Polzin, Robert and Klebanov, Ilja and Nüsken, Nikolas and Koltai, Péter
(2023)
*Nonnegative matrix factorization for coherent set identification by direct low rank maximum likelihood estimation.*
arXiv
.
pp. 1-43.
(Unpublished)

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Official URL: http://arxiv.org/abs/2308.07663

## Abstract

We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the action of a stochastic matrix in a way maximally distinguishable from other groups. The second one is a low rank factorization approach for stochastic matrices, called Direct Bayesian Model Reduction (DBMR), which estimates the low rank factors directly from observed data. We show that DBMR results in a low rank model that is a projection of the full model, and exploit this insight to infer bounds on a quantitative measure of coherence within the reduced model. Both approaches can be formulated as optimization problems, and we also prove a bound between their respective objectives. On a broader scope, this work relates the two classical loss functions of nonnegative matrix factorization, namely the Frobenius norm and the generalized Kullback–Leibler divergence, and suggests new links between likelihood- based and projection-based estimation of probabilistic models.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics |

ID Code: | 3021 |

Deposited By: | Monika Drueck |

Deposited On: | 17 Aug 2023 11:15 |

Last Modified: | 21 Feb 2024 11:08 |

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