A Government-Binding Based Parser for Warlpiri, a Free-Word Order Language

Free-word order languages have long posed significant problems for standard parsing algorithms. This thesis presents an implemented parser, based on Government-Binding (GB) theory, for a particular free-word order language, Warlpiri, an aboriginal language of central Australia. The words in a sentence of a free-word order language may swap about relatively freely with little effect on meaning: the permutations of a sentence mean essentially the same thing. It is assumed that this similarity in meaning is directly reflected in the syntax. The parser presented here properly processes free word order because it assigns the same syntactic structure to the permutations of a single sentence. The parser also handles fixed word order, as well as other phenomena. On the view presented here, there is no such thing as a "configurational" or "non-configurational" language. Rather, there is a spectrum of languages that are more or less ordered. The operation of this parsing system is quite different in character from that of more traditional rule-based parsing systems, e.g., context-free parsers. In this system, parsing is carried out via the construction of two different structures, one encoding precedence information and one encoding hierarchical information. This bipartite representation is the key to handling both free- and fixed-order phenomena. This thesis first presents an overview of the portion of Warlpiri that can be parsed. Following this is a description of the linguistic theory on which the parser is based. The chapter after that describes the representations and algorithms of the parser. In conclusion, the parser is compared to related work. The appendix contains a substantial list of test cases ??th grammatical and ungrammatical ??at the parser has actually processed.

Feature Point Detection and Curve Approximation for Early Processing of Freehand Sketches

Freehand sketching is both a natural and crucial part of design, yet is unsupported by current design automation software. We are working to combine the flexibility and ease of use of paper and pencil with the processing power of a computer to produce a design environment that feels as natural as paper, yet is considerably smarter. One of the most basic steps in accomplishing this is converting the original digitized pen strokes in the sketch into the intended geometric objects using feature point detection and approximation. We demonstrate how multiple sources of information can be combined for feature detection in strokes and apply this technique using two approaches to signal processing, one using simple average based thresholding and a second using scale space.

Measure Fields for Function Approximation

The computation of a piecewise smooth function that approximates a finite set of data points may be decomposed into two decoupled tasks: first, the computation of the locally smooth models, and hence, the segmentation of the data into classes that consist on the sets of points best approximated by each model, and second, the computation of the normalized discriminant functions for each induced class. The approximating function may then be computed as the optimal estimator with respect to this measure field. We give an efficient procedure for effecting both computations, and for the determination of the optimal number of components.

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.

Convergence Rates of Approximation by Translates

In this paper we consider the problem of approximating a function belonging to some funtion space Φ by a linear comination of n translates of a given function G. Ussing a lemma by Jones (1990) and Barron (1991) we show that it is possible to define function spaces and functions G for which the rate of convergence to zero of the erro is 0(1/n) in any number of dimensions. The apparent avoidance of the "curse of dimensionality" is due to the fact that these function spaces are more and more constrained as the dimension increases. Examples include spaces of the Sobolev tpe, in which the number of weak derivatives is required to be larger than the number of dimensions. We give results both for approximation in the L2 norm and in the Lc norm. The interesting feature of these results is that, thanks to the constructive nature of Jones" and Barron"s lemma, an iterative procedure is defined that can achieve this rate.