The numerical error of a sample Mahalanobis distance (T2=y'S-1y) with sample covariance matrix S is investigated. It is found that in order to suppress the numerical error of T2, the following conditions need to be satisfied. First, the reciprocal square root of the condition number of S should be larger than the relative error of calculating floating-point real-number variables. The second proposed condition is based on the relative error of the observed sample vector y in T2. If the relative error of y is larger than the relative error of the real-number variables, the former governs the numerical error of T2. Numerical experiments are conducted to show that the numerical error of T2 can be suppressed if the two above-mentioned conditions are satisfied.

Electroencephalography (EEG) and magnetoencephalography (MEG) measure the brain signal from spatially-distributed electrodes. In order to detect event-related synchronization and desynchronization (ERS/ERD), which are utilized for brain-computer/machine interfaces (BCI/BMI), spatial filtering techniques are often used. Common spatial potential (CSP) filtering and its extensions which are the spatial filtering methods have been widely used for BCIs. CSP transforms brain signals that have a spatial and temporal index into vectors via a covariance representation. However, the variance-covariance structure is essentially different from the vector space, and not all the information can be transformed into an element of the vector structure. Grassmannian embedding methods, therefore, have been proposed to utilize the variance-covariance structure of variational patterns. In this paper, we propose a metric learning method to classify the brain signal utilizing the covariance structure. We embed the brain signal in the extended Grassmann manifold, and classify it on the manifold using the proposed metric. Due to this embedding, the pattern structure is fully utilized for the classification. We conducted an experiment using an open benchmark dataset and found that the proposed method exhibited a better performance than CSP and its extensions.

This study examines the robustness of image quality factors in various types of environment illumination using a parameter design in the field of quality engineering. Experimental results revealed that image quality factors are influenced by environment illuminations in the following order: minimum luminance, maximum luminance and gamma.

In this paper, a new algorithm for selection of candidates for handwritten character recognition is presented. Since we adopt the concept of the marginal radius to examine the confidence of candidates, the evaluation function is required to describe the pattern distribution correctly. For this reason, we propose Simplified Mahalanobis distance and observe its behavior by simulation. In the proposed algorithm, first, for each character, two types of feature regions (multi-dimensional one and one-dimensional one) are estimated from training samples statistically. Then, by referring to the feature regions, candidates are selected and verified. Using two types of feature regions is a principal characteristic of our method. If parameters are estimated accurately, the multi-dimensional feature region is extremely effective for character recognition. But generally, estimation errors in parameters occur, especially with a small number of sample patterns. Although the recognition ability of one-dimensional feature region is not so high, it can express the distribution comparatively precisely in one-dimensional space. By combining these feature regions, they will work concurrently to overcome the defects of each other. The effectiveness of the method is shown with the results of experiments.