Canonical Correlation Analysis for Multiview Semisupervised Feature Extraction

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.

Canonical correlation analysis using within-class coupling

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.

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.

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.

Dimensionality reduction of image features using the canonical contextual correlation projection

Chapter 11 - Canonical analysis

M25 - Investigation of Relationships Between Bipolar Disorder Phenotypes And Genome-Wide Significant Loci From PGC2 Schizophrenia

A feature extraction method for Facial Expression Recognition Systems is proposed based on CCA using FMEDA and DPA. For proper classification of expression it has been trained with Recurrent neural network. The Cohn Kanade Extensive, ORL and Yale databases are used in this paper. The images have been preprocessed using image normalization and then contrast limited adaptive histogram equalization to remove the illumination variance and noises. After down-sampling, the dimensions with factor data is provided to Canonical Correlation Analysis that finds the linear combinations among two sets of variables for determining correlation with each other. DPA and FMEDA have been used to extract features from specially low frequency coefficients of the image as some of the low frequency coefficients have more discrimination power compared to others and by extracting those features a higher true recognition rate can be achieved. The results provided in this paper show the advantage of this method compared to other methods like Principal Component Analysis and Linear Discriminant Analysis which uses between and within class scatter matrices and try to maximize the discrimination in transformed domain. This method searches for best discrimination features in transformed domain. Dimensionally reduced data is provided to recurrent neural network for training purpose. Meanwhile, the proposed method is more robust and effective compared to other methods in this field.

Feature fusion is important for providing enhancements of data authenticity in both traditional and deep learning pattern analysis. Classical serial fusion concatenates multiple feature sets followed by dimensionality reduction using principal component analysis (PCA), linear discriminant analysis (LDA), canonical correlation analysis (CCA) etc. CCA-based feature fusion is a main technique for exploring the mutual relationships of multiple feature sets. It considers the correlation of multiple feature sets during dimensionality reduction. In traditional CCA-based feature fusion and extraction, the natural groupings of features are directly used. It is still unclear whether the natural groupings of features are optimal for CCA-based fusion. In this paper, we propose a feature regrouping algorithm for CCA-based feature fusion and extraction through normalized cut (FR-NC). Feature correlation analysis is incorporated into normalized cut, in which the intra-group correlation is maximized, and the extra-group correlation is minimized simultaneously. CCA-based feature fusion is performed on the regrouped features. The proposed feature regrouping algorithm aims to provide enhanced fused features for pattern classification. Extensive experiments have proved its effectiveness.

Steady-state visual evoked potential (SSVEP) has been widely applied in brain computer interface (BCI) systems. The amplitude and phase features of SSVEP were commonly extracted by Fourier analysis method from single-channel EEG data. In the multichannel case, canonical correlation analysis (CCA) has been utilized for the analysis of frequency coding SSVEP. This paper presents the analysis of phase coding SSVEP using CCA. The phase coding scheme consists of six targets flickering at 10Hz, with a 60° phase difference between any two sequential targets. For each target, 20 trials of 8s EEG signal were acquired. Using CCA, we achieve channel selection and extraction of phase features; a classification accuracy of above 80% is obtained, with the length of the time window up to 4s. The results demonstrate that phase coding SSVEP analysis based on CCA is feasible.

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.

A classification algorithm of an SSVEP brain-Computer interface based on CCA fusion wavelet coefficients

Since standard canonical correlation analysis (CCA) works with vectorized representations of data, an limitation is that it may suffer small sample size problems. Moreover, two-dimensional CCA (2D-CCA) extracts unsupervised features and thus ignores the useful prior class information. This makes the extracted features by 2D-CCA hard to discriminate the data from different classes. To solve this issue, we simultaneously take the prior class information of intra-view and inter-view samples into account and propose a new 2D-CCA method referred to as supervised two-dimensional CCA (S2CCA), which can be used for multi-view feature extraction and classification. The method we propose is available to face recognition. To verify the effectiveness of the proposed method, we perform a number of experiments on the AR, AT&T, and CMU PIE face databases. The results show that the proposed method has better recognition accuracy than other existing multi-view feature extraction methods.

Color vision deficiency (CVD), a common visual impairment, affects individuals' ability to differentiate between various colors due to malfunctioning or absent color photoreceptors in the retina. Currently available diagnostic tests require a behavioral response, rendering them unsuitable for individuals with limited physical and communication abilities, such as those with locked-in syndrome. This study introduces a novel, non-invasive method that employs brain signals, specifically Steady-State Visually Evoked Potentials (SSVEPs), along with Ishihara plates to diagnose CVD. This method aims to provide an alternative diagnostic tool that addresses the limitations of current tests. Electroencephalography (EEG) recordings were obtained from 16 subjects, including 5 with CVD (specifically Deuteranomaly), using channels O1, O2, Pz, and Cz. The subjects were exposed to visual stimuli at frequencies of 15 Hz and 18 Hz to assess the proposed method. The subjects focused on specific visual stimuli in response to questions related to the Ishihara plates. Their responses were analyzed to determine the presence of CVD. Feature extraction was performed using Power Spectral Density (PSD), Canonical Correlation Analysis (CCA), and a combined PSD + CCA, followed by classification to categorize subjects into two classes: normal vision and CVD. The results indicate that the proposed method effectively diagnoses CVD in individuals with limited communication abilities. The classification accuracy of SSVEP exceeded 75% across the three classifiers: Decision Tree (DT), K-Nearest Neighbors (KNN), and Support Vector Machine (SVM). The SVM classifier demonstrated higher accuracy compared to the other classifiers, exceeding 90%. These observations suggest that the SVM classifier, utilizing the combined feature set of PSD + CCA, may be the most effective in this classification task. These findings demonstrate that the proposed method is an accurate and reliable diagnostic tool for CVD, particularly for individuals unable to communicate.