The Experts below are selected from a list of 27 Experts worldwide ranked by ideXlab platform
Pauli Miettinen - One of the best experts on this subject based on the ideXlab platform.
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the boolean column and column Row Matrix decompositions
European conference on Machine Learning, 2008Co-Authors: Pauli MiettinenAbstract:Matrix decompositions are used for many data mining purposes. One of these purposes is to find a concise but interpretable representation of a given data Matrix. Different decomposition formulations have been proposed for this task, many of which assume a certain property of the input data (e.g., nonnegativity) and aim at preserving that property in the decomposition.
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the boolean column and column Row Matrix decompositions
Data Mining and Knowledge Discovery, 2008Co-Authors: Pauli MiettinenAbstract:Matrix decompositions are used for many data mining purposes. One of these purposes is to find a concise but interpretable representation of a given data Matrix. Different decomposition formulations have been proposed for this task, many of which assume a certain property of the input data (e.g., nonnegativity) and aim at preserving that property in the decomposition. In this paper we propose new decomposition formulations for binary matrices, namely the Boolean CX and CUR decompositions. They are natural combinations of two previously presented decomposition formulations. We consider also two subproblems of these decompositions and present a rigorous theoretical study of the subproblems. We give algorithms for the decompositions and for the subproblems, and study their performance via extensive experimental evaluation. We show that even simple algorithms can give accurate and intuitive decompositions of real data, thus demonstrating the power and usefulness of the proposed decompositions.
Longxiu Huang - One of the best experts on this subject based on the ideXlab platform.
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on column Row Matrix approximations
International Conference on Sampling Theory and Applications, 2019Co-Authors: Keaton Hamm, Longxiu HuangAbstract:This article discusses column-Row factorizations of low-rank matrices, and extensions of these to approximations of full rank matrices. We give perturbation estimates for CUR decompositions, and provide some numerical illustrations of the practical aspects of these approximations.
Hongchi Shi - One of the best experts on this subject based on the ideXlab platform.
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identity plus Row Matrix decomposition and its application in design of parallel projection algorithms
Journal of Electronic Imaging, 2001Co-Authors: Hongchi ShiAbstract:Many image processing operations can be abstracted into Matrix operations. With the help of Matrix analysis, we can understand the inherent properties of the operations and thus design better algorithms. In this paper, we propose a Matrix decomposition method referred to as identity-plus-Row decomposition. The decomposition is particularly useful in design of parallel projection algorithms on mesh-connected computers. Projection is a frequently used process in image processing and visualization. In volume graphics, projection is used to render the essential content of a three-dimensional volume onto a two-dimensional image plane. For Radon transform, projection is used to transform the image space into a parameter space. By applying the identity-plus-Row Matrix decomposition method, we solve the data redistribution problem due to the irregular data access patterns present in those applications on single instruction stream, multiple data stream (SIMD) meshconnected computers, developing fast algorithms for volume rendering and Radon transform on SIMD mesh-connected computers.
Keaton Hamm - One of the best experts on this subject based on the ideXlab platform.
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on column Row Matrix approximations
International Conference on Sampling Theory and Applications, 2019Co-Authors: Keaton Hamm, Longxiu HuangAbstract:This article discusses column-Row factorizations of low-rank matrices, and extensions of these to approximations of full rank matrices. We give perturbation estimates for CUR decompositions, and provide some numerical illustrations of the practical aspects of these approximations.
Sarah Bansilal - One of the best experts on this subject based on the ideXlab platform.
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zimbabwean in service mathematics teachers understanding of Matrix operations
The Journal of Mathematical Behavior, 2017Co-Authors: Cathrine Kazunga, Sarah BansilalAbstract:Abstract In Zimbabwe, school pupils study Matrix operations, a topic that is usually covered as part of linear algebra courses taken by most mathematics undergraduate students at university. In this study we focused on Zimbabwean teachers who were studying the topic at university while also teaching the topic to their high school pupils. The purpose of the study was to explore the mental conceptions of Matrix operations concepts of a sample of 116 in-service mathematics teachers. The Action Process Object Schema (APOS) theoretical framework describes the development in understanding of mathematics concepts through the hierarchical gRowth of mental constructions called action, process, object and schema. The results showed that many of the participants had interiorized actions on Matrix operations of addition, scalar multiplication and Matrix multiplication into processes. However, more than 50% of the participants struggled with scalar multiplication of a Row Matrix by a column Matrix. In terms of notational errors, some participants could not distinguish between brackets that denote a Matrix and that of a determinant, while some used the equal sign as an operator symbol and not as one denoting equivalence between two objects. It is recommended that future in-service teacher programs should try to create more structured opportunities to allow participants to engage more deeply with these concepts.
