Temporal and Spatial Data Mining with Second-Order Hidden Models

In the frame of designing a knowledge discovery system, we have developed stochastic models based on high-order hidden Markov models. These models are capable to map sequences of data into a Markov chain in which the transitions between the states depend on the \texttt{n} previous states according to the order of the model. We study the process of achieving information extraction fromspatial and temporal data by means of an unsupervised classification. We use therefore a French national database related to the land use of a region, named Teruti, which describes the land use both in the spatial and temporal domain. Land-use categories (wheat, corn, forest, ...) are logged every year on each site regularly spaced in the region. They constitute a temporal sequence of images in which we look for spatial and temporal dependencies. The temporal segmentation of the data is done by means of a second-order Hidden Markov Model (\hmmd) that appears to have very good capabilities to locate stationary segments, as shown in our previous work in speech recognition. Thespatial classification is performed by defining a fractal scanning ofthe images with the help of a Hilbert-Peano curve that introduces atotal order on the sites, preserving the relation ofneighborhood between the sites. We show that the \hmmd performs aclassification that is meaningful for the agronomists.Spatial and temporal classification may be achieved simultaneously by means of a 2 levels \hmmd that measures the \aposteriori probability to map a temporal sequence of images onto a set of hidden classes

ToyArchitecture: Unsupervised Learning of Interpretable Models of the World

Research in Artificial Intelligence (AI) has focused mostly on two extremes: either on small improvements in narrow AI domains, or on universal theoretical frameworks which are usually uncomputable, incompatible with theories of biological intelligence, or lack practical implementations. The goal of this work is to combine the main advantages of the two: to follow a big picture view, while providing a particular theory and its implementation. In contrast with purely theoretical approaches, the resulting architecture should be usable in realistic settings, but also form the core of a framework containing all the basic mechanisms, into which it should be easier to integrate additional required functionality. In this paper, we present a novel, purposely simple, and interpretable hierarchical architecture which combines multiple different mechanisms into one system: unsupervised learning of a model of the world, learning the influence of one's own actions on the world, model-based reinforcement learning, hierarchical planning and plan execution, and symbolic/sub-symbolic integration in general. The learned model is stored in the form of hierarchical representations with the following properties: 1) they are increasingly more abstract, but can retain details when needed, and 2) they are easy to manipulate in their local and symbolic-like form, thus also allowing one to observe the learning process at each level of abstraction. On all levels of the system, the representation of the data can be interpreted in both a symbolic and a sub-symbolic manner. This enables the architecture to learn efficiently using sub-symbolic methods and to employ symbolic inference.Comment: Revision: changed the pdftitl

The Origins of Computational Mechanics: A Brief Intellectual History and Several Clarifications

The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to identify strange attractors as the mechanism driving weak fluid turbulence via the method of reconstructing attractor geometry from measurement time series and in the mid-1980s to estimate equations of motion directly from complex time series. In providing a mathematical and operational definition of structure it addressed weaknesses of these early approaches to discovering patterns in natural systems. Since then, computational mechanics has led to a range of results from theoretical physics and nonlinear mathematics to diverse applications---from closed-form analysis of Markov and non-Markov stochastic processes that are ergodic or nonergodic and their measures of information and intrinsic computation to complex materials and deterministic chaos and intelligence in Maxwellian demons to quantum compression of classical processes and the evolution of computation and language. This brief review clarifies several misunderstandings and addresses concerns recently raised regarding early works in the field (1980s). We show that misguided evaluations of the contributions of computational mechanics are groundless and stem from a lack of familiarity with its basic goals and from a failure to consider its historical context. For all practical purposes, its modern methods and results largely supersede the early works. This not only renders recent criticism moot and shows the solid ground on which computational mechanics stands but, most importantly, shows the significant progress achieved over three decades and points to the many intriguing and outstanding challenges in understanding the computational nature of complex dynamic systems.Comment: 11 pages, 123 citations; http://csc.ucdavis.edu/~cmg/compmech/pubs/cmr.ht

Chaotic Crystallography: How the physics of information reveals structural order in materials

We review recent progress in applying information- and computation-theoretic measures to describe material structure that transcends previous methods based on exact geometric symmetries. We discuss the necessary theoretical background for this new toolset and show how the new techniques detect and describe novel material properties. We discuss how the approach relates to well known crystallographic practice and examine how it provides novel interpretations of familiar structures. Throughout, we concentrate on disordered materials that, while important, have received less attention both theoretically and experimentally than those with either periodic or aperiodic order.Comment: 9 pages, two figures, 1 table; http://csc.ucdavis.edu/~cmg/compmech/pubs/ChemOpinion.ht

A genetic approach to Markovian characterisation of H.264 scalable video

We propose an algorithm for multivariate Markovian characterisation of H.264/SVC scalable video traces at the sub-GoP (Group of Pictures) level. A genetic algorithm yields Markov models with limited state space that accurately capture temporal and inter-layer correlation. Key to our approach is the covariance-based fitness function. In comparison with the classical Expectation Maximisation algorithm, ours is capable of matching the second order statistics more accurately at the cost of less accuracy in matching the histograms of the trace. Moreover, a simulation study shows that our approach outperforms Expectation Maximisation in predicting performance of video streaming in various networking scenarios