Some results on the divergence criterion used to solve the feature selection problem

Techniques for solving the feature selection problem are presented. Topics discussed include the reduction of the number of variables in "best b", and the iterative selection of H sub i

A counter example in linear feature selection theory

The linear feature selection problem in multi-class pattern recognition is described as that of linearly transforming statistical information from n-dimensional (real Euclidean) space into k-dimensional space, while requiring that average interclass divergence in the transformed space decrease as little as possible. Divergence is the expected interclass divergence derived from Hajek two-class divergence; it is known that there always exists a k x n matrix B such that the transformation determined by B maximizes the divergence in k-dimensional space. It is known that, if Q is any k x k invertible matrix, and B is as defined above, then QB again maximizes the divergence in k-space. It is shown that the converse of this result is false: two matrices exist, B sub 1 and B sub 2, each of which maximizes transformed divergence, which are not related in the fashion B sub 2 = QB sub 1 for any k x k matrix Q

A fixed point theorem for certain operator valued maps

In this paper, we develop a family of Neuberger-like results to find points z epsilon H satisfying L(z)z = z and P(z) = z. This family includes Neuberger's theorem and has the additional property that most of the sequences q sub n converge to idempotent elements of B sub 1(H)

On Nth roots of positive operators

A bounded operator A on a Hilbert space H was positive. These operators were symmetric, and as such constitute a natural generalization of nonnegative real diagonal matrices. The following result is thus both well known and not surprising: A positive operator has a unique positive square root (under operator composition)

The role of eigenvalues in linear feature selection theory

A particular measure of pattern class distinction called the average interclass divergence, or more simply, divergence, is considered. Here divergence will be the pairwise average of the expected interclass divergence derived from Hajek's two-class divergence

Gene therapy: the end of the rainbow?

The increased understanding of the molecular basis of oral cancer has led to expectations that correction of the genetic defects will lead to improved treatments. Nevertheless, the first clinical trials for gene therapy of oral cancer occurred 20 years ago, and routine treatment is still not available. The major difficulty is that genes are usually delivered by virus vectors whose effects are weak and temporary. Viruses that replicate would be better, and the field includes many approaches in that direction. If any of these are effective in patients, then gene therapy will become available in the next few years. Without significant advances, however, the treatment of oral cancer by gene therapy will remain as remote as the legendary pot of gold at the end of the rainbow

Flexibility from energy systems integration: supporting synergies mmong sectors

Energy systems integration, or sector coupling, has several drivers that span climate impact mitigation and economics to social and regulatory considerations. A key question is what is sector coupling, and how does it impact the flexibility of the energy system? Here, the energy system includes several sectors - electricity, gas, heat, and transportation - that have been independent for decades in most countries except for their coupling via combined heat and power (CHP) units. In energy systems integration, some sectors may provide flexibility to other sectors, while other sectors will require flexibility when interlinking. To support these synergies among sectors, it is important to explore and quantify mutual interactions as well as seek examples of how these integrations can provide flexibility and other benefits. From the perspective of the electricity sector, it is important to ensure that there is enough flexibility in the interconnected systems to support decarbonization goals, such as those set in the Paris Agreement, while ensuring operational reliability