Efficient mining of distance-based subspace clusters
Kelvin Sim2009, Statistical Analysis and Data Mining
Sign up for access to the world's latest research
checkGet notified about relevant papers
checkSave papers to use in your research
checkJoin the discussion with peers
checkTrack your impact
Abstract
Traditional similarity measurements often become meaningless when dimensions of datasets increase. Subspace clustering has been proposed to find clusters embedded in subspaces of high dimensional datasets.
Related papers
Distance Based Subspace Clustering with Flexible Dimension Partitioning
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.
FINDIT: a fast and intelligent subspace clustering algorithm using dimension voting
Information and Software Technology, 2004
The aim of this paper is to present a novel subspace clustering method named FINDIT. Clustering is the process of finding interesting patterns residing in the dataset by grouping similar data objects from dissimilar ones based on their dimensional values. Subspace clustering is a new area of clustering which achieves the clustering goal in high dimension by allowing clusters to be formed with their own correlated dimensions. In subspace clustering, selecting correct dimensions is very important because the distance between points is easily changed according to the selected dimensions. However, to select dimensions correctly is difficult, because data grouping and dimension selecting should be performed simultaneously. FINDIT determines the correlated dimensions for each cluster based on two key ideas: dimension-oriented distance measure which fully utilizes dimensional difference information, and dimension voting policy which determines important dimensions in a probabilistic way based on V nearest neighbors' information. Through various experiments on synthetic data, FINDIT is shown to be very successful in the high dimensional clustering problem. FINDIT satisfies most requirements for good clustering methods such as accuracy of results, robustness to the noise and the cluster density, and scalability to the dataset size and the dimensionality. Moreover, it is gracefully scalable to full dimension without any modification to algorithm.
Pattern Based Subspace Clustering: A Review
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.
A Preview on Subspace Clustering of High Dimensional Data
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 ...
Scalable density-based subspace clustering
Proceedings of the 20th ACM international conference on Information and knowledge management - CIKM '11, 2011
Abstract For knowledge discovery in high dimensional databases, subspace clustering detects clusters in arbitrary subspace projections. Scalability is a crucial issue, as the number of possible projections is exponential in the number of dimensions. We propose a scalable density-based subspace clustering method that steers mining to few selected subspace clusters. Our novel steering technique reduces subspace processing by identifying and clustering promising subspaces and their combinations directly. Thereby, it ...
Subspace Clustering of High Dimensional Data
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.
Relevant Subspace Clustering: Mining the Most Interesting Non-redundant Concepts in High Dimensional Data
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.
Hub-based subspace clustering
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.
Clustering for High Dimensional Data: Density based Subspace Clustering Algorithms
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.
Subspace clustering for high dimensional categorical data
ACM SIGKDD Explorations Newsletter, 2004
Data clustering has been discussed extensively, but almost all known conventional clustering algorithms tend to break down in high dimensional spaces because of the inherent sparsity of the data points. Existing subspace clustering algorithms for handling high-dimensional data focus on numerical dimensions. In this paper, we designed an iterative algorithm called SUBCAD for clustering high dimensional categorical data sets, based on the minimization of an objective function for clustering. We deduced some cluster memberships changing rules using the objective function. We also designed an objective function to determine the subspace associated with each cluster. We proved various properties of this objective function that are essential for us to design a fast algorithm to find the subspace associated with each cluster. Finally, we carried out some experiments to show the effectiveness of the proposed method and the algorithm.
Related topics
Related papers
Comparative Study of Subspace Clustering Algorithms
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...
An Algorithm for the Removal of Redundant Dimensions to Find Clusters in N-Dimensional Data using Subspace Clustering
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 ...
Adapting K-Means Algorithm for Discovering Clusters in Subspaces
Lecture Notes in Computer Science, 2006
Subspace clustering is a challenging task in the field of data mining. Traditional distance measures fail to differentiate the furthest point from the nearest point in very high dimensional data space. To tackle the problem, we design minimal subspace distance which measures the similarity between two points in the subspace where they are nearest to each other. It can discover subspace clusters implicitly when measuring the similarities between points. We use the new similarity measure to improve traditional k-means algorithm for discovering clusters in subspaces. By clustering with low-dimensional minimal subspace distance first, the clusters in low-dimensional subspaces are detected. Then by gradually increasing the dimension of minimal subspace distance, the clusters get refined in higher dimensional subspaces. Our experiments on both synthetic data and real data show the effectiveness of the proposed similarity measure and algorithm.
A Generic Framework for Efficient Subspace Clustering of High-Dimensional Data
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.
Subspace clustering for high dimensional data: a review
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 ...
Segregation-based subspace clustering for huge dimensional data
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.
A meta-heuristic density-based subspace clustering algorithm for high-dimensional data
Soft Computing, 2021
Subspace clustering is one of the efficient techniques for determining the clusters in different subsets of dimensions. Ideally, these techniques should find all possible non-redundant clusters in which the data point participates. Unfortunately, existing hard subspace clustering algorithms fail to satisfy this property. Additionally, with the increase in dimensions of data, classical subspace algorithms become inefficient. This work presents a new density-based subspace clustering algorithm (S_FAD) to overcome the drawbacks of classical algorithms. S_FAD is based on a bottom-up approach and finds subspace clusters of varied density using different parameters of the DBSCAN algorithm. The algorithm optimizes parameters of the DBCAN algorithm through a hybrid meta-heuristic algorithm and uses hashing concepts to discover all non-redundant subspace clusters. The efficacy of S_FAD is evaluated against various existing subspace clustering algorithms on artificial and real datasets in terms of F_Score and rand_index. Performance is assessed based on three parameters: average ranking, SRR ranking, and scalability on varied dimensions. Statistical analysis is performed through the Wilcoxon signed-rank test. Results reveal that S_FAD performs considerably better on the majority of the datasets and scales well up to 6400 dimensions on the actual dataset.
Isc–Intelligent Subspace Clustering, A Density Based Clustering Approach For High Dimensional Dataset
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...
Clicks: An Effective Algorithm for Mining Subspace Clusters In Categorical Datasets
Data & Knowledge Engineering, 2007
INSCY: Indexing Subspace Clusters With In-Process-Removal of Redundancy
Data Mining, 2008. ICDM' …, 2009
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.