We study gender discrimination of human faces using a combination of psychophysical classification and discrimination experiments together with methods from machine learning. We reduce the dimensionality of a set of face images using principal component analysis, and then train a set of linear classifiers on this reduced representation (linear support vector machines (SVMs), relevance vector ma...

A framework for Similarity-Based Methods (SBMs) includes many neural network models as special cases. Multilayer Perceptrons (MLPs) use scalar products to compute weighted activation of neurons, combining soft hyperplanes to provide decision borders. Scalar product is replaced by a distance function between the inputs and the weights, offering a natural generalization of the standard MLP model ...

Decision-tree induction algorithms are widely used in knowledge discovery and data mining, specially in scenarios where model comprehensibility is desired. A variation of the traditional univariate approach is the so-called oblique decision tree, which allows multivariate tests in its non-terminal nodes. Oblique decision trees can model decision boundaries that are oblique to the attribute axes...

The paper introduces a new method for the graphical representation of multicriteria decision problems with discrete sets of alternatives. The approach proposed here extends projection techniques based on principal component analysis by incorporating information about preferences between alternatives in the graphical display. The advantages of principal component projection, which provides a cle...

It is well known that a two-layer perceptron network with threshold neurons is incapable of forming arbitrary decision regions in input space, while a three-layer perceptron has that capability. The effect of replacing the output neuron in a two-layer perceptron with a bithreshold element is studied. The limitations of this modified two-layer perceptron are observed. Results on the separating c...

In the constraint proposal method a mediator locates points at which the two decision makers have joint tangent hyperplanes. We give conditions under which these points are Pareto optimal and we prove that under these conditions the mediator’s problem has a solution, when the number of issues in the negotiation is two or any odd number greater than two. In practice, the mediator adjusts a hyper...

We study the convex hull of the intersection of a disjunctive set defined by parallel hyperplanes and the feasible set of a mixed integer second order cone optimization (MISOCO) problem. We extend our prior work on disjunctive conic cuts (DCCs), which has thus far been restricted to the case in which the intersection of the hyperplanes and the feasible set is bounded. Using a similar technique,...

This paper contains four main results associated with an attractor of a projective iterated function system (IFS). The first theorem characterizes when a projective IFS has an attractor which avoids a hyperplane. The second theorem establishes that a projective IFS has at most one attractor. In the third theorem the classical duality between points and hyperplanes in projective space leads to c...