Axis-aligned subspace clustering generally entails searching through enormous numbers of subspaces (feature combinations) and evaluation of cluster quality within each subspace. In this paper, we tackle the problem of identifying subsets of features with the most significant contribution to the formation of the local neighborhood surrounding a given data point. For each point, the recently-proposed Local Intrinsic Dimension (LID) model is used in identifying the axis directions along which features have the greatest local discriminability, or equivalently, the fewest number of components of LID that capture the local complexity of the data. In this paper, we develop an estimator of LID along axis projections, and provide preliminary evidence that this LID decomposition can indicate axis-aligned data subspaces that support the formation of clusters.
@cite_34: Correlation clustering aims at the detection of data points that appear as hyperplanes in the data space and, thus, exhibit common correlations between different subsets of features. Recently proposed methods for correlation clustering usually suffer from several severe drawbacks including poor robustness against noise or parameter settings, incomplete results (i.e. missed clusters), poor usability due to complex input parameters, and poor scalability. In this paper, we propose the novel correlation clustering algorithm COPAC (COrrelation PArtition Clustering) that aims at improved robustness, completeness, usability, and efficiency. Our experimental evaluation empirically shows that COPAC is superior over existing state-of-the-art correlation clustering methods in terms of runtime, accuracy, and completeness of the results.
@cite_13: In this article, we propose an efficient and effective method for finding arbitrarily oriented subspace clusters by mapping the data space to a parameter space defining the set of possible arbitrarily oriented subspaces. The objective of a clustering algorithm based on this principle is to find those among all the possible subspaces that accommodate many database objects. In contrast to existing approaches, our method can find subspace clusters of different dimensionality even if they are sparse or are intersected by other clusters within a noisy environment. A broad experimental evaluation demonstrates the robustness and effectiveness of our method. Copyright © 2008 Wiley Periodicals, Inc. Statistical Analysis and Data Mining 1: 000-000, 2008
@cite_23: The detection of correlations between different features in a set of feature vectors is a very important data mining task because correlation indicates a dependency between the features or some association of cause and effect between them. This association can be arbitrarily complex, i.e. one or more features might be dependent from a combination of several other features. Well-known methods like the principal components analysis (PCA) can perfectly find correlations which are global, linear, not hidden in a set of noise vectors, and uniform, i.e. the same type of correlation is exhibited in all feature vectors. In many applications such as medical diagnosis, molecular biology, time sequences, or electronic commerce, however, correlations are not global since the dependency between features can be different in different subgroups of the set. In this paper, we propose a method called 4C (Computing Correlation Connected Clusters) to identify local subgroups of the data objects sharing a uniform but arbitrarily complex correlation. Our algorithm is based on a combination of PCA and density-based clustering (DBSCAN). Our method has a determinate result and is robust against noise. A broad comparative evaluation demonstrates the superior performance of 4C over competing methods such as DBSCAN, CLIQUE and ORCLUS.
Some methods consider feature combinations directly or assess (linear) correlations among features. These typically rely on locally applied PCA as a primitive to assess locally relevant feature combinations @cite_23 @cite_34 or on an adaptation of the Hough transform @cite_13 , which is computationally even more expensive.