Dimension Reduction of Multimodal Data by Auto-weighted Local Discriminant Analysis

2021 ◽  
Author(s):  
Rongxiu Lu ◽  
Yingjie Cai ◽  
Jianyong Zhu ◽  
Feiping Nie ◽  
Hui Yang
Keyword(s):  
Discriminant Analysis ◽  
Dimension Reduction ◽  
Multimodal Data

scholarly journals Dimension Reduction for Objects Composed of Vector Sets

2017 ◽  
Vol 27 (1) ◽  
pp. 169-180 ◽  
Author(s):  
Marton Szemenyei ◽  
Ferenc Vajda
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Feature Selection ◽  
Discriminant Analysis ◽  
Probability Distribution ◽  
Dimension Reduction ◽  
Pose Estimation ◽  
Real World ◽  
Single Object ◽  
Real World Datasets

Abstract Dimension reduction and feature selection are fundamental tools for machine learning and data mining. Most existing methods, however, assume that objects are represented by a single vectorial descriptor. In reality, some description methods assign unordered sets or graphs of vectors to a single object, where each vector is assumed to have the same number of dimensions, but is drawn from a different probability distribution. Moreover, some applications (such as pose estimation) may require the recognition of individual vectors (nodes) of an object. In such cases it is essential that the nodes within a single object remain distinguishable after dimension reduction. In this paper we propose new discriminant analysis methods that are able to satisfy two criteria at the same time: separating between classes and between the nodes of an object instance. We analyze and evaluate our methods on several different synthetic and real-world datasets.

scholarly journals Stochastic discriminant analysis for linear supervised dimension reduction

2018 ◽  
Vol 291 ◽  
pp. 136-150 ◽  
Author(s):  
Mika Juuti ◽  
Francesco Corona ◽  
Juha Karhunen
Keyword(s):  
Discriminant Analysis ◽  
Dimension Reduction ◽  
Supervised Dimension Reduction

Equivalence between LDA/QR and Direct LDA

2012 ◽  
pp. 338-353
Author(s):  
Rong-Hua Li ◽  
Shuang Liang ◽  
George Baciu ◽  
Eddie Chan
Keyword(s):  
Discriminant Analysis ◽  
Dimension Reduction ◽  
Linear Discriminant Analysis ◽  
Classification Accuracy ◽  
Qr Decomposition ◽  
Linear Discriminant ◽  
Qr Algorithm ◽  
Special Cases ◽  
Benchmark Datasets ◽  
Pseudo Inverse

Singularity problems of scatter matrices in Linear Discriminant Analysis (LDA) are challenging and have obtained attention during the last decade. Linear Discriminant Analysis via QR decomposition (LDA/QR) and Direct Linear Discriminant analysis (DLDA) are two popular algorithms to solve the singularity problem. This paper establishes the equivalent relationship between LDA/QR and DLDA. They can be regarded as special cases of pseudo-inverse LDA. Similar to LDA/QR algorithm, DLDA can also be considered as a two-stage LDA method. Interestingly, the first stage of DLDA can act as a dimension reduction algorithm. The experiment compares LDA/QR and DLDA algorithms in terms of classification accuracy, computational complexity on several benchmark datasets and compares their first stages. The results confirm the established equivalent relationship and verify their capabilities in dimension reduction.

scholarly journals Directional representation of data in Linear Discriminant Analysis

2015 ◽  
Vol 52 (2) ◽  
pp. 55-74
Author(s):  
Jolanta Grala-Michalak
Keyword(s):  
Discriminant Analysis ◽  
Dimension Reduction ◽  
Linear Discriminant Analysis ◽  
Nonlinear Transformation ◽  
Spherical Coordinates ◽  
Artificial Data ◽  
Raw Data ◽  
Linear Discriminant ◽  
Feature Representations

Abstract Sometimes feature representations of measured individuals are better described by spherical coordinates than Cartesian ones. The author proposes to introduce a preprocessing step in LDA based on the arctangent transformation of spherical coordinates. This nonlinear transformation does not change the dimension of the data, but in combination with LDA it leads to a dimension reduction if the raw data are not linearly separated. The method is presented using various examples of real and artificial data.

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