Kenji Watanabe

Fisher's linear discriminant analysis (FLDA) is known as a method to find a discriminative feature space for multi-class classification. As a theory of extending FLDA to an ultimate nonlinear form, optimal nonlinear discriminant analysis (ONDA) has been proposed. ONDA indicates that the best theoretical nonlinear map for maximizing the Fisher's discriminant criterion is formulated by using the Bayesian a posterior probabilities. In addition, the theory proves that FLDA is equivalent to ONDA when the Bayesian a posterior probabilities are approximated by linear regression (LR). Due to some limitations of the linear model, there is room to modify FLDA by using stronger approximation/estimation methods. For the purpose of probability estimation, multi-nominal logistic regression (MLR) is more suitable than LR. Along this line, in this paper, we develop a nonlinear discriminant analysis (NDA) in which the posterior probabilities in ONDA are estimated by MLR. In addition, in this paper, we develop a way to introduce sparseness into discriminant analysis. By applying L1 or L2 regularization to LR or MLR, we can incorporate sparseness in FLDA and our NDA to increase generalization performance. The performance of these methods is evaluated by benchmark experiments using last_exam17 standard datasets and a face classification experiment.

Semantic segmentation is an object classification such as a perceptual grouping in image analysis tasks. And semantic segmentation methods have been proposed to improve the pixel-wise classification accuracies in the research field of computer vision. Recently, the methods achieve high accuracies by using convolutional neural networks (CNN). These CNN-based methods generally need large number and variety of training images to assure a generalization performance without fine tuning. However, it is difficult to prepare the large-scale image datasets which were given reliable semantic labels. In order to overcome this problem, we propose an efficient method for feature transformation to improve the generalization performance in semantic segmentation. Our method is formulated as a variant of neighborhood preserving embedding (NPE) incorporating the within-class coherency and showed best generalization performances compared with other feature transformation methods.

Various systems have been proposed to support biological image analysis, with the intent of decreasing false annotations and reducing the heavy burden on biologists. These systems generally comprise a feature extraction method and a classification method. Task-oriented methods for feature extraction leverage characteristic images for each problem, and they are very effective at improving the classification accuracy. However, it is difficult to utilize such feature extraction methods for versatile task in practice, because few biologists specialize in Computer Vision and/or Pattern Recognition to design the task-oriented methods. Thus, in order to improve the usability of these supporting systems, it will be useful to develop a method that can automatically transform the image features of general propose into the effective form toward the task of their interest. In this paper, we propose a semi-supervised feature transformation method, which is formulated as a natural coupling of principal component analysis (PCA) and linear discriminant analysis (LDA) in the framework of graph-embedding. Compared with other feature transformation methods, our method showed favorable classification performance in biological image analysis.

For object detection, large-scale databases obtained via an in-vehicle camera have been proposed. The databases are generally used to evaluate object detection methods and/or to train classifiers in these methods. When proposing a new database, we should evaluate the characteristics of a large number of the samples in the database to improve the usability of the proposed database. In the evaluation, discriminant analysis is useful for visualizing the sample distribution of the database, and the visualized distributions show the statistical characteristics of the annotated (labeled) samples. In this paper, we propose a database analysis procedure using logistic discriminant analysis and demonstrate the visualization and evaluation of an object image database.

Discriminating feature extraction is important to achieve high recognition rate in a classification problem. Fisher's linear discriminant analysis (LDA) is one of the well-known discriminating feature extraction methods and is closely related to the Mahalanobis distance metric learning. Neighborhood component analysis (NCA) is one of the Mahalanobis distance metric learning methods based on stochastic nearest neighbor assignment. The objective function of NCA can be expressed as a within-class coherency by a simple formula, and NCA extracts discriminating features by minimizing the objective function. Unfortunately, the computational cost of NCA significantly increases as the number of input data increases. For reducing the computational cost, we propose a fast distance metric learning method by taking the between-class distinguish ability into account of nearest mean classification. According to the experimental results using standard repository datasets, the computational time of our method is evaluated as 27 times shorter than that of NCA while keeping or improving the accuracy.

Linear discriminant analysis (LDA) is a well-known method to extract efficient features for multi-class classification. Otsu derived the optimal (ultimate) non-linear discriminant analysis (ONDA) by supposing underlying probabilities and showed that ONDA was closely related to Bayesian decision theory (posterior probabilities). Also Otsu pointed out that the usual LDA could be regarded as the linear approximation of this ultimate ONDA through the linear approximations of the Bayesian posterior probabilities. This theory of ONDA suggests that we can construct a novel nonlinear discriminant mapping by utilizing the estimates of the posterior probabilities. Based on this theory, logistic discriminant analysis (LgDA) was proposed by one of the authors as the approximation of ONDA. In LgDA, the posterior probabilities are estimated by logistic regression. In this paper, we propose the sparse logistic discriminant analysis in which the posterior probabilities are estimated by the sparse logistic regression with L2-or L1-regularizer to improve the generalization performance of LgDA further. Experiments using the standard datasets for classification reveal that the discriminant spaces by our proposed method (LgDA-L2 and LgDA-L1) are better than those by LDA and LgDA in terms of the recognition rates for test samples.

In time-resolved spectroscopy, composite signal sequences representing energy transfer in fluorescence materials are measured, and the physical characteristics of the materials are analyzed. Each signal sequence is represented by a sum of non-negative signal components, which are expressed by model functions. For analyzing the physical characteristics of a measured signal sequence, the parameters of the model functions are estimated. Furthermore, in order to quantitatively analyze real measurement data and to reduce the risk of improper decisions, it is necessary to obtain the statistical characteristics from several sequences rather than just a single sequence. In the present paper, we propose an automatic method by which to analyze composite signals using non-negative factorization and an information criterion. The proposed method decomposes the composite signal sequences using non-negative factorization subjected to parametric base functions. The number of components (i.e., rank) is also estimated using Akaike's information criterion. Experiments using simulated and real data reveal that the proposed method automatically estimates the acceptable ranks and parameters.

In the cancer detection from stained biopsy images, it is important to extract histologically discriminative characteristics. For this purpose, we propose a novel method to extract statistical and morphological features. At the first stage, we estimate cell component memberships at each pixel by applying an expectation maximization (EM) algorithm to the color information. Next we calculate the local co-occurrence of the memberships as image features. And then, linear discriminant analysis (LDA) is applied to those features for final decision of whether cancer or not, with enhancing the discrimination. In the experiments on real biopsy images of cancers, the resulting detection accuracy is superior to the other methods.