6 research outputs found
Action classification using a discriminative non-parametric hidden Markov model
We classify human actions occurring in videos, using the skeletal joint positions extracted from a depth image sequence as features. Each action class is represented by a non-parametric Hidden Markov Model (NP-HMM) and the model parameters are learnt in a discriminative way. Specifically, we use a Bayesian framework based on Hierarchical Dirichlet Process (HDP) to automatically infer the cardinality of hidden states and formulate a discriminative function based on distance between Gaussian distributions to improve classification performance. We use elliptical slice sampling to efficiently sample parameters from the complex posterior distribution induced by our discriminative likelihood function. We illustrate our classification results for action class models trained using this technique
Action classification using a discriminative multilevel HDP-HMM
We classify human actions occurring in depth image sequences using features based on skeletal joint positions. The action classes are represented by a multi-level Hierarchical Dirichlet Process – Hidden Markov Model (HDP-HMM). The non-parametric HDP-HMM allows the inference of hidden states automatically from training data. The model parameters of each class are formulated as transformations from a shared base distribution, thus promoting the use of unlabelled examples during training and borrowing information across action classes. Further, the parameters are learnt in a discriminative way. We use a normalized gamma process representation of HDP and margin based likelihood functions for this purpose. We sample parameters from the complex posterior distribution induced by our discriminative likelihood function using elliptical slice sampling. Experiments with two different datasets show that action class models learnt using our technique produce good classification results
Non-Parametric and Regularized Dynamical Wasserstein Barycenters for Time-Series Analysis
We consider probabilistic time-series models for systems that gradually
transition among a finite number of states. We are particularly motivated by
applications such as human activity analysis where the observed time-series
contains segments representing distinct activities such as running or walking
as well as segments characterized by continuous transition among these states.
Accordingly, the dynamical Wasserstein barycenter (DWB) model introduced in
Cheng et al. in 2021 [1] associates with each state, which we call a pure
state, its own probability distribution, and models these continuous
transitions with the dynamics of the barycentric weights that combine the pure
state distributions via the Wasserstein barycenter. Here, focusing on the
univariate case where Wasserstein distances and barycenters can be computed in
closed form, we extend [1] by discussing two challenges associated with
learning a DWB model and two improvements. First, we highlight the issue of
uniqueness in identifying the model parameters. Secondly, we discuss the
challenge of estimating a dynamically evolving distribution given a limited
number of samples. The uncertainty associated with this estimation may cause a
model's learned dynamics to not reflect the gradual transitions characteristic
of the system. The first improvement introduces a regularization framework that
addresses this uncertainty by imposing temporal smoothness on the dynamics of
the barycentric weights while leveraging the understanding of the
non-uniqueness of the problem. This is done without defining an entire
stochastic model for the dynamics of the system as in [1]. Our second
improvement lifts the Gaussian assumption on the pure states distributions in
[1] by proposing a quantile-based non-parametric representation. We pose model
estimation in a variational framework and propose a finite approximation to the
infinite dimensional problem