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Finding the preimage of a feature vector in kernel principal component analysis (KPCA) is of crucial importance when KPCA is applied in some applications such as image preprocessing. Since the exact preimage of a feature vector in the kernel feature space, normally, does not exist in the input data space, an approximate preimage is learned and encouraging results have been reported in the last few...
This paper presents a novel alternative approach, namely weakly supervised learning (WSL), to learn the pre-image of a feature vector in the feature space induced by a kernel. It is known that the exact pre-image may typically seldom exist, since the input space and the feature space are not isomorphic in general, and an approximate solution is required in past. The proposed WSL, however, would find...
In this paper, we address the pre-image problem in kernel principal component analysis (KPCA). The pre-image problem finds a pattern as the pre-image of a feature vector defined in the nonlinear principal component space produced by KPCA. Since the pre-image typically seldom exists in general, an approximate solution is appreciated. By posing a novel perspective, we find the pre-image with regularized...
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