Measurements, Models, Systems and Design

531 s.

Macrostate Data Clustering

We develop an effective nonhierarchical data clustering method using an analogy to the dynamic coarse graining of a stochastic system. Analyzing the eigensystem of an interitem transition matrix identifies fuzzy clusters corresponding to the metastable macroscopic states (macrostates) of a diffusive system. A "minimum uncertainty criterion" determines the linear transformation from eigenvectors to cluster-defining window functions. Eigenspectrum gap and cluster certainty conditions identify the proper number of clusters. The physically motivated fuzzy representation and associated uncertainty analysis distinguishes macrostate clustering from spectral partitioning methods. Macrostate data clustering solves a variety of test cases that challenge other methods.Comment: keywords: cluster analysis, clustering, pattern recognition, spectral graph theory, dynamic eigenvectors, machine learning, macrostates, classificatio

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

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

An efficient and versatile approach to trust and reputation using hierarchical Bayesian modelling

In many dynamic open systems, autonomous agents must interact with one another to achieve their goals. Such agents may be self-interested and, when trusted to perform an action, may betray that trust by not performing the action as required. Due to the scale and dynamism of these systems, agents will often need to interact with other agents with which they have little or no past experience. Each agent must therefore be capable of assessing and identifying reliable interaction partners, even if it has no personal experience with them. To this end, we present HABIT, a Hierarchical And Bayesian Inferred Trust model for assessing how much an agent should trust its peers based on direct and third party information. This model is robust in environments in which third party information is malicious, noisy, or otherwise inaccurate. Although existing approaches claim to achieve this, most rely on heuristics with little theoretical foundation. In contrast, HABIT is based exclusively on principled statistical techniques: it can cope with multiple discrete or continuous aspects of trustee behaviour; it does not restrict agents to using a single shared representation of behaviour; it can improve assessment by using any observed correlation between the behaviour of similar trustees or information sources; and it provides a pragmatic solution to the whitewasher problem (in which unreliable agents assume a new identity to avoid bad reputation). In this paper, we describe the theoretical aspects of HABIT, and present experimental results that demonstrate its ability to predict agent behaviour in both a simulated environment, and one based on data from a real-world webserver domain. In particular, these experiments show that HABIT can predict trustee performance based on multiple representations of behaviour, and is up to twice as accurate as BLADE, an existing state-of-the-art trust model that is both statistically principled and has been previously shown to outperform a number of other probabilistic trust models

Observer-based H∞ control for systems with repeated scalar nonlinearities and multiple packet losses

This paper is concerned with the H∞ control problem for a class of systems with repeated scalar nonlinearities and multiple missing measurements. The nonlinear system is described by a discrete-time state equation involving a repeated scalar nonlinearity, which typically appears in recurrent neural networks. The measurement missing phenomenon is assumed to occur, simultaneously, in the communication channels from the sensor to the controller and from the controller to the actuator, where the missing probability for each sensor/actuator is governed by an individual random variable satisfying a certain probabilistic distribution in the interval [0 1]. Attention is focused on the analysis and design of an observer-based feedback controller such that the closed-loop control system is stochastically stable and preserves a guaranteed H∞ performance. Sufficient conditions are obtained for the existence of admissible controllers. It is shown that the controller design problem under consideration is solvable if certain linear matrix inequalities (LMIs) are feasible. Three examples are provided to illustrate the effectiveness of the developed theoretical result