We introduce a novel subspace segmentation method called Minimal Squared Frobenius Norm Representation (MSFNR). MSFNR performs data clustering by solving a convex optimization problem. We theoretically prove that in the noiseless case, MSFNR is equivalent to the classical Factorization approach and always classifies data correctly. In the noisy case, we show that on both synthetic and real-word...

Energy efficiency, low latency, high estimation accuracy, and fast convergence are important goals in distributed incremental estimation algorithms for sensor networks. One approach that adds flexibility in achieving these goals is clustering. In this paper, the framework of distributed incremental estimation is extended by allowing clustering amongst the nodes. Among the observations made is t...

In order to overcome the premature convergence in the particle swarm optimization algorithm, dynamically chaotic perturbation is introduced to form a dynamically chaotic PSO, briefly denoted as DCPSO. To get rid of the drawbacks of simply finding the convex cluster and being sensitive to the initial partitions in k -means algorithm, a novel hybrid clustering algorithm combined with the DCPSO is...

Robust Clustering methods are aimed at avoiding unsatisfactory results resulting from the presence of certain amount of outlying observations in the input data of many practical applications such as biological sequences analysis or gene expressions analysis. This paper presents a fuzzy clustering algorithm based on average link and possibilistic clustering paradigm termed as AVLINK. It minimize...

In this paper, we consider unsupervised partitioning problems, such as clustering, image segmentation, video segmentation and other change-point detection problems. We focus on partitioning problems based explicitly or implicitly on the minimization of Euclidean distortions, which include mean-based change-point detection, K-means, spectral clustering and normalized cuts. Our main goal is to le...

The clustering problem as a problem of set function optimization with constraints is considered. The behavior of quasi-concave functions on antimatroids and on convex geometries is investigated. The duality of these two set function optimizations is proved. The greedy type Chain algorithm, which allows to find an optimal cluster, both as the “most distant” group on antimatroids and as a dense c...

data mining, machine learning, model fitting, regression, exploratory data analysis, error rate estimation, data modeling, data cleaning, data preparation, predictability We prove an inequality bound for the variance of the error of a regression function plus its non-smoothness as quantified by the Uniform Lipschitz condition. The coefficients in the inequality are calculated based on training ...

Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. Both have applications in VLSI design, CASE tools, software visualisation and visualisation of social networks and biological networks. Straight-line drawing algorithms for hierarchical graphs and clustered graphs have been presented in [P. Eades, Q. Feng, X. Lin and H. Nag...