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

Gravitational Clustering: A Simple, Robust and Adaptive Approach for Distributed Networks

Distributed signal processing for wireless sensor networks enables that different devices cooperate to solve different signal processing tasks. A crucial first step is to answer the question: who observes what? Recently, several distributed algorithms have been proposed, which frame the signal/object labelling problem in terms of cluster analysis after extracting source-specific features, however, the number of clusters is assumed to be known. We propose a new method called Gravitational Clustering (GC) to adaptively estimate the time-varying number of clusters based on a set of feature vectors. The key idea is to exploit the physical principle of gravitational force between mass units: streaming-in feature vectors are considered as mass units of fixed position in the feature space, around which mobile mass units are injected at each time instant. The cluster enumeration exploits the fact that the highest attraction on the mobile mass units is exerted by regions with a high density of feature vectors, i.e., gravitational clusters. By sharing estimates among neighboring nodes via a diffusion-adaptation scheme, cooperative and distributed cluster enumeration is achieved. Numerical experiments concerning robustness against outliers, convergence and computational complexity are conducted. The application in a distributed cooperative multi-view camera network illustrates the applicability to real-world problems.Comment: 12 pages, 9 figure

A fuzzy probabilistic inference methodology for constrained 3D human motion classification

Enormous uncertainties in unconstrained human motions lead to a fundamental challenge that many recognising algorithms have to face in practice: efficient and correct motion recognition is a demanding task, especially when human kinematic motions are subject to variations of execution in the spatial and temporal domains, heavily overlap with each other,and are occluded. Due to the lack of a good solution to these problems, many existing methods tend to be either effective but computationally intensive or efficient but vulnerable to misclassification. This thesis presents a novel inference engine for recognising occluded 3D human motion assisted by the recognition context. First, uncertainties are wrapped into a fuzzy membership function via a novel method called Fuzzy Quantile Generation which employs metrics derived from the probabilistic quantile function. Then, time-dependent and context-aware rules are produced via a genetic programming to smooth the qualitative outputs represented by fuzzy membership functions. Finally, occlusion in motion recognition is taken care of by introducing new procedures for feature selection and feature reconstruction. Experimental results demonstrate the effectiveness of the proposed framework on motion capture data from real boxers in terms of fuzzy membership generation, context-aware rule generation, and motion occlusion. Future work might involve the extension of Fuzzy Quantile Generation in order to automate the choice of a probability distribution, the enhancement of temporal pattern recognition with probabilistic paradigms, the optimisation of the occlusion module, and the adaptation of the present framework to different application domains.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Integrated bio-search approaches with multi-objective algorithms for optimization and classification problem

Optimal selection of features is very difficult and crucial to achieve, particularly for the task of classification. It is due to the traditional method of selecting features that function independently and generated the collection of irrelevant features, which therefore affects the quality of the accuracy of the classification. The goal of this paper is to leverage the potential of bio-inspired search algorithms, together with wrapper, in optimizing multi-objective algorithms, namely ENORA and NSGA-II to generate an optimal set of features. The main steps are to idealize the combination of ENORA and NSGA-II with suitable bio-search algorithms where multiple subset generation has been implemented. The next step is to validate the optimum feature set by conducting a subset evaluation. Eight (8) comparison datasets of various sizes have been deliberately selected to be checked. Results shown that the ideal combination of multi-objective algorithms, namely ENORA and NSGA-II, with the selected bio-inspired search algorithm is promising to achieve a better optimal solution (i.e. a best features with higher classification accuracy) for the selected datasets. This discovery implies that the ability of bio-inspired wrapper/filtered system algorithms will boost the efficiency of ENORA and NSGA-II for the task of selecting and classifying features