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Time-stamped data are ubiquitous in our daily life, such as twitter data, academic papers and sensor data. Finding clusters and their evolutionary trends in time-stamped data sets are receiving increasing attention from researchers. Most existing methods, however, can only tackle the clustering problem of a data set without time-stamped information which is inherent in almost all the data objects. Actually, not only the performance can be improved by effectively incorporating the time-stamped information in the clustering process on most data sets, but also we can find the evolutionary trends of the clusters with time information. In this paper, we introduce an approach for clustering time-stamped data and discovering the evolutionary trends of the clusters by using Multiple Nonnegative Matrices Factorization (MNMF) with smooth constraint over time. To utilize time-stamped information in the clustering process, an extra object-time matrix is constructed in our proposed method. Then, we jointly factorize multiple feature matrices using smooth constraint to perform the object-time matrix to obtain the clusters and their evolutionary trends. Experimental results on real data sets demonstrate that our proposed approach outperforms the comparative algorithms with respect to Fscore, NMI or Entropy. [ABSTRACT FROM AUTHOR]

Most of kmeans-type clustering algorithms rely on only intra-cluster compactness, i.e. the dispersions of a cluster. Inter-cluster separation which is widely used in classification algorithms, however, is rarely considered in a clustering process. In this paper, we present a new discriminative subspace kmeans-type clustering algorithm (DSKmeans), which integrates the intra-cluster compactness and the inter-cluster separation simultaneously. Different to traditional weighting kmeans-type algorithms, a 3-order tensor is constructed to evaluate the importance of different features in order to integrate the aforementioned two types of information. First, a new objective function for clustering is designed. To optimize the objective function, the corresponding updating rules for the algorithm are then derived analytically. The properties and performance of DSKmeans are investigated on several numerical and categorical data sets. Experimental results corroborate that our proposed algorithm outperforms the state-of-the-art kmeans-type clustering algorithms with respects to four metrics: Accuracy, RandIndex, Fscore and Normal Mutual Information(NMI). [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a Crotch Ensemble classification model for high dimensional data. A Crotch Ensemble is obtained from a decision cluster tree built by calling a clustering algorithm recursively. A crotch is an inner node of the tree together with its direct children. If the children of a crotch have more than one dominant class, the crotch is defined as a crotch predictor. Each crotch predictor constructs a classifier by itself. A Crotch Ensemble consists of a set of crotch predictors. When classifying a new object, a subset of crotch predictors is selected according to the distances between the object and the crotch predictors. A classification is made on the object as the class predicted by the crotch predictors with the maximum accumulative weights. The experimental results on both synthetic and real data have shown that the Crotch Ensemble model can get better classification results on high dimensional data than other classification methods. [Copyright &y& Elsevier]

This paper proposes TW-$(k)$-means, an automated two-level variable weighting clustering algorithm for multiview data, which can simultaneously compute weights for views and individual variables. In this algorithm, a view weight is assigned to each view to identify the compactness of the view and a variable weight is also assigned to each variable in the view to identify the importance of the variable. Both view weights and variable weights are used in the distance function to determine the clusters of objects. In the new algorithm, two additional steps are added to the iterative $(k)$-means clustering process to automatically compute the view weights and the variable weights. We used two real-life data sets to investigate the properties of two types of weights in TW-$(k)$-means and investigated the difference between the weights of TW-$(k)$-means and the weights of the individual variable weighting method. The experiments have revealed the convergence property of the view weights in TW-$(k)$-means. We compared TW-$(k)$-means with five clustering algorithms on three real-life data sets and the results have shown that the TW-$(k)$-means algorithm significantly outperformed the other five clustering algorithms in four evaluation indices. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes a new method to weight subspaces in feature groups and individual features for clustering high-dimensional data. In this method, the features of high-dimensional data are divided into feature groups, based on their natural characteristics. Two types of weights are introduced to the clustering process to simultaneously identify the importance of feature groups and individual features in each cluster. A new optimization model is given to define the optimization process and a new clustering algorithm FG-k-means is proposed to optimize the optimization model. The new algorithm is an extension to k-means by adding two additional steps to automatically calculate the two types of subspace weights. A new data generation method is presented to generate high-dimensional data with clusters in subspaces of both feature groups and individual features. Experimental results on synthetic and real-life data have shown that the FG-k-means algorithm significantly outperformed four k-means type algorithms, i.e., k-means, W-k-means, LAC and EWKM in almost all experiments. The new algorithm is robust to noise and missing values which commonly exist in high-dimensional data. [Copyright &y& Elsevier]

Abstract: Clustering is one of the important data mining tasks. Nested clusters or clusters of multi-density are very prevalent in data sets. In this paper, we develop a hierarchical clustering approach—a cluster tree to determine such cluster structure and understand hidden information present in data sets of nested clusters or clusters of multi-density. We embed the agglomerative k-means algorithm in the generation of cluster tree to detect such clusters. Experimental results on both synthetic data sets and real data sets are presented to illustrate the effectiveness of the proposed method. Compared with some existing clustering algorithms (DBSCAN, X-means, BIRCH, CURE, NBC, OPTICS, Neural Gas, Tree-SOM, EnDBSAN and LDBSCAN), our proposed cluster tree approach performs better than these methods. [Copyright &y& Elsevier]