We introduce the problem of cluster-grouping and show that it integrates several important data mining tasks, i.e. subgroup discovery, mining correlated patterns and aspects from clustering. The problem of cluster-grouping can be regarded as a new type of inductive optimization query that asks for the k best patterns according to a convex criterion. The algorithm CG for solving cluster-grouping...

We present a novel linear clustering framework (DIFFRAC) which relies on a linear discriminative cost function and a convex relaxation of a combinatorial optimization problem. The large convex optimization problem is solved through a sequence of lower dimensional singular value decompositions. This framework has several attractive properties: (1) although apparently similar to K-means, it exhib...

In this study, we propose a novel evolutionary algorithm-based clustering method, named density-sensitive evolutionary clustering (DSEC). In DSEC, each individual is a sequence of real integer numbers representing the cluster representatives, and each data item is assigned to a cluster representative according to a novel density-sensitive dissimilarity measure which can measure the geodesic dis...

Low-rank matrix is desired in many machine learning and computer vision problems. Most of the recent studies use the nuclear norm as a convex surrogate of the rank operator. However, all singular values are simply added together by the nuclear norm, and thus the rank may not be well approximated in practical problems. In this paper, we propose using a log-determinant (LogDet) function as a smoo...

We propose SoF (Soft-cluster matrix Factorization), a probabilistic clustering algorithm which softly assigns each data point into clusters. Unlike model-based clustering algorithms, SoF does not make assumptions about the data density distribution. Instead, we take an axiomatic approach to define 4 properties that the probability of co-clustered pairs of points should satisfy. Based on the pro...

Many non-convex problems in machine learning such as embedding and clustering have been solved using convex semidefinite relaxations. These semidefinite programs (SDPs) are expensive to solve and are hence limited to run on very small data sets. In this paper we show how we can improve the quality and speed of solving a number of these problems by casting them as low-rank SDPs and then directly...

background: liver cirrhosis was one of the most important liver diseases. other chronic liver diseases could be lead to liver cirrhosis. liver cirrhosis could be lead one kind of liver cancers named hepatocellular carcinoma. cirrhosis in the early stages just by laboratory and imaging testes could be diagnosed. in this study cirrhotic patients were classified based on laboratory symptoms. for t...

sensor networks generally consist of a very great number of sensor nodes which will be spread into a vast environment and aggregate data out of it. the sensor nodes are afflicted with some limitations as follows memory, reception, communication as well as calculation capability, and battery power. the transmission of a great amount of extra data increases data transmission and proportionally in...

Abstract Sparse convex clustering is to group observations and conduct variable selection simultaneously in the framework of clustering. Although a weighted $$L_1$$ L 1 norm usually employed for regularization term sparse clustering, its use increases dependence on data...