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Consider a high-dimensional data set, in which for every data-point there is incomplete information. Each object in the data set represents a real entity, which is described by a point in high-dimensional space. We model the lack of…
Subspace clustering methods which embrace a self-expressive model that represents each data point as a linear combination of other data points in the dataset provide powerful unsupervised learning techniques. However, when dealing with…
Subspace clustering refers to the problem of clustering high-dimensional data points into a union of low-dimensional linear subspaces, where the number of subspaces, their dimensions and orientations are all unknown. In this paper, we…
Clustering in high-dimensional spaces is a difficult problem which is recurrent in many domains, for example in image analysis. The difficulty is due to the fact that high-dimensional data usually live in different low-dimensional subspaces…
In this paper we study skyline queries in the distributed computational model, where we have $s$ remote sites and a central coordinator (the query node); each site holds a piece of data, and the coordinator wants to compute the skyline of…
The development of external evaluation criteria for soft clustering (SC) has received limited attention: existing methods do not provide a general approach to extend comparison measures to SC, and are unable to account for the uncertainty…
Class imbalance is one of the challenging problems for machine learning in many real-world applications, such as coal and gas burst accident monitoring: the burst premonition data is extreme smaller than the normal data, however, which is…
Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling…
In Stochastic blockmodels, which are among the most prominent statistical models for cluster analysis of complex networks, clusters are defined as groups of nodes with statistically similar link probabilities within and between groups. A…
We consider the problem of subspace clustering: given points that lie on or near the union of many low-dimensional linear subspaces, recover the subspaces. To this end, one first identifies sets of points close to the same subspace and uses…
Clustering is one of the most fundamental problems in data analysis and it has been studied extensively in the literature. Though many clustering algorithms have been proposed, clustering theories that justify the use of these clustering…
We introduce a density-based clustering method called skeleton clustering that can detect clusters in multivariate and even high-dimensional data with irregular shapes. To bypass the curse of dimensionality, we propose surrogate density…
Missing datasets, in which some objects have missing values in certain dimensions, are prevalent in the Real-world. Existing clustering algorithms for missing datasets first impute the missing values and then perform clustering. However,…
We describe the development of a scientific cloud computing (SCC) platform that offers high performance computation capability. The platform consists of a scientific virtual machine prototype containing a UNIX operating system and several…
Spectral clustering is a popular method for community detection in network graphs: starting from a matrix representation of the graph, the nodes are clustered on a low dimensional projection obtained from a truncated spectral decomposition…
Given a set of vectors $\F=\{f_1,\dots,f_m\}$ in a Hilbert space $\HH$, and given a family $\CC$ of closed subspaces of $\HH$, the {\it subspace clustering problem} consists in finding a union of subspaces in $\CC$ that best approximates…
Positioning benefits from channel models that capture geometric effects and, in particular, from the signal properties of the first arriving path and the spatial consistency of the propagation condition of multiple links. The models that…
Statistical modeling often involves identifying an optimal estimate to some underlying probability distribution known to satisfy some given constraints. I show here that choosing as estimate the centroid, or center of mass, of the set…
Suppose $k$ centers are fit to $m$ points by heuristically minimizing the $k$-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with $p\geq 4$ bounded moments; in…
Modeling of high-dimensional data is very important to categorize different classes. We develop a new mixture model called Multinomial cluster-weighted model (MCWM). We derive the identifiability of a general class of MCWM. We estimate the…