Partially Markov models and unsupervised segmentation of semi-Markov chains hidden with long dependence noise

Multiclass classification problems such as document classification, medical diagnosis or scene classification are very challenging to address due to similarities between mutual classes. The use of reliable tools is necessary to get good classification results. This paper addresses the scene classification problem using objects as attributes. The process of classification is modeled by a famous mathematical tool: The Hidden Markov Models. We introduce suitable relations that scale the parameters of the Hidden Markov Model into variables of scene classification. The construction of Hidden Markov Chains is supported with weight measures and sorting functions. Lastly, inference algorithms extract most suitable scene categories from the Discrete Markov Chain. A parallelism approach constructs several Discrete Markov Chains in order to improve the accuracy of the classification process. We provide numerous tests on different datasets and compare classification accuracies with some state of the art methods. The proposed approach distinguishes itself by outperforming the other.

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Markov Chains and Hidden Markov Models

Introduction to Mathematical Methods in Bioinformatics ◽

10.1007/978-3-540-48426-4_3 ◽

2006 ◽

pp. 25-73

Keyword(s):

Markov Chains ◽

Hidden Markov Models ◽

Markov Models ◽

Hidden Markov

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Introducing User-Prescribed Constraints in Markov Chains for Nonlinear Dimensionality Reduction

Neural Computation ◽

10.1162/neco_a_01184 ◽

2019 ◽

Vol 31 (5) ◽

pp. 980-997 ◽

Cited By ~ 1

Author(s):

Purushottam D. Dixit

Keyword(s):

Markov Chain ◽

Markov Chains ◽

Dimensionality Reduction ◽

Markov Models ◽

Transition Probabilities ◽

Central Component ◽

Nonlinear Dimensionality Reduction ◽

Entropy Maximization ◽

Symmetric Kernel ◽

Data Points

Stochastic kernel-based dimensionality-reduction approaches have become popular in the past decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified by the kernel through row normalization. However, in many cases, it is desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Unfortunately, no systematic framework exists to impose such user-defined constraints. Here, based on our previous work on inference of Markov models, we introduce a path entropy maximization based approach to derive the transition probabilities of Markov chains using a kernel and additional user-specified constraints. We illustrate the usefulness of these Markov chains with examples.

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