Asymptotic Properties of Support Vector Machines in High-Dimension, Low-Sample-Size Settings under a Spiked Model
Under a spiked HDLSS model, standard SVM is inconsistent; a spike-corrected SVM needs growing sample size.
The paper analyzes support vector machines in high-dimension, low-sample-size settings when the covariance follows a spiked model. It shows the usual geometric representation fails, the Gram matrix converges to a random matrix in a space whose dimension equals the number of spikes, and both SVM and bias-corrected SVM do not achieve consistency. A proposed spike-corrected SVM is consistent as sample size grows, while any projection-based procedure fails at fixed sample size; simulations support the theory.
- Geometric HDLSS representations fail when covariance eigenvalues are spiked.
- Standard SVM and bias-corrected SVM lack consistency under the spiked model.
- Proposed spike-corrected SVM is consistent only as sample size grows; fixed-n projections fail.
From the original article
1 min read at arxiv.orgIn this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings under a spiked model. The existing theory of the SVM in the HDLSS context relies on the geometric representation of HDLSS data, which requires that the eigenvalues of the covariance matrices are not dominant.
By Yugo Nakayama · arxiv.org
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