Natural Object Categorization

This thesis addresses the problem of categorizing natural objects. To provide a criteria for categorization we propose that the purpose of a categorization is to support the inference of unobserved properties of objects from the observed properties. Because no such set of categories can be constructed in an arbitrary world, we present the Principle of Natural Modes as a claim about the structure of the world. We first define an evaluation function that measures how well a set of categories supports the inference goals of the observer. Entropy measures for property uncertainty and category uncertainty are combined through a free parameter that reflects the goals of the observer. Natural categorizations are shown to be those that are stable with respect to this free parameter. The evaluation function is tested in the domain of leaves and is found to be sensitive to the structure of the natural categories corresponding to the different species. We next develop a categorization paradigm that utilizes the categorization evaluation function in recovering natural categories. A statistical hypothesis generation algorithm is presented that is shown to be an effective categorization procedure. Examples drawn from several natural domains are presented, including data known to be a difficult test case for numerical categorization techniques. We next extend the categorization paradigm such that multiple levels of natural categories are recovered; by means of recursively invoking the categorization procedure both the genera and species are recovered in a population of anaerobic bacteria. Finally, a method is presented for evaluating the utility of features in recovering natural categories. This method also provides a mechanism for determining which features are constrained by the different processes present in a multiple modal world.

An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.

Micro-layered-photolithography for Micro-Fabrication and Micro-Molding

A novel process based on the principle of layered photolithography has been proposed and tested for making real three-dimensional micro-structures. An experimental setup was designed and built for doing experiments on this micro-fabrication process. An ultraviolet (UV) excimer laser at the wavelength of 248 nm was used as the light source and a single piece of photo-mask carrying a series of two dimensional (2D) patterns sliced from a three dimensional (3D) micro-part was employed for the photolithography process. The experiments were conducted on the solidification of liquid photopolymer from single layer to multiple layers. The single-layer photolithography experiments showed that certain photopolymers could be applied for the 3D micro-fabrication, and solid layers with sharp shapes could be formed from the liquid polymer identified. By using a unique alignment technique, multiple layers of photolithography was successfully realized for a micro-gear with features at 60 microns. Electroforming was also conducted for converting the photopolymer master to a metal cavity of the micro-gear, which proved that the process is feasible for micro-molding.