects on clustering performance. In this paper, we propose a distance-based subspace clustering model, called nCluster, to find groups of objects that have similar values on subsets of dimensions. Instead of using a grid based approach to partition the data space into non-overlapping rectangle cells as in the density based subspace clustering algorithms, the nCluster model uses a more flexible method to partition the dimensions to preserve meaningful and significant clusters. We develop an efficient algorithm to mine only maximal nClusters. A set of experiments are conducted to show the efficiency of the proposed algorithm and the effectiveness of the new model in preserving significant clusters.

2019

101 Published By: Blue Eyes Intelligence Engineering & Sciences Publication Retrieval Number: A5498108118/19©BEIESP Abstract: Clustering High dimensional data is a propitious research area in current scenario. Now it becomes a crucial task to cluster multi-dimensional dataset as data-objects are largely dispersed in multi-dimensional space. Most of the conventional algorithms for clustering work on all dimensions of the feature space for calculating clusters. Whereas only few attributes are relevant. Thus their performance is not very Precise. A modified subspace clustering is proposed in this research paper, which does not use all attributes of high-dimensional feature space simultaneously rather, it determine a subspace of attributes which are important for each individual cluster. This subspace of attributes may be same or different for the different cluster. The comparison between conventional K-Means and modified subspace K-means clustering algorithms were done based on variou...

2015

A cluster is a collection of data objects that are similar to one another within the same cluster and are dissimilar to the objects in other clusters. Subspace clustering is an enhanced form of the traditional clustering which is used for identifying clusters in high dimensional data sets. There are two major subspace clustering approaches namely : Top-down approach which use sampling techniques that randomly pick up sample data points to identify the subspace and then assigns all the data points to form original clusters and Bottom-up approach, where dense regions in low dimensional spaces are found and then combined to form clusters. The paper discusses details of the top-down algorithm PROCLUS which is applied for customer segmentation, Trend Analysis, Classification, etc. which needs disjoint partition of datasets and CLIQUE which is used to identify overlapping clusters. The paper highlights the important steps of both the algorithms with flowcharts and an experimental study ha...

2004

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, using both synthetic and real data sets. In particular, our results show the feasibility of the proposed technique to perform simultaneous clustering of genes and conditions in microarray data.

International Journal of Advanced Computer Science and Applications, 2010

The task of biclustering or subspace clustering is a data mining technique that allows simultaneous clustering of rows and columns of a matrix. Though the definition of similarity varies from one biclustering model to another, in most of these models the concept of similarity is often based on such metrics as Manhattan distance, Euclidean distance or other L p distances. In other words, similar objects must have close values in at least a set of dimensions. Pattern-based clustering is important in many applications, such as D A micro-array data analysis, automatic recommendation systems and target marketing systems. However, pattern-based clustering in large databases is challenging. On the one hand, there can be a huge number of clusters and many of them can be redundant and thus makes the pattern-based clustering ineffective. On the other hand, the previous proposed methods may not be efficient or scalable in mining large databases. The objective of this paper is to perform a comparative study of all subspace clustering algorithms in terms of efficiency, accuracy and time complexity.

2009

Many real-world data sets consist of a very high dimensional feature space. Most clustering techniques use the distance or similarity between objects as a measure to build clusters. But in high dimensional spaces, distances between points become relatively uniform. In such cases, density based approaches may give better results. Subspace Clustering algorithms automatically identify lower dimensional subspaces of the higher dimensional feature space in which clusters exist. In this paper, we propose a new clustering algorithm, ISC – Intelligent Subspace Clustering, which tries to overcome three major limitations of the existing state-of-art techniques. ISC determines the input parameter such as є – distance at various levels of Subspace Clustering which helps in finding meaningful clusters. The uniform parameters approach is not suitable for different kind of databases. ISC implements dynamic and adaptive determination of Meaningful clustering parameters based on hierarchical filteri...

The data mining has emerged as a powerful tool to extract knowledge from huge databases. Researchers have introduced several machine learning algorithms to explore the databases to discover information, hidden patterns, and rules from the data which were not known at the data recording time. Due to the remarkable developments in the storage capacities, processing and powerful algorithmic tools, practitioners are developing new and improved algorithms and techniques in several areas of data mining to discover the rules and relationship among the attributes in simple and complex higher dimensional databases. Furthermore data mining has its implementation in large variety of areas ranging from banking to marketing, engineering to bioinformatics and from investment to risk analysis and fraud detection. Practitioners are analyzing and implementing the techniques of artificial neural networks for classification and regression problems because of accuracy, efficiency. The aim of his short ...

