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 a square system of analytic equations, a Newton-invariant subspace is a set which contains the resulting point of a Newton iteration applied to each point in the subspace. For example, if the equations have real coefficients, then the set of real points form a Newtoninvariant subspace. Starting with any point for which Newton’s method quadratically converges to a solution, this article uses...

This paper presents a compact and efficient shape signature that can be applied to shape retrieval from handdrawn sketches. The two proposed invariant features that constitute our affine invariant signature are: (a) angle between spoke vectors, and (b) cumulated normalized area between consecutive spoke vectors. The signature can be computed efficiently from an input shape and supports fast sim...

The dynamics of linear positive systems map the orthant to itself. In other words, it maps a set vectors with zero sign variations This raises following question: what $k$ itself? We address this question using tools from theory cooperative dynamical and totally matrices. yields generalization called $k$-positive systems, that reduces for $k=1$. describe applications new type analysis nonlinear...