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...

The data structure at the core of nowadays largescale search engines, social networks, and storage architectures is the inverted index. Given a collection of documents, consider for each distinct term t appearing in the collection the integer sequence `t , listing in sorted order all the identifiers of the documents (docIDs in the following) in which the term appears. The sequence `t is called ...

We propose applying the linear Granger Causality concept to very high-dimensional time series. The approach is based on integrating dimensionality reduction into a multivariate time series model. If residuals of dimensionality reduced models can be transformed back into the original space, prediction errors in the high–dimensional space may be computed, and a Granger Causality Index (GCI) is pr...

In allusion to similarity calculation difficulty caused by high maintenance of image data, this paper introduces sparse principal component algorithm to figure out embedded subspace after dimensionality reduction of image visual words on the basis of traditional spectral hashing image index method so that image high-dimension index results can be explained overall. This method is called sparse ...

A fundamental problem in machine learning is identifying the most representative subset of features from which we can construct a predictive model for a classification task. This paper aims to present a validation study of dimensionality reduction effect on the classification accuracy of mammographic images. The studied dimensionality reduction methods were: locality-preserving projection (LPP)...

In this paper and in the forthcoming Part II we introduce a Morse complex for a class of functions f defined on an infinite dimensional Hilbert manifold M , possibly having critical points of infinite Morse index and co-index. The idea is to consider an infinite dimensional subbundle or more generally an essential subbundle of the tangent bundle of M , suitably related with the gradient flow of...

Let G be a simple graph with vertex set V(G) {v1,v2 ,...vn} . For every vertex i v , ( ) i  v represents the degree of vertex i v . The h-th order of Randić index, h R is defined as the sum of terms 1 2 1 1 ( ), ( )... ( ) i i ih  v  v  v  over all paths of length h contained (as sub graphs) in G . In this paper , some bounds for higher Randić index and a method for computing the higher R...

The notorious “dimensionality curse” is a well-known phenomenon for any multi-dimensional indexes attempting to scale up to high dimensions. One well known approach to overcoming degradation in performance with respect to increasing dimensions is to reduce the dimensionality of the original dataset before constructing the index. However, identifying the correlation among the dimensions and effe...

We prove that finiteness of the index of the intersection of a finite set of finite index subalgebras in a von Neumann algebra (with small centre) is equivalent to the finite dimensionality of the algebra generated by the conditional expectations onto the subalgebras. 2000 Mathematics Subject Classification. 46S99, 81R10.