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]. Ass...

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A. Two quite different forms of nonlinear principal component analysis have been proposed in the literature. The first one is associated with the names of Guttman, Burt, Hayashi, Benzécri, McDonald, De Leeuw, Hill, Nishisato. We call itmultiple correspondence analysis. The second form has been discussed by Kruskal, Shepard, Roskam, Takane, Young, De Leeuw, Winsberg, Ramsay. We call it no...

Principal Component Analysis (PCA) is a feature extraction approach directly based on a whole vector pattern and acquires a set of projections that can realize the best reconstruction for an original data in the mean squared error sense. In this paper, the progressive PCA (PrPCA) is proposed, which could progressively extract features from a set of given data with large dimensionality and the e...

Principal component analysis (PCA) is a dimensionality reduction modeling technique that transforms a set of process variables by rotating their axes of representation. Maximum Likelihood PCA (MLPCA) is an extension that accounts for different noise contributions in each variable. Neither PCA nor its extensions utilize external information about the model or data such as the range or distributi...

In many experiments, the data points collected live in high-dimensional observation spaces, yet can be assigned a set of labels or parameters. In electrophysiological recordings, for instance, the responses of populations of neurons generally depend on mixtures of experimentally controlled parameters. The heterogeneity and diversity of these parameter dependencies can make visualization and int...