Canonical correlation analysis using within-class coupling

Dimensionality reduction of image features using the canonical contextual correlation projection

The canonical correlation analysis (CCA) aims at measuring linear relationships between two sets of variables (views) that can be used for feature extraction in classification problems with multiview data. However, the correlated features extracted by the CCA may not be class discriminative, since CCA does not utilize the class labels in its traditional formulation. Although there is a method called discriminative CCA (DCCA) that aims to increase the discriminative ability of CCA inspired from the linear discriminant analysis (LDA), it has been shown that the extracted features with this method are identical to those by the LDA with respect to an orthogonal transformation. Therefore, DCCA is simply equivalent to applying single-view (regular) LDA to each one of the views separately. Besides, DCCA and the other similar DCCA approaches have generalization problems due to the sample covariance matrices used in their computation, which are sensitive to outliers and noisy samples. In this paper, we propose a method, called discriminative alternating regression (D-AR), to explore correlated and also discriminative features. D-AR utilizes two (alternating) multilayer perceptrons, each with a linear hidden layer, learning to predict both the class labels and the outputs of each other. We show that the features found by D-AR on training sets significantly accomplish higher classification accuracies on test sets of facial expression recognition, object recognition, and image retrieval experimental data sets.

Video event carries very rich and complex semantics, and video event analysis is intrinsically multi-view learning problem. In this paper, by revealing the relationship between canonical correlation analysis (CCA) and linear discriminant analysis (LDA), we propose a new convenient multi-view learning architecture, i.e., multi-view discriminative fusion on CCA (MvDF-CCA). Instead of pair-wise relation consideration among different views, MvDF-CCA separately aligns each view space to the target one comprised by labeled indicators, which is easy expanding to additional view data. MvDF-CCA leverages the discriminative ability in LDA and the strengths in CCA, and maps all view spaces to the same target labeled space, which can be concurrent execution on large scale video categorization. Competitive results are reported on the well-known UCF101 and Columbia Consumer Video (CCV) benchmarks.

Steady State Visual Evoked Potential (SSVEP) has been commonly adopted in Brain Computer Interface (BCI) applications. For wearable BCI applications, several aspects of SSVEP-based BCI systems, such as speed, subject variability, and accurate target detection, are under ongoing research investigations. Up to date, Canonical Correlation Analysis (CCA) has been considered the state-of-the-art feature extraction method for SSVEP-based BCI systems. Nevertheless, although CCA outperforms traditional SSVEP detection methods, such as Power Spectral Density Analysis (PSDA), achieving high accuracies when detecting target frequencies is still a challenging task due to user variation and physiological changes in the human body. In this paper, we investigate an SSVEP-based BCI application using wireless EEG recording and an Android tablet-based user interface. We propose a fusion of CCA and PSDA solutions at the score level by dividing their score space into multiple partitions, and extract and combine their complementary discriminative information to minimize the detection error in a linear fashion. We investigated transforming the fusion score space to lower dimensions with the purpose of alleviating redundancy. As such, we employed Principal Component Analysis (PCA), and Linear Discriminant Analysis (LDA). Our experimental results demonstrated that our proposed score fusion method is effective in reducing the effect of noise and non-stationary elements in EEG dynamics. Average detection accuracies improved from 63% for CCA to 72% for fusion+PCA and further improved to 98% for fusion+LDA.

Chapter 11 - Canonical analysis

We address the problem of comparing sets of images for object recognition, where the sets may represent variations in an object's appearance due to changing camera pose and lighting conditions. Canonical Correlations (also known as principal or canonical angles), which can be thought of as the angles between two d-dimensional subspaces, have recently attracted attention for image set matching. Canonical correlations offer many benefits in accuracy, efficiency, and robustness compared to the two main classical methods: parametric distribution-based and nonparametric sample-based matching of sets. Here, this is first demonstrated experimentally for reasonably sized data sets using existing methods exploiting canonical correlations. Motivated by their proven effectiveness, a novel discriminative learning method over sets is proposed for set classification. Specifically, inspired by classical Linear Discriminant Analysis (LDA), we develop a linear discriminant function that maximizes the canonical correlations of within-class sets and minimizes the canonical correlations of between-class sets. Image sets transformed by the discriminant function are then compared by the canonical correlations. Classical orthogonal subspace method (OSM) is also investigated for the similar purpose and compared with the proposed method. The proposed method is evaluated on various object recognition problems using face image sets with arbitrary motion captured under different illuminations and image sets of 500 general objects taken at different views. The method is also applied to object category recognition using ETH-80 database. The proposed method is shown to outperform the state-of-the-art methods in terms of accuracy and efficiency.

