Canonical correlation analysis (CCA) is a widely used multivariate analysis technique for explaining the relation between two sets of variables. It achieves this goal by finding linear combinations of the variables with maximal correlation. Recently, under the assumption that leading canonical directions are sparse, various penalized CCA procedures have been proposed for high dimensional data applications. However, all these procedures have the inconvenience of not preserving the sparsity among the retained leading canonical directions. To address this issue, two new sparse CCA methods are proposed in this paper. The first method is obtained by diagonal thresholding of two square matrices derived from the cross-covariance matrix of the two sets of variables where each matrix characterizes one set of variables. A model selection criterion is used to select the number of variables to retain from each matrix diagonal. The second method is derived within an adaptive alternating penalized least squares framework where the 1 2-norm is used as a penalty promoting block sparsity. Compared to existing sparse CCA methods, the proposed methods have the advantage of preserving the sparsity across the retained canonical loading vectors. Their performance are illustrated in an extended experimental study which shows the superior performance of the proposed methods.

Principal component analysis (PCA) is widely used for feature extraction and dimension reduction in pattern recognition and data analysis. Despite its popularity, the reduced dimension obtained from the PCA is difficult to interpret due to the dense structure of principal loading vectors. To address this issue, several methods have been proposed for sparse PCA, all of which estimate loading vectors with few non-zero elements. However, when more than one principal component is estimated, the associated loading vectors do not possess the same sparsity pattern. Therefore, it becomes difficult to determine a small subset of variables from the original feature space that have the highest contribution in the principal components. To address this issue, an adaptive block sparse PCA method is proposed. The proposed method is guaranteed to obtain the same sparsity pattern across all principal components. Experiments show that applying the proposed sparse PCA method can help improve the performance of feature selection for image processing applications. We further demonstrate that our proposed sparse PCA method can be used to improve the performance of blind source separation for functional magnetic resonance imaging data.

BACKGROUND: We consider data from a time course microarray experiment that was conducted on grapevines over the development cycle of the grape berries at two different vineyards in South Australia. Although the underlying biological process of berry development is the same at both vineyards, there are differences in the timing of the development due to local conditions. We aim to align the data from the two vineyards to enable an integrated analysis of the gene expression and use the alignment of the expression profiles to classify likely developmental function. RESULTS: We present a novel alignment method based on hidden Markov models (HMMs) and use the method to align the motivating grapevine data. We show that our alignment method is robust against subsets of profiles that are not suitable for alignment, investigate alignment diagnostics under the model and demonstrate the classification of developmentally driven genes. CONCLUSIONS: The classification of developmentally driven genes both validates that the alignment we obtain is meaningful and also gives new evidence that can be used to identify the role of genes with unknown function. Using our alignment methodology, we find at least 1279 grapevine probe sets with no current annotated function that are likely to be controlled in a developmental manner.

Isolating relevant information and reducing the dimensionality of the original data set are key areas of interest in pattern recognition and machine learning. In this paper, a novel approach to reducing dimensionality of the feature space by employing independent component analysis (ICA) is introduced. While ICA is primarily a feature extraction technique, it is used here as a feature selection/construction technique in a generic way. The new technique, called feature selection based on independent component analysis (FS_ICA), efficiently builds a reduced set of features without loss in accuracy and also has a fast incremental version. When used as a first step in supervised learning, FS_ICA outperforms comparable methods in efficiency without loss of classification accuracy. For large data sets as in medical image segmentation of high-resolution computer tomography images, FS_ICA reduces dimensionality of the data set substantially and results in efficient and accurate classification.

This letter is concerned with the problem of selecting the best or most informative dimension for dimension reduction and feature extraction in high-dimensional data. The dimension of the data is reduced by principal component analysis; subsequent application of independent component analysis to the principal component scores determines the most nongaussian directions in the lower-dimensional space. A criterion for choosing the optimal dimension based on bias-adjusted skewness and kurtosis is proposed. This new dimension selector is applied to real data sets and compared to existing methods. Simulation studies for a range of densities show that the proposed method performs well and is more appropriate for nongaussian data than existing methods.

Two methods for assessing the variability of image segmentation are proposed: coverage plots and percentile intervals. Both methods are based on bootstrap techniques and provide graphical information about the performance and accuracy of segmentation methods across the entire image. The methods are applied to median based image segmentation which is characterised by the filter size and a data-driven thresholding choice. Computer simulations of simulated medical X-ray images demonstrate the superiority of coverage plots in assessing the performance of segmentation methods.