SOTXTSTREAM: Density-based self-organizing clustering of text streams

A streaming data clustering algorithm is presented building upon the density-based selforganizing stream clustering algorithm SOSTREAM. Many density-based clustering algorithms are limited by their inability to identify clusters with heterogeneous density. SOSTREAM addresses this limitation through the use of local (nearest neighbor-based) density determinations. Additionally, many stream clustering algorithms use a two-phase clustering approach. In the first phase, a micro-clustering solution is maintained online, while in the second phase, the micro-clustering solution is clustered offline to produce a macro solution. By performing self-organization techniques on micro-clusters in the online phase, SOSTREAM is able to maintain a macro clustering solution in a single phase. Leveraging concepts from SOSTREAM, a new density-based self-organizing text stream clustering algorithm, SOTXTSTREAM, is presented that addresses several shortcomings of SOSTREAM. Gains in clustering performance of this new algorithm are demonstrated on several real-world text stream datasets

Classification methods for Hilbert data based on surrogate density

An unsupervised and a supervised classification approaches for Hilbert random curves are studied. Both rest on the use of a surrogate of the probability density which is defined, in a distribution-free mixture context, from an asymptotic factorization of the small-ball probability. That surrogate density is estimated by a kernel approach from the principal components of the data. The focus is on the illustration of the classification algorithms and the computational implications, with particular attention to the tuning of the parameters involved. Some asymptotic results are sketched. Applications on simulated and real datasets show how the proposed methods work.Comment: 33 pages, 11 figures, 6 table

Consistency, breakdown robustness, and algorithms for robust improper maximum likelihood clustering

The robust improper maximum likelihood estimator (RIMLE) is a new method for robust multivariate clustering finding approximately Gaussian clusters. It maximizes a pseudo-likelihood defined by adding a component with improper constant density for accommodating outliers to a Gaussian mixture. A special case of the RIMLE is MLE for multivariate finite Gaussian mixture models. In this paper we treat existence, consistency, and breakdown theory for the RIMLE comprehensively. RIMLE's existence is proved under non-smooth covariance matrix constraints. It is shown that these can be implemented via a computationally feasible Expectation-Conditional Maximization algorithm.Comment: The title of this paper was originally: "A consistent and breakdown robust model-based clustering method

A Distributed and Approximated Nearest Neighbors Algorithm for an Efficient Large Scale Mean Shift Clustering

In this paper we target the class of modal clustering methods where clusters are defined in terms of the local modes of the probability density function which generates the data. The most well-known modal clustering method is the k-means clustering. Mean Shift clustering is a generalization of the k-means clustering which computes arbitrarily shaped clusters as defined as the basins of attraction to the local modes created by the density gradient ascent paths. Despite its potential, the Mean Shift approach is a computationally expensive method for unsupervised learning. Thus, we introduce two contributions aiming to provide clustering algorithms with a linear time complexity, as opposed to the quadratic time complexity for the exact Mean Shift clustering. Firstly we propose a scalable procedure to approximate the density gradient ascent. Second, our proposed scalable cluster labeling technique is presented. Both propositions are based on Locality Sensitive Hashing (LSH) to approximate nearest neighbors. These two techniques may be used for moderate sized datasets. Furthermore, we show that using our proposed approximations of the density gradient ascent as a pre-processing step in other clustering methods can also improve dedicated classification metrics. For the latter, a distributed implementation, written for the Spark/Scala ecosystem is proposed. For all these considered clustering methods, we present experimental results illustrating their labeling accuracy and their potential to solve concrete problems.Comment: Algorithms are available at https://github.com/Clustering4Ever/Clustering4Eve

Laplacian Mixture Modeling for Network Analysis and Unsupervised Learning on Graphs

Laplacian mixture models identify overlapping regions of influence in unlabeled graph and network data in a scalable and computationally efficient way, yielding useful low-dimensional representations. By combining Laplacian eigenspace and finite mixture modeling methods, they provide probabilistic or fuzzy dimensionality reductions or domain decompositions for a variety of input data types, including mixture distributions, feature vectors, and graphs or networks. Provable optimal recovery using the algorithm is analytically shown for a nontrivial class of cluster graphs. Heuristic approximations for scalable high-performance implementations are described and empirically tested. Connections to PageRank and community detection in network analysis demonstrate the wide applicability of this approach. The origins of fuzzy spectral methods, beginning with generalized heat or diffusion equations in physics, are reviewed and summarized. Comparisons to other dimensionality reduction and clustering methods for challenging unsupervised machine learning problems are also discussed.Comment: 13 figures, 35 reference