A Novel Separating Hyperplane Classification Framework to Unify Nearest-Class-Model Methods for High-Dimensional Data
TL;DR: A novel separating hyperplane classification (SHC) framework to unify three nearest-class-model methods for high-dimensional data is established and a new theorem for the dual analysis of NCCM is proposed by discovering the relationship between a convex cone and its polar cone.
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Abstract: In this article, we establish a novel separating hyperplane classification (SHC) framework to unify three nearest-class-model methods for high-dimensional data: the nearest subspace method (NSM), the nearest convex hull method (NCHM), and the nearest convex cone method (NCCM). Nearest-class-model methods are an important paradigm for the classification of high-dimensional data. We first introduce the three nearest-class-model methods and then conduct dual analysis for theoretically investigating them, to understand deeply their underlying classification mechanisms. A new theorem for the dual analysis of NCCM is proposed in this article by discovering the relationship between a convex cone and its polar cone. We then establish the new SHC framework to unify the nearest-class-model methods based on the theoretical results. One important application of this new SHC framework is to help explain empirical classification results: why one class model has a better performance than others on certain data sets. Finally, we propose a new nearest-class-model method, the soft NCCM, under the novel SHC framework to solve the overlapping class model problem. For illustrative purposes, we empirically demonstrate the significance of our SHC framework and the soft NCCM through two types of typical real-world high-dimensional data: the spectroscopic data and the face image data.
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Figures
Fig. 11: The discriminative abilities of two normal vectors and the mean discriminative abilities of NSM, NCHM, NCCM and soft NCCM for the Yale face database B. 
Fig. 10: The classification accuracies of SVM, NSM, NCHM, NCCM and soft NCCM on the face image data. 
Fig. 8: The discriminative abilities, denoted by wS , wCH , wCC and wSCC , of the normal vectors of NSM, NCHM, NCCM and soft NCCM, respectively, for the two spectroscopic datasets. 
Fig. 7: The classification accuracies of SVM, NSM, NCHM, NCCM and soft NCCM on the two spectroscopic datasets. 
Fig. 9: Example face images in the Yale face database B. 
Fig. 3: Illustrative examples of (a) Theorem III.2 of NSM, (b) Theorem III.3 of NCHM and (c) Theorem III.4 of NCCM.
Citations
Face Recognition by Multiple Constrained Mutual Subspace Method
Masashi Nishiyama,Osamu Yamaguchi,Kazuhiro Fukui +2 more
- 20 Nov 2003
TL;DR: In this article, the authors proposed a method named the Multiple Constrained Mutual Subspace Method which increases the accuracy of face recognition by introducing a framework provided by ensemble learning, where the set of patterns were represented as a low-dimensional subspace, and calculated the similarity between an input subspace and a reference subspace.
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Constrained mutual convex cone method for image set based recognition
TL;DR: A convex cone based framework is established, which mathematically defines multiple angles between two convex cones, and then defines the geometric similarity between the cones using the angles, and a discriminant space is introduced that maximizes the between-class variance (gaps) and minimizes the within- class variance (Gaps) on the discriminantspace.
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Constrained mutual convex cone method for image set based recognition
01 Jan 2022
TL;DR: Wang et al. as mentioned in this paper proposed a convex cone-based framework for image-set classification, which maximizes gaps between cones and minimizes the within-class variance.
Ensemble Classifier with Hybrid Feature Transformation for High Dimensional Data in Healthcare
B. Gunasundari,S. Arun +1 more
- 28 Apr 2022
TL;DR: Wang et al. as mentioned in this paper proposed an ensemble classifier with hybrid feature transformation for handling extremely complex dimensional data, which is proven to be efficient for selecting and extracting features from a very large dataset in a classification task.
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Analyzing RNA-Seq Gene Expression Data for Cancer Classification Through ML Approach
Abdul Wahid,M. Tariq Banday +1 more
TL;DR: The study analyzes RNA-Seq gene expression data to classify cancer into five different forms using an ensemble approach of machine learning algorithms. The results show that the proposed ensemble classifier achieved an accuracy of 99.59%, outperforming existing approaches.
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