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Kernelized Supervised Laplacian Eigenmap for Visualization and Classification of Multi-Label Data
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DOI：10.1016/j.patcog.2021.108399.png)
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Abstract
En 中文
We had previously proposed a supervised Laplacian eigenmap for visualization (SLE-ML) that can handle multi-label data. In addition, SLE-ML can control the trade-off between the class separability and local structure by a single trade-off parameter. However, SLE-ML cannot transform new data, that is, it has the out-of-sample problem. In this paper, we show that this problem is solvable, that is, it is possible to simulate the same transformation perfectly using a set of linear sums of reproducing kernels (KSLEML) with a nonsingular Gram matrix. We experimentally showed that the difference between training and testing is not large; thus, a high separability of classes in a low-dimensional space is realizable with KSLE-ML by assigning an appropriate value to the trade-off parameter. This offers the possibility of separability-guided feature extraction for classification. In addition, to optimize the performance of KSLEML, we conducted both kernel selection and parameter selection. As a result, it is shown that parameter selection is more important than kernel selection. We experimentally demonstrated the advantage of using KSLE-ML for visualization and for feature extraction compared with a few typical algorithms. (c) 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
Keywords:
Supervised Laplacian eigenmaps
Out-of-sample problem
Multi-label problems
Kernel trick
Separability-guided feature extraction
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