Personalized learning that is tailored to individual needs, preference, and interests may improve student learning experience and outcome. With the aid of computing technology, it is becoming possible to deliver personalized learning to a large and diverse student population. One of the key problems involved is the determination of the pathway which each learner follows to complete a learning program. Existing methods generally rely on a priori knowledge of subject content prerequisite relationship or constraint to determine the sequencing of instructional materials without any consideration of student learning outcome. In this paper, we formulate the selection of learning pathways as an optimization problem based on competencies and student learning outcome. We show that the resulting pathway selection problem can be modeled as a Markov Decision Process (MDP). Decision rules can thus be defined and applied to select personalized learning pathways to optimize student learning outcome according to desired performance criteria.

We investigate adaptive vector quantization for image compression based the idea of gold-washing. The technique is a mechanism for testing the usefulness of a code vector in a codebook. It thus provides a tool for developing new ways of creating code vectors dynamically based on the input data. In this paper, we propose a new algorithm to quantize an input for which a close enough code vector can not be found. It guarantees that the compressed result is within pre-set distortion. We also use a learning algorithm to produce new code vectors from useful existing ones.

This paper describes a neural network inspired dynamical system approach to a perceptual grouping problem-figure-ground separation. In this approach, a non-linear differential equation is defined at each pixel site and coupled with those at its neighbours. The steady state solution would determine whether a pixel is part of a salient structure or background/noise. The neighbourhood couplings are used to achieve spatial interactions that are essential to perceptual grouping, such as excitation and inhibition. Experimental results on the grouping of dots in synthetic and real-world images demonstrate the efficacy of the proposed approach.

Minimizing the distortion subject to a cost constraint is fundamental in the design of tree-structured vector quantizers. Because of various competing cost measures, the use of single-cost constraints has led to undesirable results. The author studies the relationships among several cost functions and shows how multiple-cost constraints can be used to significantly improve tree design.

Vector quantization is a technique used extensively and successfully to compress digitized data such as speech and images. The design of a vector quantizer is very computationally intensive. Parallel algorithms based on various architectures have been proposed for related applications in clustering. These algorithms are in general not practical for the vector quantization problem because of the magnitude of the parameters involved. We present a parallel SIMD algorithm which can run efficiently on parallel machines of variable sizes. The speedup and efficiency of the algorithms are high across a wide range of input parameters.

This paper considers optimal vector quantizers which minimize the expected distortion subject to a cost such as the number of leaves (storage cost), the leaf entropy (lossless encoding rate), the expected depth (average quantization time), or the maximum depth (maximum quantization time). It analyzes the heuristic of successive partitioning, and develops a class of strategies subsuming most of those used in the past. Experimental results show that these strategies are more efficient than existing methods, and achieve comparable or better compression. The relationship among different cost functions is considered and ways of combining multiple cost constraints are proposed.>

The authors analyze the approximate performance of tree search and provide tight upper bounds on the amount of error resulting from tree search and for a single input vector. These bounds are not encouraging but fortunately, the performance of tree-structured VQ in practice does not seem to be as bad. From the analysis, they derive a simple heuristic to improve the approximation of tree search. The strategy is to identify for each code vector some of its closest neighboring code vectors determined by the partition. After a code vector is found for an input vector by tree search, the closest neighboring code vectors are then searched for the best match. Unfortunately, the average number of neighboring code vectors of a given code vector can be as many as the total number of code vectors. Thus, the performance improvement of the strategy depends on the number of code vectors that are searched. Experimental results show that a number logarithmic in the size of the codebook provides significant performance gain while preserving the asymptotic search time complexity.>

Tree-structured vector quantization is a technique to represent a codebook that simplifies encoding as well as quantizer design. The authors define the notion of an optimal pruned tree subject to a cost constraint, and study the computational complexity of finding such a tree. Under the assumption that all trees are equally probable, it is shown that on average the number of pruned trees in a given tree is exponential in the number of leaves. Finding an optimal pruned tree subject to constraints such as entropy or the expected depth is NP-hard. However, when the constraint is the number of leaves, the problem can be solved in O(nk) time, where n is the size of the initial tree and k the constraint size. Experimental results for image compression show the performance of the optimal pruned tree to be comparable with that of full-search vector quantizers.>

A novel class of information-theoretic divergence measures based on the Shannon entropy is introduced. Unlike the well-known Kullback divergences, the new measures do not require the condition of absolute continuity to be satisfied by the probability distributions involved. More importantly, their close relationship with the variational distance and the probability of misclassification error are established in terms of bounds. These bounds are crucial in many applications of divergence measures. The measures are also well characterized by the properties of nonnegativity, finiteness, semiboundedness, and boundedness.>