2005

Subspace clustering has been investigated extensively since traditional clustering algorithms often fail to detect meaningful clusters in high-dimensional data spaces. Many recently proposed subspace clustering methods suffer from two severe problems: First, the algorithms typically scale exponentially with the data dimensionality and/or the subspace dimensionality of the clusters. Second, for performance reasons, many algorithms use a global density threshold for clustering, which is quite questionable since clusters in subspaces of significantly different dimensionality will most likely exhibt significantly varying densities. In this paper, we propose a generic framework to overcome these limitations. Our framework is based on an efficient filterrefinement architecture that scales at most quadratic w.r.t. the data dimensionality and the dimensionality of the subspace clusters. It can be applied to any clustering notions including notions that are based on a local density threshold. A broad experimental evaluation on synthetic and real-world data empirically shows that our method achieves a significant gain of runtime and quality in comparison to state-of-the-art subspace clustering algorithms.

2004

Abstract Clustering techniques often define the similarity between instances using distance measures over the various dimensions of the data [12, 14]. Subspace clustering is an extension of traditional clustering that seeks to find clusters in different subspaces within a dataset. Traditional clustering algorithms consider all of the dimensions of an input dataset in an attempt to learn as much as possible about each instance described. In high dimensional data, however, many of the dimensions are often irrelevant.

International Journal of Computer Applications, 2013

Finding clusters in high dimensional data is a challenging task as the high dimensional data comprises hundreds of attributes. Subspace clustering is an evolving methodology which, instead of finding clusters in the entire feature space, it aims at finding clusters in various overlapping or non-overlapping subspaces of the high dimensional dataset. Density based subspace clustering algorithms treat clusters as the dense regions compared to noise or border regions. Many momentous density based subspace clustering algorithms exist in the literature. Each of them is characterized by different characteristics caused by different assumptions, input parameters or by the use of different techniques etc. Hence it is quite unfeasible for the future developers to compare all these algorithms using one common scale. In this paper, we presented a review of various density based subspace clustering algorithms together with a comparative chart focusing on their distinguishing characteristics such as overlapping / non-overlapping, axis parallel / arbitrarily oriented and so on.

2009 Ninth IEEE International Conference on Data Mining, 2009

Subspace clustering aims at detecting clusters in any subspace projection of a high dimensional space. As the number of possible subspace projections is exponential in the number of dimensions, the result is often tremendously large. Recent approaches fail to reduce results to relevant subspace clusters. Their results are typically highly redundant, i.e. many clusters are detected multiple times in several projections.

International Journal of Data Mining & Knowledge Management Process, 2013

Subspace clustering discovers the clusters embedded in multiple, overlapping subspaces of high dimensional data. Many significant subspace clustering algorithms exist, each having different characteristics caused by the use of different techniques, assumptions, heuristics used etc. A comprehensive classification scheme is essential which will consider all such characteristics to divide subspace clustering approaches in various families. The algorithms belonging to same family will satisfy common characteristics. Such a categorization will help future developers to better understand the quality criteria to be used and similar algorithms to be used to compare results with their proposed clustering algorithms. In this paper, we first proposed the concept of SCAF (Subspace Clustering Algorithms' Family). Characteristics of SCAF will be based on the classes such as cluster orientation, overlap of dimensions etc. As an illustration, we further provided a comprehensive, systematic description and comparison of few significant algorithms belonging to "Axis parallel, overlapping, density based" SCAF.

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.

Neurocomputing

Data often exists in subspaces embedded within a high-dimensional space. Subspace clustering seeks to group data according to the dimensions relevant to each subspace. This requires the estimation of subspaces as well as the clustering of data. Subspace clustering becomes increasingly challenging in high dimensional spaces due to the curse of dimensionality which affects reliable estimations of distances and density. Recently, another aspect of high-dimensional spaces has been observed, known as the hubness phenomenon, whereby few data points appear frequently as nearest neighbors of the rest of the data. The distribution of neighbor occurrences becomes skewed with increasing intrinsic dimensionality of the data, and few points with high neighbor occurrences emerge as hubs. Hubs exhibit useful geometric properties and have been leveraged for clustering data in the full-dimensional space. In this paper, we study hubs in the context of subspace clustering. We present new characterizations of hubs in relation to subspaces, and design graph-based meta-features to identify a subset of hubs which are well fit to serve as seeds for the discovery of local latent subspaces and clusters. We propose and evaluate a hubnessdriven algorithm to find subspace clusters, and show that our approach is superior to the baselines, and is competitive against state-of-the-art subspace clustering methods. We also identify the data characteristics that make hubs suitable for subspace clustering. Such characterization gives valuable guidelines to data mining practitioners.

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.