Simultaneous Learning of Nonlinear Manifold and Dynamical Models for High-dimensional Time Series

The goal of this work is to learn a parsimonious and informative representation for high-dimensional time series. Conceptually, this comprises two distinct yet tightly coupled tasks: learning a low-dimensional manifold and modeling the dynamical process. These two tasks have a complementary relationship as the temporal constraints provide valuable neighborhood information for dimensionality reduction and conversely, the low-dimensional space allows dynamics to be learnt efficiently. Solving these two tasks simultaneously allows important information to be exchanged mutually. If nonlinear models are required to capture the rich complexity of time series, then the learning problem becomes harder as the nonlinearities in both tasks are coupled. The proposed solution approximates the nonlinear manifold and dynamics using piecewise linear models. The interactions among the linear models are captured in a graphical model. By exploiting the model structure, efficient inference and learning algorithms are obtained without oversimplifying the model of the underlying dynamical process. Evaluation of the proposed framework with competing approaches is conducted in three sets of experiments: dimensionality reduction and reconstruction using synthetic time series, video synthesis using a dynamic texture database, and human motion synthesis, classification and tracking on a benchmark data set. In all experiments, the proposed approach provides superior performance.National Science Foundation (IIS 0308213, IIS 0329009, CNS 0202067

Deep Markov Random Field for Image Modeling

Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic factors to capture local patterns. In this paper, we move beyond such limitations, and propose a novel MRF model that uses fully-connected neurons to express the complex interactions among pixels. Through theoretical analysis, we reveal an inherent connection between this model and recurrent neural networks, and thereon derive an approximated feed-forward network that couples multiple RNNs along opposite directions. This formulation combines the expressive power of deep neural networks and the cyclic dependency structure of MRF in a unified model, bringing the modeling capability to a new level. The feed-forward approximation also allows it to be efficiently learned from data. Experimental results on a variety of low-level vision tasks show notable improvement over state-of-the-arts.Comment: Accepted at ECCV 201

Time-delay neural network for continuous emotional dimension prediction from facial expression sequences

"(c) 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works."Automatic continuous affective state prediction from naturalistic facial expression is a very challenging research topic but very important in human-computer interaction. One of the main challenges is modeling the dynamics that characterize naturalistic expressions. In this paper, a novel two-stage automatic system is proposed to continuously predict affective dimension values from facial expression videos. In the first stage, traditional regression methods are used to classify each individual video frame, while in the second stage, a Time-Delay Neural Network (TDNN) is proposed to model the temporal relationships between consecutive predictions. The two-stage approach separates the emotional state dynamics modeling from an individual emotional state prediction step based on input features. In doing so, the temporal information used by the TDNN is not biased by the high variability between features of consecutive frames and allows the network to more easily exploit the slow changing dynamics between emotional states. The system was fully tested and evaluated on three different facial expression video datasets. Our experimental results demonstrate that the use of a two-stage approach combined with the TDNN to take into account previously classified frames significantly improves the overall performance of continuous emotional state estimation in naturalistic facial expressions. The proposed approach has won the affect recognition sub-challenge of the third international Audio/Visual Emotion Recognition Challenge (AVEC2013)1