Principal components analysis is a well-known statistical method in dealing with large dependent data sets. It is also used in functional data for both purposes of data reduction as well as variation representation. On the other hand "handwriting" is one of the objects, studied in various statistical fields like pattern recognition and shape analysis. Considering time as the argument,...

university of tehran administers a test known as the university of tehran english proficiency test (the utept) to phd candidates on a yearly basis. by definition, the test can be considered a high-stakes one. the validity of high stakes tests needs to be known (roever, 2001). as mesick (1988) maintains, if the validity of high stakes tests are not known, it might have some undesirable consequen...

the relative impacts of different types of land use on the surface water quality are yet to be ascertained and quantified. in this paper, the influence of different types of land use on surface water quality is investigated. rain events samples from different land use in the central plateau, iran, were analyzed for major ions. statistical analyses were employed to examine the statistical relati...

We consider the online version of the well known Principal Component Analysis (PCA) problem. In standard PCA, the input to the problem is a set of ddimensional vectors X = [x1, . . . ,xn] and a target dimension k < d; the output is a set of k-dimensional vectors Y = [y1, . . . ,yn] that minimize the reconstruction error: minΦ ∑ i ‖xi − Φyi‖2. Here, Φ ∈ Rd×k is restricted to being isometric. The...

Derivation of PCA I: For a set of d-dimensional data vectors {x}i=1, the principal axes {e}qj=1 are those orthonormal axes onto which the retained variance under projection is maximal. It can be shown that the vectors ej are given by the q dominant eigenvectors of the sample covariance matrix S, such that Sej = λjej . The q principal components of the observed vector xi are given by the vector ...

Principal components analysis is an important and well-studied subject in statistics and signal processing. The literature has an abundance of algorithms for solving this problem, where most of these algorithms could be grouped into one of the following three approaches: adaptation based on Hebbian updates and deflation, optimization of a second order statistical criterion (like reconstruction ...

Let X be an n× p matrix whose rows are iid random vectors Xi· with mean μ ∈ R and covariance Σ ∈ Sp+— for example, they might be (Xi·) iid ∼ No(μ,Σ). For many problems (such as multivariate regression of some Y on X) we might wish to reduce the dimension p of these rows. For example, if we have a vector of p = 1000 possible explanatory variables about each individual, we may hope that a small s...