Graham Taylor's Homepage

Current Research Interests

Generative Models for Time-Series Analysis

My PhD research is situated within the field of statistical machine learning. In collaboration with my supervisors, Geoff Hinton and Sam Roweis, I have been developing rich probabilistic models built from real-world data. In the first year of my PhD, I looked at two ways of learning invariances in images. In my second year, I became interested in models for high-dimensional time series, and the subtle differences from models of static data.

Simple statistical models, such as autoregressive or Markov (n-gram) models are limited in the structure that they can represent, as their definition does not permit the concept of memory or “hidden” state. The current observation is a function only of the past few observations, and to model any long-range dependencies, the model must have a prohibitively large number of parameters. Hidden Markov models (HMMs) introduce a hidden state which, in theory, can model arbitrarily long dependencies but in fact, is extremely limited. The HMM can have an arbitrary non-linear relationship between hidden state and observable variables, but must capture the whole history of the time series in a K-state multinomial variable. This leads to an exponential explosion in the number of state variables and thus parameters. State-space models (also known as dynamical systems) have a rich, continuous state, but inference and learning are exact and tractable only if a linear relationship is assumed between the hidden state and observations.

In the third year of my PhD, we introduced a powerful generative model for time series, which was trained on human motion (mocap) data. Given its high-dimensional nature and long-range dependencies, I believe that mocap data is ideal for both studying the limitations of such a time-series model, and demonstrating its effectiveness. Our model has a rich, distributed hidden state and can model non-linear dynamics. It uses binary latent variables which are symmetrically connected to real-valued “visible” variables that represent joint angles. The latent variables at each time step receive directed connections from the latent variables at one or two previous time-steps. The undirected observation model makes online inference efficient and allows us to use a simple approximate learning procedure. Trained in this way, our architecture can find a single set of parameters that captures several different kinds of motion.

We have already demonstrated that our model can synthesize various motion sequences and that data lost during the motion capture process can be filled in online. This has applications to animation and motion tracking. Currently I am collaborating with Niko Troje (Psychology, Queen’s University) to study invariances in human motion across different actions. Later this year, I hope to collaborate with Leonid Sigal, a post-doctoral researcher in the computer vision group, to apply our model as a prior for motion tracking. Over the longer term, I would like to develop and experiment with a new model that has simpler dynamics (similar to but more powerful than a HMM) and a non-linear static model constraining pose at each time step. The advantage of this model is that we can perform exact smoothing (inferring the whole hidden state sequence, given the observed sequence) whereas in the previous model, hidden state was only predicted from past and current observations. Additionally, I am interested in extending these models to utilize directional units, where angular data is modeled as a circular variable, and not a real-valued unconstrained variable. The latter method requires a pre-processing step to transform the rotational data to a suitable representation.

Previous Research Projects

Observer-dependent Image Enhancement

Traditional image enhancement algorithms do not account for the subjective evaluation of human observers. Objective image metrics have been used to ascertain the quality of processed images, but the metric usually does not correlate with the human perception of the image. This distinction between objectivity and subjectivity is the first major problem in human-machine interaction. The second is the fact that different people judge image quality quite differently. Observer-dependent image enhancement approaches these problems with the tools of image processing, machine intelligence, pattern analysis, human physiology and psychology.

The future promises increased reliance on digital images. Many experts may be required to gather information from a particular image, but each may need to spend time manipulating image enhancement parameters to bring the image to a personal acceptable level. An example of this is the use of medical images for diagnosis. Several experts may collaborate on an analysis using a digital image of a patient, but each may require the image to be brought to a different level of detail, contrast, sharpness, etc. An automated observer-dependent image enhancement process would learn to manipulate each image, based on the current state of the image in a way ideal for each independent expert. Such a method would benefit the public by saving time and improving the resulting diagnosis.

Reinforced Contrast Adaptation

Every observer has a different opinion of an ideally enhanced image. Automated Techniques for obtaining a subjectively ideal image enhancement are desirable, but currently do not exist. In this research, we have demonstrated that Reinforcement Learning is a potential method for solving this problem. We have developed an agent that uses the Q-learning algorithm. The agent modifies contrast of an image with a simple linear point transformation based on the histogram of the image and feedback it receives from human observers. The results of several testing sessions have indicated that the agent performs well within a limited number of iterations.

Differential Hysteresis Processing

Differential Hysteresis Processing (DHP) is a powerful algorithm for enhancing images such that they are pleasant to the human eye. This algorithm can emphasize certain levels of contrast to provide details that would normally not be noticeable to an observer. Implementation of the algorithm on a PC workstation requires a tremendous amount of processing time. We have explored a variety of methods to decrease the processing time associated with DHP. We first examined an alternative 2-D extension of the hysteresis algorithm. We then introduced two reliable pre-processing techniques, Wavelet compression and Edge-detection which were used to reduce the computational time associated with DHP. The latter two methods were evaluated both subjectively and objectively.

Clinical Data Warehousing for Obstetrics

This work concentrated on the development of a Data Warehouse for the OB/GYN department at St. Joseph's Health Centre, London. Dimensional modeling techniques were used to create a centralized data store to facilitate
1) access to local, regional, provincial and national information on maternal and fetal characteristics, fetal outcomes and the use of obstetrical interventions; and
2) the coordination of the information gathering efforts of the East, Southeast and Southwest Ontario regions.

The warehouse eventually will permit sophisticated research through through data mining.

Hurdle Preflight in Biomechanics

Attempts to increase dive height by introducing a period of flight in the final approach step preceding the hurdle of dives from forward and reverse groups were investigated. One study involved 11 collegiate-level divers experienced in both traditional and hurdle preflight techniques. In a second study, dives executed by 9 national-level women were compared. Dives with a hurdle preflight had shorter final approach steps and greater hurdle flight durations. Flight time differences in favor of hurdle preflight techniques diminished from final approach step through hurdle flight to dive flight. Although the collegiate-level divers had longer dive flight times when using a hurdle preflight, it was suggested that the costs of these techniques may outweigh their potential benefits.

Miller, D.I., Zecevic, A., and Taylor, G.W. (2002) Hurdle Preflight in Springboard Diving: A Case of Diminishing Returns. Research Quarterly for Exercise and Sport. 73: 134-145