Online Spectral Clustering on Network Streams

Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirements certainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the parallelization of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be predetermined. The third challenge is the very limited existing work. In addition, there exists multiple limitations in the existing method, such as computational inefficiency on large similarity changes, the lack of sound theoretical basis, and the lack of effective way to handle accumulated approximate errors and large data variations over time. In this thesis, we proposed a new online spectral graph clustering approach with a family of three novel spectrum approximation algorithms. Our algorithms incrementally update the eigenpairs in an online manner to improve the computational performance. Our approaches outperformed the existing method in computational efficiency and scalability while retaining competitive or even better clustering accuracy. We derived our spectrum approximation techniques GEPT and EEPT through formal theoretical analysis. The well established matrix perturbation theory forms a solid theoretic foundation for our online clustering method. We facilitated our clustering method with a new metric to track accumulated approximation errors and measure the short-term temporal variation. The metric not only provides a balance between computational efficiency and clustering accuracy, but also offers a useful tool to adapt the online algorithm to the condition of unexpected drastic noise. In addition, we discussed our preliminary work on approximate graph mining with evolutionary process, non-stationary Bayesian Network structure learning from non-stationary time series data, and Bayesian Network structure learning with text priors imposed by non-parametric hierarchical topic modeling

A Minimum Relative Entropy Principle for Learning and Acting

This paper proposes a method to construct an adaptive agent that is universal with respect to a given class of experts, where each expert is an agent that has been designed specifically for a particular environment. This adaptive control problem is formalized as the problem of minimizing the relative entropy of the adaptive agent from the expert that is most suitable for the unknown environment. If the agent is a passive observer, then the optimal solution is the well-known Bayesian predictor. However, if the agent is active, then its past actions need to be treated as causal interventions on the I/O stream rather than normal probability conditions. Here it is shown that the solution to this new variational problem is given by a stochastic controller called the Bayesian control rule, which implements adaptive behavior as a mixture of experts. Furthermore, it is shown that under mild assumptions, the Bayesian control rule converges to the control law of the most suitable expert.Comment: 36 pages, 11 figure

Rejection-oriented learning without complete class information

Machine Learning is commonly used to support decision-making in numerous, diverse contexts. Its usefulness in this regard is unquestionable: there are complex systems built on the top of machine learning techniques whose descriptive and predictive capabilities go far beyond those of human beings. However, these systems still have limitations, whose analysis enable to estimate their applicability and confidence in various cases. This is interesting considering that abstention from the provision of a response is preferable to make a mistake in doing so. In the context of classification-like tasks, the indication of such inconclusive output is called rejection. The research which culminated in this thesis led to the conception, implementation and evaluation of rejection-oriented learning systems for two distinct tasks: open set recognition and data stream clustering. These system were derived from WiSARD artificial neural network, which had rejection modelling incorporated into its functioning. This text details and discuss such realizations. It also presents experimental results which allow assess the scientific and practical importance of the proposed state-of-the-art methodology.Aprendizado de Máquina é comumente usado para apoiar a tomada de decisão em numerosos e diversos contextos. Sua utilidade neste sentido é inquestionável: existem sistemas complexos baseados em técnicas de aprendizado de máquina cujas capacidades descritivas e preditivas vão muito além das dos seres humanos. Contudo, esses sistemas ainda possuem limitações, cuja análise permite estimar sua aplicabilidade e confiança em vários casos. Isto é interessante considerando que a abstenção da provisão de uma resposta é preferível a cometer um equívoco ao realizar tal ação. No contexto de classificação e tarefas similares, a indicação desse resultado inconclusivo é chamada de rejeição. A pesquisa que culminou nesta tese proporcionou a concepção, implementação e avaliação de sistemas de aprendizado orientados `a rejeição para duas tarefas distintas: reconhecimento em cenário abertos e agrupamento de dados em fluxo contínuo. Estes sistemas foram derivados da rede neural artificial WiSARD, que teve a modelagem de rejeição incorporada a seu funcionamento. Este texto detalha e discute tais realizações. Ele também apresenta resultados experimentais que permitem avaliar a importância científica e prática da metodologia de ponta proposta