Supervised Dimensionality Reduction Method Research Articles

Dimensionality reduction-based spoken emotion recognition

To improve effectively the performance on spoken emotion recognition, it is needed to perform nonlinear dimensionality reduction for speech data lying on a nonlinear manifold embedded in a high-dimensional acoustic space. In this paper, a new supervised manifold learning algorithm for nonlinear dimensionality reduction, called modified supervised locally linear embedding algorithm (MSLLE) is proposed for spoken emotion recognition. MSLLE aims at enlarging the interclass distance while shrinking the intraclass distance in an effort to promote the discriminating power and generalization ability of low-dimensional embedded data representations. To compare the performance of MSLLE, not only three unsupervised dimensionality reduction methods, i.e., principal component analysis (PCA), locally linear embedding (LLE) and isometric mapping (Isomap), but also five supervised dimensionality reduction methods, i.e., linear discriminant analysis (LDA), supervised locally linear embedding (SLLE), local Fisher discriminant analysis (LFDA), neighborhood component analysis (NCA) and maximally collapsing metric learning (MCML), are used to perform dimensionality reduction on spoken emotion recognition tasks. Experimental results on two emotional speech databases, i.e. the spontaneous Chinese database and the acted Berlin database, confirm the validity and promising performance of the proposed method.

Hierarchical anatomical brain networks for MCI prediction: revisiting volumetric measures.

Owning to its clinical accessibility, T1-weighted MRI (Magnetic Resonance Imaging) has been extensively studied in the past decades for prediction of Alzheimer's disease (AD) and mild cognitive impairment (MCI). The volumes of gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF) are the most commonly used measurements, resulting in many successful applications. It has been widely observed that disease-induced structural changes may not occur at isolated spots, but in several inter-related regions. Therefore, for better characterization of brain pathology, we propose in this paper a means to extract inter-regional correlation based features from local volumetric measurements. Specifically, our approach involves constructing an anatomical brain network for each subject, with each node representing a Region of Interest (ROI) and each edge representing Pearson correlation of tissue volumetric measurements between ROI pairs. As second order volumetric measurements, network features are more descriptive but also more sensitive to noise. To overcome this limitation, a hierarchy of ROIs is used to suppress noise at different scales. Pairwise interactions are considered not only for ROIs with the same scale in the same layer of the hierarchy, but also for ROIs across different scales in different layers. To address the high dimensionality problem resulting from the large number of network features, a supervised dimensionality reduction method is further employed to embed a selected subset of features into a low dimensional feature space, while at the same time preserving discriminative information. We demonstrate with experimental results the efficacy of this embedding strategy in comparison with some other commonly used approaches. In addition, although the proposed method can be easily generalized to incorporate other metrics of regional similarities, the benefits of using Pearson correlation in our application are reinforced by the experimental results. Without requiring new sources of information, our proposed approach improves the accuracy of MCI prediction from (of conventional volumetric features) to (of hierarchical network features), evaluated using data sets randomly drawn from the ADNI (Alzheimer's Disease Neuroimaging Initiative) dataset.

Large correlation analysis

In this paper, a novel supervised dimensionality reduction method is developed based on both the correlation analysis and the idea of large margin learning. The method aims to maximize the minimal correlation between each dimensionality-reduced instance and its class label, thus named as large correlation analysis (LCA). Unlike most existing correlation analysis methods such as CCA, CCAs and CDA, which all maximize the total or ensemble correlation over all training instances, LCA devotes to maximizing the individual correlations between given instances and its associated labels and is established by solving a relaxed quadratic programming with box-constraints. Experimental results on real-world datasets from both UCI and USPS show its effectiveness compared to the existing canonical correlation analysis methods.

Central Subspace Dimensionality Reduction Using Covariance Operators

We consider the task of dimensionality reduction informed by real-valued multivariate labels. The problem is often treated as Dimensionality Reduction for Regression (DRR), whose goal is to find a low-dimensional representation, the central subspace, of the input data that preserves the statistical correlation with the targets. A class of DRR methods exploits the notion of inverse regression (IR) to discover central subspaces. Whereas most existing IR techniques rely on explicit output space slicing, we propose a novel method called the Covariance Operator Inverse Regression (COIR) that generalizes IR to nonlinear input/output spaces without explicit target slicing. COIR's unique properties make DRR applicable to problem domains with high-dimensional output data corrupted by potentially significant amounts of noise. Unlike recent kernel dimensionality reduction methods that employ iterative nonconvex optimization, COIR yields a closed-form solution. We also establish the link between COIR, other DRR techniques, and popular supervised dimensionality reduction methods, including canonical correlation analysis and linear discriminant analysis. We then extend COIR to semi-supervised settings where many of the input points lack their labels. We demonstrate the benefits of COIR on several important regression problems in both fully supervised and semi-supervised settings.

Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

We consider the problem of combining multiple dissimilarity representations via the Cartesian product of their embeddings. For concreteness, we choose the inferential task at hand to be classification. The high dimensionality of this Cartesian product space implies the necessity of dimensionality reduction before training a classifier. We propose a supervised dimensionality reduction method, which utilizes the class label information, to help achieve a favorable combination. The simulation and real data results show that our approach can improve classification accuracy compared to the alternatives of principal components analysis and no dimensionality reduction at all.

