Abstract
The approximate linear dependence (ALD) method is a sparsification procedure used to build a dictionary of samples extracted from a dataset. The extracted samples are approximately linearly independent in a high-dimensional kernel reproducing Hilbert space. In this paper, we argue that the ALD method itself can be used to select relevant prototypes from a training dataset and use them to classify new samples using kernelized distances. The results obtained from intensive experimentation with several datasets indicate that the proposed approach is viable to be used as a standalone classifier.
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Notes
- 1.
Let \(\mathcal {X}\) be a nonempty set. A kernel \(k(\cdot ,\cdot )\) is called conditionally positive definite if and only if it is symmetric and \(\sum _{j,k}^n c_j c_k k(\mathbf {x}_j,\mathbf {x}_k ) \ge 0\), for \(n\ge 1\), \(c_1, \ldots , c_n \in \mathbb {R}\) with \(\sum _{j=1}^n c_j = 0\) and \(\mathbf {x}_1, \ldots , \mathbf {x}_n \in \mathcal {X}\).
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Acknowledgments
This study was financed by the following Brazilian research funding agencies: CAPES (Finance Code 001) and CNPq (grant 309451/2015-9).
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Coelho, D.N., Barreto, G.A. (2020). Approximate Linear Dependence as a Design Method for Kernel Prototype-Based Classifiers. In: Vellido, A., Gibert, K., Angulo, C., Martín Guerrero, J. (eds) Advances in Self-Organizing Maps, Learning Vector Quantization, Clustering and Data Visualization. WSOM 2019. Advances in Intelligent Systems and Computing, vol 976. Springer, Cham. https://doi.org/10.1007/978-3-030-19642-4_24
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