A Survey on Soft Subspace Clustering <s> (2) LAC <s> Abstract 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. <s> BIB001 </s> A Survey on Soft Subspace Clustering <s> (2) LAC <s> 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. <s> BIB002 </s> A Survey on Soft Subspace Clustering <s> (2) LAC <s> 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. <s> BIB003
The weighting in the Local Adaptive Clustering (LAC) algorithm BIB003 is also controllable by entropy. The objective function can be expressed as The objective functions of EWKM and LAC are indeed very similar. The only difference is that BIB001 the effect of cluster size is considered in LAC but disregarded in EWKM. In addition to the entropy weighting LAC in BIB003 , Domeniconi proposed an alternative LAC algorithm with a different objective function BIB002 as follows Note that the objective function is maximized to solve the solution variables, which is distinct from the entropy-based LAC approach BIB003 discussed earlier.