The bag of words (BOW) represents a corpus in a matrix whose elements are the frequency of words. However, each row in the matrix is a very high-dimensional sparse vector. Dimension reduction (DR) is a popular method to address sparsity and high-dimensionality issues. Among different strategies to develop DR method, Unsupervised Feature Transformation (UFT) is a popular strategy to map all words on a new basis to represent BOW. The recent increase of text data and its challenges imply that DR area still needs new perspectives. Although a wide range of methods based on the UFT strategy has been developed, the fuzzy approach has not been considered for DR based on this strategy. This research investigates the application of fuzzy clustering as a DR method based on the UFT strategy to collapse BOW matrix to provide a lower-dimensional representation of documents instead of the words in a corpus. The quantitative evaluation shows that fuzzy clustering produces superior performance and features to Principal Components Analysis (PCA) and Singular Value Decomposition (SVD), two popular DR methods based on the UFT strategy.
Some studies have applied fuzzy approach to develop dimensionality reduction methods based on supervised- and unsupervised- feature selection strategies such as Rough Set Attribute Reduction (RSAR) @cite_7 . The current fuzzy-based dimension reduction methods rely on retaining important features, and removing irrelevant and redundant (noisy) features @cite_36 ; however, this strategy loses some information. This research investigates the potential of fuzzy clustering as a DR method and compares its performance with powerful current DR methods based on the UFT strategy.
@cite_36 @cite_7
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We apply the framework of kernel dimension reduction, originally designed for supervised problems, to unsupervised dimensionality reduction. In this framework, kernel-based measures of independence are used to derive low-dimensional representations that maximally capture information in covariates in order to predict responses. We extend this idea and develop similarly motivated measures for unsupervised problems where covariates and responses are the same. Our empirical studies show that the resulting compact representation yields meaningful and appealing visualization and clustering of data. Furthermore, when used in conjunction with supervised learners for classification, our methods lead to lower classification errors than state-of-the-art methods, especially when embedding data in spaces of very few dimensions. The problem of similarity search in large time series databases has attracted much attention recently. It is a non-trivial problem because of the inherent high dimensionality of the data. The most promising solutions involve first performing dimensionality reduction on the data, and then indexing the reduced data with a spatial access method. Three major dimensionality reduction techniques have been proposed: Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and more recently the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Piecewise Aggregate Approximation (PAA). We theoretically and empirically compare it to the other techniques and demonstrate its superiority. In addition to being competitive with or faster than the other methods, our approach has numerous other advantages. It is simple to understand and to implement, it allows more flexible distance measures, including weighted Euclidean queries, and the index can be built in linear time. Semantics-preserving dimensionality reduction refers to the problem of selecting those input features that are most predictive of a given outcome; a problem encountered in many areas such as machine learning, pattern recognition, and signal processing. This has found successful application in tasks that involve data sets containing huge numbers of features (in the order of tens of thousands), which would be impossible to process further. Recent examples include text processing and Web content classification. One of the many successful applications of rough set theory has been to this feature selection area. This paper reviews those techniques that preserve the underlying semantics of the data, using crisp and fuzzy rough set-based methodologies. Several approaches to feature selection based on rough set theory are experimentally compared. Additionally, a new area in feature selection, feature grouping, is highlighted and a rough set-based feature grouping technique is detailed. 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.