QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively…

In the context of college physical education curriculum reform, fostering students' interest and promoting lifelong physical exercise have become crucial. Aerobics, an integral component of physical education, plays a key role in achieving these objectives. However, existing data flow analysis technologies lack integration, limiting their ability…

Structural equation models offer a valuable tool for delineating the complicated interrelationships among multiple variables, including observed and latent variables. Over the last few decades, structural equation models have successfully analyzed complete and right-censored survival data, exemplified by wide applications in psychological, social,…

Data harmonization is an emerging approach to strategically combining data from multiple independent studies, enabling addressing new research questions that are not answerable by a single contributing study. A fundamental psychometric challenge for data harmonization is to create commensurate measures for the constructs of interest across…

Cognitive diagnosis models (CDMs) are the statistical framework for cognitive diagnostic assessment in education and psychology. They generally assume that subjects' latent attributes are dichotomous--mastery or nonmastery, which seems quite deterministic. As an alternative to dichotomous attribute mastery, attention is drawn to the use of a…

Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

Discusses sequential patterns, data mining, knowledge acquisition, and fuzzy sequential patterns described by natural language. Proposes a fuzzy data mining technique to discover fuzzy sequential patterns by using the simple partition method which allows the linguistic interpretation of each fuzzy set to be easily obtained. (Author/LRW)

Presents a class of distortion controlled vector quantizers that are capable of compressing images so they comply with certain distortion requirements. Highlights include tree-structured vector quantizers; multiresolution vector quantization; error coding vector quantizer; error coding multiresolution algorithm; and Huffman coding of the quad-tree…

Bond criticized the base-free measure of change proposed by Tucker, Damarin, and Messick by pointing to an incorrect derivation which is here viewed instead as a correct derivation entailing an inadequately specified assumption. Bond's revision leads to negatively biased estimates, whereas the original approach leads to unbiased estimates.…

Analyzes the computational complexity of optimal binary tree pruning for tree-structured vector quantization. Topics discussed include the combinatorial nature of the optimization problem; the complexity of optimal tree pruning; and finding a minimal size pruned tree. (11 references) (LRW)

Describes a string-searching algorithm for multiple patterns in a text string; explains the construction of a pattern-matching machine; presents a theoretical analysis and empirical evidence that supports the sublinearity of the algorithm; and compares this algorithm with the Boyer-Moore algorithm for a single pattern. (Contains 10 references.)…

Discusses the minimum average codeword length coding under the constraint that the codewords are monotonically nondecreasing in length. Bounds on the average length of an optimal monotonic code are derived, and sufficient conditions are given such that algorithms for optimal alphabetic codes can be used to find the optimal monotonic code. (six…

Discusses latent semantic indexing (LSI) that would allow search engines to reduce the dimension of the document space by mapping it into a space spanned by conceptual indices. Topics include vector space models; singular value decomposition (SVD); unitary operators; the Haar transform; and new algorithms. (Author/LRW)

Describes a modified frequency-sensitive self-organization (FSO) algorithm for image data compression and the associated VLSI architecture. Topics discussed include vector quantization; VLSI neural processor architecture; detailed circuit implementation; and a neural network vector quantization prototype chip. Examples of images using the FSO…

Discussion of information retrieval focuses on an Interaction Information Retrieval model in which documents are interconnected; queries and documents are treated in the same way; and retrieval is the result of the interconnection between query and documents. A theoretical mathematical formulation of this type of retrieval is given. (Contains 31…