Dimensionality Reduction for Tensor Data Based on Local Decision Margin Maximization

2021 ◽  
Vol 30 ◽  
pp. 234-248
Author(s):  
Shujie Zhang ◽  
Zhengming Ma ◽  
Weichao Gan
Keyword(s):  
Dimensionality Reduction ◽  
Local Decision ◽  
Margin Maximization ◽  
Tensor Data

Dimensionality reduction of tensor data based on local linear embedding and mode product

2021 ◽  
pp. 1-18
Author(s):  
Ting Gao ◽  
Zhengming Ma ◽  
Wenxu Gao ◽  
Shuyu Liu
Keyword(s):  
Dimensionality Reduction ◽  
Learning Algorithm ◽  
Vector Data ◽  
Global Features ◽  
Global Mode ◽  
Local Linear Embedding ◽  
Local Linear ◽  
Clustering And Classification ◽  
Linear Embedding ◽  
Tensor Data

There are three contributions in this paper. (1) A tensor version of LLE (short for Local Linear Embedding algorithm) is deduced and presented. LLE is the most famous manifold learning algorithm. Since its proposal, various improvements to LLE have kept emerging without interruption. However, all these achievements are only suitable for vector data, not tensor data. The proposed tensor LLE can also be used a bridge for various improvements to LLE to transfer from vector data to tensor data. (2) A framework of tensor dimensionality reduction based on tensor mode product is proposed, in which the mode matrices can be determined according to specific criteria. (3) A novel dimensionality reduction algorithm for tensor data based on LLE and mode product (LLEMP-TDR) is proposed, in which LLE is used as a criterion to determine the mode matrices. Benefiting from local LLE and global mode product, the proposed LLEMP-TDR can preserve both local and global features of high-dimensional tenser data during dimensionality reduction. The experimental results on data clustering and classification tasks demonstrate that our method performs better than 5 other related algorithms published recently in top academic journals.

scholarly journals A tensor compression algorithm using Tucker decomposition and dictionary dimensionality reduction

2020 ◽  
Vol 16 (4) ◽  
pp. 155014772091640
Author(s):  
Chenquan Gan ◽  
Junwei Mao ◽  
Zufan Zhang ◽  
Qingyi Zhu
Keyword(s):  
Dimensionality Reduction ◽  
Sparse Representation ◽  
Original Data ◽  
Compression Algorithm ◽  
Tucker Decomposition ◽  
Compression Algorithms ◽  
Multidimensional Signals ◽  
Sparse Coefficient ◽  
Tensor Data ◽  
The Relationship

Tensor compression algorithms play an important role in the processing of multidimensional signals. In previous work, tensor data structures are usually destroyed by vectorization operations, resulting in information loss and new noise. To this end, this article proposes a tensor compression algorithm using Tucker decomposition and dictionary dimensionality reduction, which mainly includes three parts: tensor dictionary representation, dictionary preprocessing, and dictionary update. Specifically, the tensor is respectively performed by the sparse representation and Tucker decomposition, from which one can obtain the dictionary, sparse coefficient, and core tensor. Furthermore, the sparse representation can be obtained through the relationship between sparse coefficient and core tensor. In addition, the dimensionality of the input tensor is reduced by using the concentrated dictionary learning. Finally, some experiments show that, compared with other algorithms, the proposed algorithm has obvious advantages in preserving the original data information and denoising ability.

Dimensionality reduction for tensor data based on projection distance minimization and hilbert-schmidt independence criterion maximization1

2021 ◽  
Vol 40 (5) ◽  
pp. 10307-10322
Author(s):  
Weichao Gan ◽  
Zhengming Ma ◽  
Shuyu Liu
Keyword(s):  
Dimensionality Reduction ◽  
High Dimensional ◽  
Tensor Algebra ◽  
Reduction Algorithm ◽  
Subspace Projection ◽  
Vector Data ◽  
Projection Distance ◽  
Distance Minimization ◽  
Tensor Data ◽  
Independence Criterion

Tensor data are becoming more and more common in machine learning. Compared with vector data, the curse of dimensionality of tensor data is more serious. The motivation of this paper is to combine Hilbert-Schmidt Independence Criterion (HSIC) and tensor algebra to create a new dimensionality reduction algorithm for tensor data. There are three contributions in this paper. (1) An HSIC-based algorithm is proposed in which the dimension-reduced tensor is determined by maximizing HSIC between the dimension-reduced and high-dimensional tensors. (2) A tensor algebra-based algorithm is proposed, in which the high-dimensional tensor are projected onto a subspace and the projection coordinate is set to be the dimension-reduced tensor. The subspace is determined by minimizing the distance between the high-dimensional tensor data and their projection in the subspace. (3) By combining the above two algorithms, a new dimensionality reduction algorithm, called PDMHSIC, is proposed, in which the dimensionality reduction must satisfy two criteria at the same time: HSIC maximization and subspace projection distance minimization. The proposed algorithm is a new attempt to combine HSIC with other algorithms to create new algorithms and has achieved better experimental results on 8 commonly-used datasets than the other 7 well-known algorithms.

scholarly journals Maximum Discriminant Difference Criterion for Dimensionality Reduction of Tensor Data

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 193593-193607
Author(s):  
Xinya Peng ◽  
Zhengming Ma ◽  
Haowei Xu
Keyword(s):  
Dimensionality Reduction ◽  
Tensor Data ◽  
Difference Criterion

Analysis on Research Paper Publication Recommendation System with Composition of Papers and Conferences Matrices

