## Search

Now showing items 21-30 of 35

#### A Finite Newton Method for Classi cation Problems

(2001)

A fundamental classi cation problem of data mining and machine
learning is that of minimizing a strongly convex, piecewise quadratic
function on the n-dimensional real space Rn. We show nite termination
of a Newton ...

#### Support Vector Machine Classi cation via Parameterless Robust Linear Programming

(2003)

We show that the problem of minimizing the sum of arbitrary-norm
real distances to misclassi ed points, from a pair of parallel bounding
planes of a classi cation problem, divided by the margin (distance) be-
tween the ...

#### Absolute Value Equations

(2005)

We investigate existence and nonexistence of solutions for NP-hard equations in-
volving absolute values of variables: Ax ? |x| = b, where A is an arbitrary n � n real matrix.
By utilizing an equivalence relation to the ...

#### Large Scale Kernel Regression via Linear Programming

(1999)

The problem of tolerant data tting by a nonlinear surface, in-
duced by a kernel-based support vector machine [24], is formulated as
a linear program with fewer number of variables than that of other
linear programming ...

#### Knowledge-Based Support Vector Machine Classi ers

(2001)

Prior knowledge in the form of multiple polyhedral sets, each belonging
to one of two categories, is introduced into a reformulation
of a linear support vector machine classi er. The resulting formulation
leads to a ...

#### Probability of Unique Integer Solution to a System of Linear Equations

(2009)

We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient
conditions for the existence of a unique solution to the system that is integer: x ? {?1,1}n. We achieve this by
reformulating ...

#### Set Containment Characterization

(2001)

Characterization of the containment of a polyhedral set in a closed halfspace, a key factor in
generating knowledge-based support vector machine classi ers [7], is extended to the following:
(i) Containment of one ...

#### Privacy-Preserving Horizontally Partitioned Linear Programs

(2010)

We propose a simple privacy-preserving reformulation of a linear program whose equality constraint
matrix is partitioned into groups of rows. Each group of matrix rows and its corresponding right hand side
vector are ...

#### Data Mining via Support Vector Machines

(2001)

Support vector machines (SVMs) have played a key role in broad
classes of problems arising in various elds. Much more recently, SVMs
have become the tool of choice for problems arising in data classi -
cation and mining. ...

#### Proximal Knowledge-Based Classification

(2008-06-26)

Prior knowledge over general nonlinear sets is incor-
porated into proximal nonlinear kernel classification
problems as linear equalities. The key tool in this
incorporation is the conversion of general nonlinear
prior ...