Deflated manifold embedding PCA framework via multiple instance factorings
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Deflated manifold embedding PCA framework via multiple instance factorings Ernest Domanaanmwi Ganaa1,2 · Xiang-Jun Shen1,3 · Timothy Apasiba Abeo4 Received: 15 February 2020 / Revised: 17 August 2020 / Accepted: 2 September 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract Principal component analysis is a widely used technique. However, it is sensitive to noise and considers data samples to be linearly distributed globally. To tackle these challenges, a novel technique robust to noise termed deflated manifold embedding PCA is proposed. In this framework, we unify PCA with manifold embedding to preserve both global and local geometric structures of linear and non-linear data in sub-manifolds. Additionally, a scaling-factor is imposed in the instance space to mitigate the impact of noise in pursuing projections. By using cosine similarity and total distance approaches, we iteratively learn the relationships between instances and projections in order to discriminate between authentic and corrupt instances. Further, a deflation technique is applied to establish multirelationships between instances and every pursued projection for thorough discrimination. Experimental evaluation of the proposed methods on five datasets show great improvements in their performances over six state-of-the-art techniques. Keywords Principal component analysis · Manifold embedding · Dimension reduction · Deflation · Instance factorings
1 Introduction In computer vision and pattern recognition fields such as fingerprint identification, bioinformatics, speech recognition, face recognition and content-based image retrieval, many applications are usually confronted with very high-dimensional data. Dimensionality reduction (DR) presents an effective way of dealing with such high-dimensional data. As a result, Xiang-Jun Shen
[email protected] 1
School of Computer Science and Communication Engineering, Jiangsu University, Zhenjiang, 212013, China
2
School of Applied Science and Technology, Wa Technical University, Box 553, Wa, Ghana
3
Jingkou New-Generation Information Technology Industry Institute, JiangSu University, JiangSu, China
4
School of Applied Science, Tamale Technical University, Box 3ER, Tamale, Ghana
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DR has received great attention from the machine learning community, where several successful techniques have been presented in the past years. Some of these techniques include principal component analysis (PCA) [57] which transforms high-dimensional data into a low-dimensional space while aiming to minimize information loss. Linear discriminant analysis (LDA) [7] considers class labels of data while seeking to maximize between-class scatter and minimize within-class scatter. Neighbourhood preserving embedding (NPE) [74] seeks to preserve local neighbourhood structure in a reduced space by representing each instance as a linear combination of its neighbors using a weight matrix as the combination coefficients. Random projection (RP) [29] is another DR techn
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