Hotelling’s Canonical Correlation Analysis (CCA) works with two sets of related variables, also called views, and its goal is to find their linear projections with maximal mutual correlation. CCA is most suitable for unsupervised feature extraction when given two views but it has been also long known that in supervised learning when there is only a single view of data given, the supervision signal (class-labels) can be given to CCA as the second view and CCA simply reduces to Fisher’s Linear Discriminant Analysis (LDA). However, it is unclear how to use this equivalence for extracting features from multiview data in semisupervised setting (i.e. what modification to the CCA mechanism could incorporate the class-labels along with the two views of the data when labels of some samples are unknown). In this paper, a CCA-based method supplemented by the essence of LDA is proposed for semi-supervised feature extraction from multiview data.KeywordsSemisupervised LearningFeature ExtractionMultiview LearningLDACCA

Learning representations that disentangle hidden explanatory factors in data has proven beneficial for effective pattern classification. Slow feature analysis (SFA) is a nonlinear dimensionality reduction technique that provides a useful representation for classification if the training data is sequential and transitions between classes are rare. The pattern discrimination ability of SFA has been attributed to the equivalence of linear SFA and linear discriminant analysis (LDA) under certain conditions. LDA, however, is often outperformed by locality preserving projections (LPP) when the data lies on or near a low-dimensional manifold. Here, we take a unified manifold learning perspective on LPP, LDA and SFA. We suggest that the discrimination ability of SFA is better explained by its relation to LPP than to LDA, and give an example of a situation where linear SFA outperforms LDA. We then propose a novel supervised manifold learning architecture that combines hierarchical nonlinear expansions, as commonly used for SFA, with supervised LPP. It learns a nonlinear parametric data representation that explicitly takes both the class labels and the manifold structure of the data into account. As an experimental validation, we show that this approach outperforms previously proposed models on the NORB object recognition dataset.

Face recognition using direct, weighted linear discriminant analysis and modular subspaces

Classification accuracy and correlation: LDA in failure prediction

Vegetation indices derived from remote sensing measurements are commonly used to describe and monitor vegetation. However, the same plant community can have a different NDVI (normalized difference vegetation index) depending on weather conditions, and this complicates classification of plant communities. The present study develops methods of classifying the types of plant communities based on long-term NDVI data (MODIS/Aqua). The number of variables is reduced by introducing two integrated parameters of the NDVI seasonal series, facilitating classification of the meadow, steppe, and forest plant communities in Siberia using linear discriminant analysis. The quality of classification conducted by using the markers characterizing NDVI dynamics during 2003–2017 varies between 94% (forest and steppe) and 68% (meadow and forest). In addition to determining phenological markers, canonical correlations have been calculated between the time series of the proposed markers and the time series of monthly average air temperatures. Based on this, each pixel with a definite plant composition can be characterized by only four values of canonical correlation coefficients over the entire period analyzed. By using canonical correlations between NDVI and weather parameters and employing linear discriminant analysis, one can obtain a highly accurate classification of the study plant communities.

Canonical correlation analysis (CCA) has recently attracted great attention and many experimental results have illustrated its effectiveness. In this paper, we study the relationship between CCA classifier and minimum squared error (MSE) classifier. It helps us look into the nature of CCA classifier. In traditional CCA method, the class-membership matrix is deliberately coded in full rank. Under this case, we will prove CCA is equivalent to MSE classifier. It is also shown that even the class-membership matrix is centered and thus not in full rank, CCA is equivalent to Fisher linear discriminant analysis (FDA). Some experiments are presented to verify the results.

Face recognition using direct, weighted linear discriminant analysis and modular subspaces

Facial Expression recognition has become vital considering its numerous applications including Human Computer Interaction, security, medical field etc. In order to effectively implement these applications, the proposed method aims to increase the overall accuracy and robustness of the recognition system. Fusion of two feature extraction methods, namely Gabor and Local Directional Pattern (LDP) that are complementary in nature is carried out. Gabor Features focuses on the structural details whereas LDP targets the textural and subtler details in a robust manner. Fusion is carried out using Canonical Correlation Analysis (CCA) based fusion, as it effectively utilizes the correlation between the two features for fusion. For the efficient training of the classifiers, optimal feature vector is obtained by projecting the original feature vector on Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) subspace. To prove the robustness of the proposed method, it is tested on benchmark datasets under ideal as well as different conditions such as noisy environment, low resolution, small sample space, different facial components etc. The method has shown better performance than the state of the art methods.

Heavy metal lead (Pb) is a primary pollutant that pollutes aquatic environments and can be enriched in aquatic animals. Here, the effects of waterborne Pb on grass carp (Ctenopharyngodon idella) within 96 h of exposure were detected, and the association between microbiota alterations in the intestines and water was analysed. Results revealed that the intestinal barrier was damaged, including the intestinal morphology change, the structure-related genes (villin-1 and Claudin-7) expression down-regulation, the antioxidant (GST and GSH-Px) and immune-related genes (TNF-α and IL-8) expression up-regulation. The MiSeq sequencing data revealed a decrease in diversity and an increase in microbiota richness in the intestines and water after Pb exposure. Linear discriminant analysis (LDA) results revealed an increase in the dominant bacteria (P_proteobacteria and C_Gammaproteobacteria) in the water, which enriched bacteria in the intestines. Canonical correlation analysis (CCA) found that there were correlations between intestinal microbiota and water microbiota, intestinal structure morphology and immune factors. Based on these results, we speculated that the effects of Pb on the grass carp intestinal barrier may be related to changes in the intestinal structure of grass carp and the water microbial community. These findings improve our understanding of the effects of heavy metals on the fish–microbe relationships after polluting aquatic habitats.