scholarly journals Kernel Local Fisher Discriminant Analysis of Principal Components (KLFDAPC) significantly improves the accuracy of predicting geographic origin of individuals

2021 ◽  
Author(s):  
Xinghu Qin ◽  
Charleston W.K. Chiang ◽  
Oscar Eduardo Gaggiotti
Keyword(s):  
Population Structure ◽  
Discriminant Analysis ◽  
Principal Components ◽  
Geographic Origin ◽  
Real Data ◽  
Fisher Discriminant Analysis ◽  
Linear Discriminant ◽  
Fisher Discriminant ◽  
Geographic Patterns ◽  
Local Fisher Discriminant Analysis

Geographic patterns of human genetic variation provide important insights into human evolution and disease. A commonly used tool to detect geographic patterns from genetic data is principal components analysis (PCA) or a hybrid linear discriminant analysis of principal components (DAPC). However, genetic features produced from both approaches are only linear combinations of genotypes, which ineluctably miss nonlinear patterns hidden in the genetic variations and could fail to characterize the correct population structure for more complex cases. In this study, we introduce Kernel Local Fisher Discriminant Analysis of Principal Components (KLFDAPC), a nonlinear approach for inferring individual geographic genetic structure that could rectify the limitations of these linear approaches by preserving the nonlinear information and the multimodal space of samples. We tested the power of KLFDAPC to infer population structure and to predict individual geographic origin using simulations and real data sets. Simulation results showed that KLFDAPC significantly improved the population separability compared with PCA and DAPC. The application to POPRES and CONVERGE datasets indicated that the first two reduced features of KLFDAPC correctly recapitulated the geography of individuals and significantly improved the accuracy of predicting individual geographic origin when compared to PCA and DAPC. Therefore, KLFDAPC can be useful for geographic ancestry inference, design of genome scans and correction for spatial stratification in GWAS that link genes to adaptation or disease susceptibility.

Optimal multi-kernel local fisher discriminant analysis for feature dimensionality reduction and fault diagnosis

2021 ◽  
pp. 1748006X2110093
Author(s):  
Qing Zhang ◽  
Heng Li ◽  
Xiaolong Zhang ◽  
Haifeng Wang
Keyword(s):  
Fault Diagnosis ◽  
Discriminant Analysis ◽  
Feature Space ◽  
High Dimensional ◽  
Fisher Discriminant Analysis ◽  
Vibration Signals ◽  
Fisher Discriminant ◽  
Local Fisher Discriminant Analysis ◽  
Diagnosis Accuracy ◽  
Diagnosis Model

To achieve a more desirable fault diagnosis accuracy by applying multi-domain features of vibration signals, it is significative and challenging to refine the most representative and intrinsic feature components from the original high dimensional feature space. A novel dimensionality reduction method for fault diagnosis is proposed based on local Fisher discriminant analysis (LFDA) which takes both label information and local geometric structure of the high dimensional features into consideration. Multi-kernel trick is introduced into the LFDA to improve its performance in dealing with the nonlinearity of mapping high dimensional feature space into a lower one. To obtain an optimal diagnosis accuracy by the reduced features of low dimensionality, binary particle swarm optimization (BPSO) algorithm is utilized to search for the most appropriate parameters of kernels and K-nearest neighbor (kNN) recognition model. Samples with labels are used to train the optimal multi-kernel LFDA and kNN (OMKLFDA-kNN) fault diagnosis model to obtain the optimal transformation matrix. Consequently, the trained fault diagnosis model implements the recognition of machinery health condition with the most representative feature space of vibration signals. A bearing fault diagnosis experiment is conducted to verify the effectiveness of proposed diagnostic approach. Performance comparison with some other methods are investigated, and the improvement for fault diagnosis of the proposed method are confirmed in different aspects.

UNCORRELATED LOCAL FISHER DISCRIMINANT ANALYSIS FOR FACE RECOGNITION

2011 ◽  
Vol 25 (06) ◽  
pp. 863-887 ◽  
Author(s):  
HONG HUANG ◽  
JIAMIN LIU ◽  
HAILIANG FENG
Keyword(s):  
Face Recognition ◽  
Discriminant Analysis ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Fisher Discriminant Analysis ◽  
Global Optimal Solution ◽  
Fisher Discriminant ◽  
Local Fisher Discriminant Analysis ◽  
Global Optimal ◽  
Eigen Decomposition

An improved manifold learning method, called Uncorrelated Local Fisher Discriminant Analysis (ULFDA), for face recognition is proposed. Motivated by the fact that statistically uncorrelated features are desirable for dimension reduction, we propose a new difference-based optimization objective function to seek a feature submanifold such that the within-manifold scatter is minimized, and between-manifold scatter is maximized simultaneously in the embedding space. We impose an appropriate constraint to make the extracted features statistically uncorrelated. The uncorrelated discriminant method has an analytic global optimal solution, and it can be computed based on eigen decomposition. As a result, the proposed algorithm not only derives the optimal and lossless discriminative information, but also guarantees that all extracted features are statistically uncorrelated. Experiments on synthetic data and AT&T, extended YaleB and CMU PIE face databases are performed to test and evaluate the proposed algorithm. The results demonstrate the effectiveness of the proposed method.

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