Kernel based learning has found wide applications in several data mining problems. In this paper, we propose a modified classical linear kernel using an automatic smoothing parameter (Sp) selection compared with the existing approach. We designed the Sp values using the Eigen values computed from the dataset. Experiment results using some classification related benchmark datasets reveal that th...

The main thrust of this paper is to investigate the ridge regression problem in multicollinear data. The properties of ridge estimator are discussed. Variance inflation factors, eigen values and standardization problem are studied through an empirical comparison between OLS and ridge regression method by regressing number of persons employed on five variables. Methods to choose biasing paramete...

An universality theorem on the approximation of analytic functions by shifts ζ(s+iτ, F ) of zeta-functions of normalized Hecke-eigen forms F , where τ takes values from the set {kαh : k = 0, 1, 2, . . . } with fixed 0 < α < 1 and h > 0, is obtained.

Fitting only the leading principal components allows genetic covariance matrices to be modelled parsimoniously, yielding reduced rank estimates. If principal components with non-zero variances are omitted from the model, genetic variation is moved into the covariance matrices for residuals or other random effects. The resulting bias in estimates of genetic eigen-values and -vectors is examined.

Leading order semi-classical asymptotics are given for the distribution of the eigen-values of Dirac and Pauli operators describing an electron in an electromagnetic eld. Minimal conditions are assumed on the electric and magnetic potentials to ensure the existence of only a nite number of eigenvalues outside the essential spectra. The method used is based on coherent state analysis.

In a three-dimensional context, it is shown how wave functions may be chosen from among the solutions of the Schrodinger equation in a consistent way without demanding single valuedness, but by imposing an invariance condition on the domain of certain given linear operators. This leads to multiple-valued wave functions in certain situations, but disallows unquantized monopoles and "unusual" ang...