We present a new method that we call generalized discriminant analysis (GDA) to deal with nonlinear discriminant analysis using kernel function operator. The underlying theory is close to the support vector machines (SVM) insofar as the GDA method provides a mapping of the input vectors into high-dimensional feature space. In the transformed space, linear properties make it easy to extend and g...

We fix an integer N ≥ 1 and an elliptic curve E over Z[1/6N ], given by an equation y = f(x) with f(x) a cubic in Z[1/6N ] whose discriminant is invertible in Z[1/6N ]. On E we have the differential of the first kind ω = dx/y and the differential of the second kind η = xdx/y. For each prime p not dividing 6N , we look at this data mod p, and apply the Cartier operator Cp. We get quantities αp, ...

BACKGROUND A reliable and precise classification is essential for successful diagnosis and treatment of cancer. Gene expression microarrays have provided the high-throughput platform to discover genomic biomarkers for cancer diagnosis and prognosis. Rational use of the available bioinformation can not only effectively remove or suppress noise in gene chips, but also avoid one-sided results of s...

In this paper, we propose a new parametric distribution which called as the Beta Modified Weibull Power Series (BMWPS) distribution. This distribution is obtained by compounding Beta Modified Weibull (BMW) and power series distributions. BMWPS distribution contains, as special sub-models, such as Beta Modified Weibull Poisson (BMWP) distribution, Beta Modified Weibull Geometric (BMWG) distribut...

introduction: in most bci articles which aim to separate movement imaginations, µ and β frequency bands have been used. in this paper, the effect of presence and absence of γ band on performance improvement is discussed since movement imaginations affect γ frequency band as well. methods: in this study we used data set 2a from bci competition iv. in this data set, 9 healthy subjects have perfor...

In two-group discriminant analysis, the Neyman-Pearson Lemma establishes that the ROC curve for an arbitrary linear function is everywhere below the ROC curve for the true likelihood ratio. The weighted area between these two curves can be used as a risk function for finding good discriminant functions. The weight function corresponds to the objective of the analysis, for example to minimize th...

Using Taylor's series we propose a modified secant relation to get a more accurate approximation of the second curvature of the objective function. Then, based on this modified secant relation we present a new BFGS method for solving unconstrained optimization problems. The proposed method make use of both gradient and function values while the usual secant relation uses only gradient values. U...