2020 ◽  
pp. 120-127
Author(s):  
Htay Htay Win ◽  
Aye Thida Myint ◽  
Mi Cho Cho
Keyword(s):  
Social Network ◽  
Dimensionality Reduction ◽  
Correspondence Analysis ◽  
Recommendation System ◽  
Research Paper ◽  
Topic Modelling ◽  
Research Papers ◽  
The Right ◽  
Publication Recommendation

For years, achievements and discoveries made by researcher are made aware through research papers published in appropriate journals or conferences. Many a time, established s researcher and mainly new user are caught up in the predicament of choosing an appropriate conference to get their work all the time. Every scienti?c conference and journal is inclined towards a particular ?eld of research and there is a extensive group of them for any particular ?eld. Choosing an appropriate venue is needed as it helps in reaching out to the right listener and also to further one’s chance of getting their paper published. In this work, we address the problem of recommending appropriate conferences to the authors to increase their chances of receipt. We present three di?erent approaches for the same involving the use of social network of the authors and the content of the paper in the settings of dimensionality reduction and topic modelling. In all these approaches, we apply Correspondence Analysis (CA) to obtain appropriate relationships between the entities in question, such as conferences and papers. Our models show hopeful results when compared with existing methods such as content-based ?ltering, collaborative ?ltering and hybrid ?ltering.

Speech Emotion Recognition Based on Sparse Representation

2013 ◽  
Vol 38 (4) ◽  
pp. 465-470 ◽  
Author(s):  
Jingjie Yan ◽  
Xiaolan Wang ◽  
Weiyi Gu ◽  
LiLi Ma
Keyword(s):  
Dimensionality Reduction ◽  
Emotion Recognition ◽  
Least Squares ◽  
Partial Least Squares ◽  
Partial Least Squares Regression ◽  
Speech Emotion Recognition ◽  
Least Squares Regression ◽  
Computer Science Pedagogy ◽  
Reduction Methods ◽  
Analysis Computer

Abstract Speech emotion recognition is deemed to be a meaningful and intractable issue among a number of do- mains comprising sentiment analysis, computer science, pedagogy, and so on. In this study, we investigate speech emotion recognition based on sparse partial least squares regression (SPLSR) approach in depth. We make use of the sparse partial least squares regression method to implement the feature selection and dimensionality reduction on the whole acquired speech emotion features. By the means of exploiting the SPLSR method, the component parts of those redundant and meaningless speech emotion features are lessened to zero while those serviceable and informative speech emotion features are maintained and selected to the following classification step. A number of tests on Berlin database reveal that the recogni- tion rate of the SPLSR method can reach up to 79.23% and is superior to other compared dimensionality reduction methods.

Nonlinear Dimensionality Reduction for Data on Manifold with Rings

2009 ◽  
Vol 19 (11) ◽  
pp. 2908-2920
Author(s):  
De-Yu MENG ◽  
Nan-Nan GU ◽  
Zong-Ben XU ◽  
Yee LEUNG
Keyword(s):  
Dimensionality Reduction ◽  
Nonlinear Dimensionality Reduction

СONTRIBUTION OF POLYMORPHIC VARIATION OF ТP53 AND XRCC1 GENES TO THE SUSCEPTIBILITY TO BREAST CANCER FOR WOMEN OF KYRGYZ AND BELARUSIAN NATIONALITY - A COMPARATIVE STUDY ON MULTIFACTOR DIMENSIONALITY REDUCTION METHODS

2018 ◽  
Vol 64 (1) ◽  
pp. 95-101
Author(s):  
Nazira Aldasheva ◽  
Vyacheslav Kipen ◽  
Zhaynagul Isakova ◽  
Sergey Melnov ◽  
Raisa Smolyakova ◽  
...  
Keyword(s):  
Breast Cancer ◽  
Breast Cancer Risk ◽  
Cancer Risk ◽  
Dimensionality Reduction ◽  
Multifactor Dimensionality Reduction ◽  
Rflp Analysis ◽  
Kyrgyz Republic ◽  
Increased Risk ◽  
Polymorphic Variants ◽  
The Republic

Basing on Multifactor Dimensionality Reduction method we showed that polymorphic variants p.Q399R (rs25487, XRCC1) and p.P72R (rs1042522, TP53) correlated with increased risk of breast cancer for women from the Kyrgyz Republic and the Republic of Belarus. Cohort for investigation included patients with clinically verified breast cancer: 117 women from the Kyrgyz Republic (nationality - Kyrgyz) and 169 - of the Republic of Belarus (nationality - Belarusians). Group for comparison included (healthy patients without history of cancer pathology at the time of blood sampling) 102 patients from the Kyrgyz Republic, 185 - from the Republic of Belarus. Respectively genotyping of polymorphic variants p.Q399R (rs25487, XRCC1) and p.P72R (rs1042522, TP53) was done by PCR-RFLP. Analysis of the intergenic interactions conducted with MDR 3.0.2 software. Both ethnic groups showed an increase of breast cancer risk in the presence of alleles for SNPs Gln p.Q399R (XRCC1) in the heterozygous state: for the group “Kyrgyz” - OR=2,78 (95% CI=[1,60-4,82]), p=0,001; for the group “Belarusians” - OR=1,85 (95% СІ=[1Д1-2,82], p=0,004. Carriers with combination of alleles Gln (p.Q399R, XRCC1) and Pro (p.P72R, TP53) showed statistically significance increases of breast cancer risk as for patients from the Kyrgyz Republic (OR=2,89, 95% CI=[1,33-6,31]), so as for patients from the Republic of Belarus (OR=3,01, 95% CI=[0,79-11,56]).

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