the principle of dimensionality reduction with pca is the representation of the dataset ‘x’in terms of eigenvectors ei ∈ rn  of its covariance matrix. the eigenvectors oriented in the direction with the maximum variance of x in rn carry the most      relevant information of x. these eigenvectors are called principal components [8]. assume that n images in a set are originally represented in mat...

For vectors $X, Yin mathbb{R}^{n}$, we say $X$ is left matrix majorized by $Y$ and write $X prec_{ell} Y$ if for some row stochastic matrix $R, ~X=RY.$ Also, we write $Xsim_{ell}Y,$ when $Xprec_{ell}Yprec_{ell}X.$ A linear operator $Tcolon mathbb{R}^{p}to mathbb{R}^{n}$ is said to be a linear preserver of a given relation $prec$ if $Xprec Y$ on $mathbb{R}^{p}$ implies that $TXprec TY$ on $mathb...

In this work an R-tree variant, which uses minimum volume covering ellipsoids instead of usual minimum bounding rectangles, is presented. The most significant aspects, which determine R-tree index structure performance, is an amount of dead space coverage and overlaps among the covering regions. Intuitively, ellipsoid as a quadratic surface should cover data more tightly, leading to less dead s...

in this paper, we characterize multiresolution analysis(mra) parseval frame multiwavelets in l^2(r^d) with matrix dilations of the form (d f )(x) = sqrt{2}f (ax), where a is an arbitrary expanding dtimes d matrix with integer coefficients, such that |deta| =2. we study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of mra tight frame multiwav...

1.1. Notations. Let n be the number of elements and Sn be set of all possible n! permutations or rankings of these of n elements. Our interest is in learning non-negative valued functions f defined on Sn, i.e. f : Sn → R+, where R+ = {x ∈ R : x ≥ 0}. The support of f is defined as supp (f) = {σ ∈ Sn : f(σ) 6= 0} . The cardinality of support, | supp (f) | is called the sparsity of f and denoted ...