A Survey on Soft Subspace Clustering

Subspace clustering (SC) is a promising clustering technology to identify clusters based on their associations with subspaces in high dimensional spaces. SC can be classified into hard subspace clustering (HSC) and soft subspace clustering (SSC). While HSC algorithms have been extensively studied and well accepted by the scientific community, SSC algorithms are relatively new but gaining more attention in recent years due to better adaptability. In the paper, a comprehensive survey on existing SSC algorithms and the recent development are presented. The SSC algorithms are classified systematically into three main categories, namely, conventional SSC (CSSC), independent SSC (ISSC) and extended SSC (XSSC). The characteristics of these algorithms are highlighted and the potential future development of SSC is also discussed.Comment: This paper has been published in Information Sciences Journal in 201

Sparsity-Inducing Fuzzy Subspace Clustering

This paper considers a fuzzy subspace clustering problem and proposes to introduce an original sparsity-inducing regularization term. The minimization of this term, which involves a l$_{0}$ penalty, is considered from a geometric point of view and a novel proximal operator is derived. A subspace clustering algorithm, Prosecco, is proposed to optimize the cost function using both proximal and alternate gradient descent. Experiments comparing this algorithm to the state of the art in sparse fuzzy subspace clustering show the relevance of the proposed approach

ONLINE FUZZY CLUSTERING OF HIGH DIMENSION DATA STREAMS BASED ON NEURAL NETWORK ENSEMBLES

The subject matter of the article is fuzzy clustering of high-dimensional data based on the ensemble approach, provided that a number and shape of clusters are not known. The goal of the work is to create the neuro-fuzzy approach for clustering data when the data stream is fed for online processing and a number and shape of clusters are unknown. The following tasks are solved in the article - the input feature space is compressed in the online mode; the model of neural network ensembles for data clustering is built; the ensemble of neuro-fuzzy networks for clustering high-dimensional data is developed; the approach for clustering data in the online mode is worked out. The following results are obtained - the main idea of the proposed approach is based on a modification of the fuzzy C-means algorithm. To reduce the dimension of the input space, the modified Hebb-Sanger network is suggested to be used; this net is characterized by the increased speed and is built on the basis of the modified Oja neurons. A speed-optimized learning algorithm for the Oja neuron is proposed. Such a network implements the method of principal components in the online mode with high speed. Conclusions. In the event the reduction-compression procedure cannot be used due to the probability of losing the physical meaning of the original space, a new clustering criterion was introduced; this criterion contains both a well-known polynomial fuzzifier and the weighment of individual components of the deviations of presented images from cluster centroids. The recurrent modification based on the algorithms proposed in this article is introduced. A mathematical model is developed to determine the quality of clustering with the use of the Xi-Beni index, which was modified for the online mode. The experimental results confirm the fact that the proposed system enables solving a wide range of Data Mining tasks when data sets are processed online, provided that a number and shape of clusters are not known and there is a large number of observations as well

A Novel Fuzzy c -Means Clustering Algorithm Using Adaptive Norm

Abstract(#br)The fuzzy c -means (FCM) clustering algorithm is an unsupervised learning method that has been widely applied to cluster unlabeled data automatically instead of artificially, but is sensitive to noisy observations due to its inappropriate treatment of noise in the data. In this paper, a novel method considering noise intelligently based on the existing FCM approach, called adaptive-FCM and its extended version (adaptive-REFCM) in combination with relative entropy, are proposed. Adaptive-FCM, relying on an inventive integration of the adaptive norm, benefits from a robust overall structure. Adaptive-REFCM further integrates the properties of the relative entropy and normalized distance to preserve the global details of the dataset. Several experiments are carried out,..

Identifying, ranking and tracking systemically important financial institutions (SIFIs), from a global, EU and Eurozone perspective

This paper develops a methodology to identify systemically important financial institutions building on that developed by the BCBS (2011) and used by the Financial Stability Board in its yearly G-SIFIs identification. This methodology is based on publicly available data, providing fully transparent results with a G-SIFIs list that helps to bridge the gap between market knowledge and supervisory decisions. Moreover the results encompass a complete ranking of the banks considered, according to their systemic importance scores. The methodology has then been applied to EU and Eurozone samples of banks to obtain their systemic importance ranking and SIFIs lists. A statistical analysis and some geographical and historical evidence provide further insight into the notion of systemic importance, its policy implications and the future applications of this methodology

Identifying and tracking systemically important financial institutions (SIFIs) with public data

This paper develops a methodology to identify systemically important financial institutions building on that developed by the BCBS (2011) and used by the Financial Stability Board in its yearly G-SIFIs identification. This methodology is based on publicly available data, providing fully transparent results with a G-SIFIs list that helps to bridge the gap between market knowledge and supervisory decisions. Moreover the results encompass a complete ranking of the banks considered, according to their systemic importance scores. The methodology has then been applied to EU and Eurozone samples of banks to obtain their systemic importance ranking and SIFIs lists. A statistical analysis and some geographical and historical evidence provide further insight into the notion of systemic importance, its policy implications and the future applications of this methodology

Identifying, ranking and tracking systemically important financial institutions (SIFIs), from a global, EU and Eurozone perspective

This paper develops a methodology to identify systemically important financial institutions building on that developed by the BCBS (2011) and used by the Financial Stability Board in its yearly G-SIFIs identification. This methodology is based on publicly available data, providing fully transparent results with a G-SIFIs list that helps to bridge the gap between market knowledge and supervisory decisions. Moreover the results encompass a complete ranking of the banks considered, according to their systemic importance scores. The methodology has then been applied to EU and Eurozone samples of banks to obtain their systemic importance ranking and SIFIs lists. A statistical analysis and some geographical and historical evidence provide further insight into the notion of systemic importance, its policy implications and the future applications of this methodology

Identifying and tracking systemically important financial institutions (SIFIs) with public data

This paper develops a methodology to identify systemically important financial institutions building on that developed by the BCBS (2011) and used by the Financial Stability Board in its yearly G-SIFIs identification. This methodology is based on publicly available data, providing fully transparent results with a G-SIFIs list that helps to bridge the gap between market knowledge and supervisory decisions. Moreover the results encompass a complete ranking of the banks considered, according to their systemic importance scores. The methodology has then been applied to EU and Eurozone samples of banks to obtain their systemic importance ranking and SIFIs lists. A statistical analysis and some geographical and historical evidence provide further insight into the notion of systemic importance, its policy implications and the future applications of this methodology

Fuzzy clustering with weighting of data variables

We introduce an objective function-based fuzzy clustering technique that assigns one in uence parameter to each single data variable for each cluster. Our method is not only suited to detect structures or groups in unevenly over the structure's single domains distributed data, but gives also information about the in uence of individual variables on the detected groups. In addition, our approach can be seen as a generalization of the well-known fuzzy c-means clustering algorithm