Mining Naturally Smooth Evolution of Clusters from Dynamic Data

Abstract

Many clustering algorithms have been proposed to partition a set of static data points into groups. In this paper, we consider an evolutionary clustering problem where the input data points may move, disappeare, and emerge. Generally, these changes should result in a smooth evolution of the clusters. Mining this naturally smooth evolution is valuable for providing an aggregated view of the numerous individual behaviors.We solve this novel and generalized form of clustering problem by converting it into a Bayesian learning problem. Analogous to that the EM clustering algorithm clusters static data points by learning a Gaussian mixture model, our method mines the evolution of clusters from dynamic data points by learning a hidden semi-Markov model (HSMM). By utilizing characteristics of the evolutionary clustering problem, we derive a new unsupervised learning algorithm which is much more efficient than the algorithms used to learn traditional variable-duration HSMMs. Because the HSMM models the probabilistic relationship between the dynamic data set and corresponding evolving clusters, we can interpret the learned parameters as the evolving clusters intuitively using the Viterbi filtering technique. Because learning an HSMM is in fact learning an optimal Viterbi filter, the learned cluster evolutions are smooth and fit well with the data. We demonstrate the effectiveness of this method by experiments on both synthetic data and real data.

Adaptive evolutionary clustering

“…Finally, there has also been recent interest in model-based evolutionary clustering. In addition to the aforementioned method involving mixtures of exponential families (Zhang et al, 2009), methods have also been proposed using semi-Markov models (Wang et al, 2007), Dirichlet process mixtures (DPMs) (Ahmed and Xing, 2008;Xu et al, 2008b), hierarchical DPMs (Xu et al, 2008b,a;Zhang et al, 2010), and smooth plaid models (Mankad et al, 2011). For these methods, the temporal evolution is controlled by hyperparameters that can be estimated in some cases.…”

Contrast and change mining

“…A first, formally sound solution to the problem of finding a temporally coherent sequence of cluster sets was proposed by Wang et al 81 Inspired by the EM (Expectation Maximisation) algorithm they formulated the problem as a generalized form of a clustering problem based on Bayesian methods. Analogous to how the EM algorithm clusters data points by learning a Gaussian mixture model, their approach produces a temporally coherent sequence of cluster sets by learning a hidden semi-Markov model (HSMM).…”

Streamed Sampling on Dynamic data as Support for Classification Model

“…Data mining task on this kind of data have to be done continuously. Several researches have done dynamic data mining [1][2][3][4][5][6][7][8][9]. In short conclusion, they all use sampling method.…”

“…There is a relation between [10][11][12][13][14][15]. This issue was not touched in the previous researches [1][2][3][4][5][6][7][8][9]. Even though random sampling method can make class distribution on sample not the same as on database.…”