Generalized Low-Rank Approximations

We study the frequent problem of approximating a target matrix with a matrix of lower rank. We provide a simple and efficient (EM) algorithm for solving {\\em weighted} low rank approximation problems, which, unlike simple matrix factorization problems, do not admit a closed form solution in general. We analyze, in addition, the nature of locally optimal solutions that arise in this context, demonstrate the utility of accommodating the weights in reconstructing the underlying low rank representation, and extend the formulation to non-Gaussian noise models such as classification (collaborative filtering).

Context-Based Vision System for Place and Object Recognition

While navigating in an environment, a vision system has to be able to recognize where it is and what the main objects in the scene are. In this paper we present a context-based vision system for place and object recognition. The goal is to identify familiar locations (e.g., office 610, conference room 941, Main Street), to categorize new environments (office, corridor, street) and to use that information to provide contextual priors for object recognition (e.g., table, chair, car, computer). We present a low-dimensional global image representation that provides relevant information for place recognition and categorization, and how such contextual information introduces strong priors that simplify object recognition. We have trained the system to recognize over 60 locations (indoors and outdoors) and to suggest the presence and locations of more than 20 different object types. The algorithm has been integrated into a mobile system that provides real-time feedback to the user.

Activity Zones for Context-Aware Computing

Location is a primary cue in many context-aware computing systems, and is often represented as a global coordinate, room number, or Euclidean distance various landmarks. A user?s concept of location, however, is often defined in terms of regions in which common activities occur. We show how to partition a space into such regions based on patterns of observed user location and motion. These regions, which we call activity zones, represent regions of similar user activity, and can be used to trigger application actions, retrieve information based on previous context, and present information to users. We suggest that context-aware applications can benefit from a location representation learned from observing users. We describe an implementation of our system and present two example applications whose behavior is controlled by users? entry, exit, and presence in the zones.

Roles of Knowledge in Motor Learning

The goal of this thesis is to apply the computational approach to motor learning, i.e., describe the constraints that enable performance improvement with experience and also the constraints that must be satisfied by a motor learning system, describe what is being computed in order to achieve learning, and why it is being computed. The particular tasks used to assess motor learning are loaded and unloaded free arm movement, and the thesis includes work on rigid body load estimation, arm model estimation, optimal filtering for model parameter estimation, and trajectory learning from practice. Learning algorithms have been developed and implemented in the context of robot arm control. The thesis demonstrates some of the roles of knowledge in learning. Powerful generalizations can be made on the basis of knowledge of system structure, as is demonstrated in the load and arm model estimation algorithms. Improving the performance of parameter estimation algorithms used in learning involves knowledge of the measurement noise characteristics, as is shown in the derivation of optimal filters. Using trajectory errors to correct commands requires knowledge of how command errors are transformed into performance errors, i.e., an accurate model of the dynamics of the controlled system, as is demonstrated in the trajectory learning work. The performance demonstrated by the algorithms developed in this thesis should be compared with algorithms that use less knowledge, such as table based schemes to learn arm dynamics, previous single trajectory learning algorithms, and much of traditional adaptive control.

A Multiple-Context Equality-Based Reasoning System

Expert systems are too slow. This work attacks that problem by speeding up a useful system component that remembers facts and tracks down simple consequences. The redesigned component can assimilate new facts more quickly because it uses a compact, grammar-based internal representation to deal with whole classes of equivalent expressions at once. It can support faster hypothetical reasoning because it remembers the consequences of several assumption sets at once. The new design is targeted for situations in which many of the stored facts are equalities. The deductive machinery considered here supplements stored premises with simple new conclusions. The stored premises include permanently asserted facts and temporarily adopted assumptions. The new conclusions are derived by substituting equals for equals and using the properties of the logical connectives AND, Or, and NOT. The deductive system provides supporting premises for its derived conclusions. Reasoning that involves quantifiers is beyond the scope of its limited and automatic operation. The expert system of which the reasoning system is a component is expected to be responsible for overall control of reasoning.