English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We propose a framework, named Aggregated Wasserstein, for computing adissimilarity measure or distance between two Hidden Markov Models with stateconditional distributions being Gaussian. For such HMMs, the marginaldistribution at any time position follows a Gaussian mixture distribution, afact exploited to softly match, aka register, the states in two HMMs. We referto such HMMs as Gaussian mixture model-HMM (GMM-HMM). The registration ofstates is inspired by the intrinsic relationship of optimal transport and theWasserstein metric between distributions. Specifically, the components of themarginal GMMs are matched by solving an optimal transport problem where thecost between components is the Wasserstein metric for Gaussian distributions.The solution of the optimization problem is a fast approximation to theWasserstein metric between two GMMs. The new Aggregated Wasserstein distance isa semi-metric and can be computed without generating Monte Carlo samples. It isinvariant to relabeling or permutation of states. The distance is definedmeaningfully even for two HMMs that are estimated from data of differentdimensionality, a situation that can arise due to missing variables. Thisdistance quantifies the dissimilarity of GMM-HMMs by measuring both thedifference between the two marginal GMMs and that between the two transitionmatrices. Our new distance is tested on tasks of retrieval, classification, andt-SNE visualization of time series. Experiments on both synthetic and real datahave demonstrated its advantages in terms of accuracy as well as efficiency incomparison with existing distances based on the Kullback-Leibler divergence.

Aggregated Wasserstein Metric and State Registration for Hidden Markov Models