Convex Formulation for Kernel PCA and Its Use in Semisupervised Learning

• Published in: IEEE transaction on neural networks and learning systems Vol. 29; no. 8; pp. 3863 - 3869
• Main Authors: Alaiz, Carlos M., Fanuel, Michael, Suykens, Johan A. K.
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.08.2018; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Classification; Computational geometry; Convex analysis; Convex functions; Convexity; Eigenvalues and eigenfunctions; Kernel; Kernel principal component analysis (KPCA); kernel spectral clustering; Lagrange multiplier; Mathematical models; Optimization; Principal component analysis; Principal components analysis; Regularization; Saddle points; Semi-supervised learning; Semisupervised learning; Support vector machines

In this brief, kernel principal component analysis (KPCA) is reinterpreted as the solution to a convex optimization problem. Actually, there is a constrained convex problem for each principal component, so that the constraints guarantee that the principal component is indeed a solution, and not a me...