Support vector machines (SVMs) naturally embody sparseness due to their use
of hinge loss functions. However, SVMs can not directly estimate conditional
class probabilities. In this paper we propose and study a family of coherence
functions, which are convex and differentiable, as surrogates of the hinge
function. The coherence function is derived by using the maximum-entropy
principle and is characterized by a temperature parameter. It bridges the hinge
function and the logit function in logistic regression.
Spectral clustering is a broad class of clustering procedures in which an
intractable combinatorial optimization formulation of clustering is "relaxed"
into a tractable eigenvector problem, and in which the relaxed solution is
subsequently "rounded" into an approximate discrete solution to the original
problem. In this paper we present a novel margin-based perspective on multiway
spectral clustering.