Let X be a data matrix of rank ρ, representing n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input matrix X. We prove that, with high probability, the margin and minimum enclosing ball in the feature ...

In this paper the face recognition system based on the shape information extracted with the Active Shape Model is presented. Three different classification approaches have been used: the Normal Bayes Classifier, the Linear Support Vector Machine (LSVM) with a hard margin and the LSVM with a soft margin. The influence of the shape extraction algorithm parameters on the classification efficiency ...

A Support-Vector-Machine (SVM) learns for given 2-classdata a classifier that tries to achieve good generalisation by maximising the minimal margin between the two classes. The performance can be evaluated using cross-validation testing strategies. But in case of low sample size data, high dimensionality might lead to strong side-effects that can significantly bias the estimated performance of ...

We consider the fundamental problem of linear regression in which the designer can actively choose observations. This model naturally captures various experiment design settings in medical experiments, ad placement problems and more. Whereas previous literature addresses the soft-margin or mean-square-error variants of the problem, we consider a natural machine learning hard-margin criterion. I...

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...