Principal component analysis (pca) is a multivariate technique that analyzes a data table in which observations are described by several inter-correlated quantitative dependent variables. Its goal is to extract the important information from the table, to represent it as a set of new orthogonal variables called principal components, and to display the pattern of similarity of the observations and of the variables as points in maps. The quality of the pca model can be evaluated using cross-validation techniques such as the bootstrap and the jackknife. Pca can be generalized as correspondence analysis (ca) in order to handle qualitative variables and as multiple factor analysis (mfa) in order to handle heterogenous sets of variables. Mathematically, pca depends upon the eigen-decomposition of positive semi-definite matrices and upon the singular value decomposition (svd) of rectangular matrices.
Partial least squares (pls) regression (a.k.a projection on latent structures) is a recent technique that combines features from and generalizes principal component analysis (pca) and multiple linear regression. Its goal is to predict a set of dependent variables from a set of independent variables or predictors. This prediction is achieved by extracting from the predictors a set of orthogonal factors called latent variables which have the best predictive power. These latent variables can be used to create displays akin to pca displays. The quality of the prediction obtained from a pls regression model is evaluated with cross-validation techniques such as the bootstrap and jackknife. There are two main variants of pls regression: The most common one separates the rôles of independent and independent variables; the second one-used mostly to analyze brain imaging data-gives the same rôles to dependent and independent variables.
Evidence of category specificity from neuroimaging in the human visual system is generally limited to a few relatively coarse categorical distinctions—e.g., faces versus bodies, or animals versus artifacts—leaving unknown the neural underpinnings of fine-grained category structure within these large domains. Here we use functional magnetic resonance imaging (fMRI) to explore brain activity for a set of categories within the animate domain, including six animal species—two each from three very different biological classes: primates, birds, and insects. Patterns of activity throughout ventral object vision cortex reflected the biological classes of the stimuli. Specifically, the abstract representational space—measured as dissimilarity matrices defined between species-specific multivariate patterns of brain activity—correlated strongly with behavioral judgments of biological similarity of the same stimuli. This biological class structure was uncorrelated with structure measured in retinotopic visual cortex, which correlated instead with a dissimilarity matrix defined by a model of V1 cortex for the same stimuli. Additionally, analysis of the shape of the similarity space in ventral regions provides evidence for a continuum in the abstract representational space—with primates at one end and insects at the other. Further investigation into the cortical topography of activity that contributes to this category structure reveals the partial engagement of brain systems active normally for inanimate objects in addition to animate regions.
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