A neural net was used to analyse samples of natural images and text. For the natural images, components resemble derivatives of Gaussian operators, similar to those found in visual cortex and inferred from psychophysics 4]. While the results from natural images do not depend on scale, those from text images are highly scale dependent. Convolution of one of the text components with an original i...

With the availability of high-density genotype information, principal components analysis (PCA) is now routinely used to detect and quantify the genetic structure of populations in both population genetics and genetic epidemiology. An important issue is how to make appropriate and correct inferences about population relationships from the results of PCA, especially when admixed individuals are ...

Usually, principal components analysis is carried out by calculating the eigenvalues and eigenvectors of the correlation matrix. With N cases and P variables, if we write X for the N × P matrix which has been standardised so that columns have zero mean and unit standard deviation, we find the eigenvalues and eigenvectors of the P × P matrix X.X (which is N or (N − 1) times the correlation matri...

© 2007 Wiley Periodicals, Inc. • Published online 22 January 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/asi.20537 three fundamental components: a set of documents, a set of posed information needs, and a set of relevance judgments. Relevance judgments are the collections of documents that should be retrieved for each information need, and a posed information need is a...

This paper provides parametric and rank-based optimal tests for eigenvectors and eigenvalues of covariance or scatter matrices in elliptical families. The parametric tests extend the Gaussian likelihood ratio tests of Anderson (1963) and their pseudo-Gaussian robustifications by Tyler (1981, 1983) and Davis (1977), with which their Gaussian versions are shown to coincide, asymptotically, under ...

This paper proposes a new approach for the encoding of images by only a few important components. Classically, this is done by the Principal Component Analysis (PCA). Recently, the Independent Component Analysis (ICA) has found strong interest in the neural network community. Applied to images, we aim for the most important source patterns with the highest occurrence probability or highest info...

We use principal component analysis (PCA) to reduce the dimensionality of features of video frames for the purpose of content description. This low dimensional description makes practical the direct use of all the frames of a video sequence in later analysis. The PCA representation circumvents or eliminates several of the stumbling blocks in current analysis methods, and makes new analyses feas...

In this work we apply the method of diagonal regression to derive an alternative version of Principal Component Analysis (PCA). “Diagonal regression” was introduced by Ragnar Frisch (the first economics Nobel laureate) in his paper “Correlation and Scatter in Statistical Variables” (1928). The benefits of using diagonal regression in PCA are that it provides components that are scale-invariant ...

One feature of contemporary datasets is that instead of the single point value in the p-dimensional space < seen in classical data, the data may take interval values thus producing hypercubes in <. This paper extends the methodology of classical principal components to that for interval-valued data. Two methods are proposed, viz., a vertices method which uses all the vertices of the observation...

The goal of combining the predictions of multiple learned models is to form an improved estimator. A combining strategy must be able to robustly handle the inherent correlation, or multicollinearity, of the learned models while identifying the unique contributions of each. A progression of existing approaches and their limitations with respect to these two issues are discussed. A new approach, ...