Linear discriminant projection embedding based on patches alignment

Dimensionality reduction is often required as a preliminary stage in many data analysis applications. In this paper, we propose a novel supervised dimensionality reduction method, called linear discriminant projection embedding (LDPE), for pattern recognition. LDPE first chooses a set of overlapping patches which cover all data points using a minimum set cover algorithm with geodesic distance constraint. Then, principal component analysis (PCA) is applied on each patch to obtain the data's local representations. Finally, patches alignment technique combined with modified maximum margin criterion (MMC) is used to yield the discriminant global embedding. LDPE takes both label information and structure of manifold into account, thus it can maximize the dissimilarities between different classes and preserve data's intrinsic structures simultaneously. The efficiency of the proposed algorithm is demonstrated by extensive experiments using three standard face databases (ORL, YALE and CMU PIE). Experimental results show that LDPE outperforms other classical and state of art algorithms.

Feature extraction by learning Lorentzian metric tensor and its extensions

We develop a supervised dimensionality reduction method, called Lorentzian discriminant projection (LDP), for feature extraction and classification. Our method represents the structures of sample data by a manifold, which is furnished with a Lorentzian metric tensor. Different from classic discriminant analysis techniques, LDP uses distances from points to their within-class neighbors and global geometric centroid to model a new manifold to detect the intrinsic local and global geometric structures of data set. In this way, both the geometry of a group of classes and global data structures can be learnt from the Lorentzian metric tensor. Thus discriminant analysis in the original sample space reduces to metric learning on a Lorentzian manifold. We also establish the kernel, tensor and regularization extensions of LDP in this paper. The experimental results on benchmark databases demonstrate the effectiveness of our proposed method and the corresponding extensions.

Semi-supervised local Fisher discriminant analysis for dimensionality reduction

When only a small number of labeled samples are available, supervised dimensionality reduction methods tend to perform poorly because of overfitting. In such cases, unlabeled samples could be useful in improving the performance. In this paper, we propose a semi-supervised dimensionality reduction method which preserves the global structure of unlabeled samples in addition to separating labeled samples in different classes from each other. The proposed method, which we call SEmi-supervised Local Fisher discriminant analysis (SELF), has an analytic form of the globally optimal solution and it can be computed based on eigen-decomposition. We show the usefulness of SELF through experiments with benchmark and real-world document classification datasets.

Neighborhood discriminant tensor mapping

Linear dimensionality reduction (feature extraction) methods have been widely used in computer vision and pattern recognition. Two of the most representative methods are principal component analysis ( PCA) and linear discriminant analysis ( LDA). However, when dealing with a multidimensional dataset of dimension R m 1 ⊗ R m 1 ⊗ ⋯ ⊗ R m N (e.g. for images N = 2 , videos N = 3 ), these methods usually first transform the original data to high dimensional vectors in R m 1 × m 2 × ⋯ × m N , and then analyze the data in such a high dimensional space. In this paper, we propose a supervised dimensionality reduction method called neighborhood discriminative tensor mapping ( NDTM), which can directly process the multidimensional data as tensors. Moreover, NDTM can make use of the local information of the dataset to achieve a better classification result. Experimental results on face recognition show the superiority of our algorithm to traditional dimensionality reduction methods.

Face Recognition Using Classification-Based Linear Projections

Subspace methods have been successfully applied to face recognition tasks. In this study we propose a face recognition algorithm based on a linear subspace projection. The subspace is found via utilizing a variant of the neighbourhood component analysis (NCA) algorithm which is a supervised dimensionality reduction method that has been recently introduced. Unlike previously suggested supervised subspace methods, the algorithm explicitly utilizes the classification performance criterion to obtain the optimal linear projection. In addition to its feature extraction capabilities, the algorithm also finds the optimal distance-metric that should be used for face-image retrieval in the transformed space. The proposed face-recognition technique significantly outperforms traditional subspace-based approaches particulary in very low-dimensional representations. The method performance is demonstrated across a range of standard face databases.

Incremental Linear Discriminant Analysis for Face Recognition

Dimensionality reduction methods have been successfully employed for face recognition. Among the various dimensionality reduction algorithms, linear (Fisher) discriminant analysis (LDA) is one of the popular supervised dimensionality reduction methods, and many LDA-based face recognition algorithms/systems have been reported in the last decade. However, the LDA-based face recognition systems suffer from the scalability problem. To overcome this limitation, an incremental approach is a natural solution. The main difficulty in developing the incremental LDA (ILDA) is to handle the inverse of the within-class scatter matrix. In this paper, based on the generalized singular value decomposition LDA (LDA/GSVD), we develop a new ILDA algorithm called GSVD-ILDA. Different from the existing techniques in which the new projection matrix is found in a restricted subspace, the proposed GSVD-ILDA determines the projection matrix in full space. Extensive experiments are performed to compare the proposed GSVD-ILDA with the LDA/GSVD as well as the existing ILDA methods using the face recognition technology face database and the Carneggie Mellon University Pose, Illumination, and Expression face database. Experimental results show that the proposed GSVD-ILDA algorithm gives the same performance as the LDA/GSVD with much smaller computational complexity. The experimental results also show that the proposed GSVD-ILDA gives better classification performance than the other recently proposed ILDA algorithms.