• Journal of the Korean Statistical Society
• /
• v.16 no.1
• /
• pp.45-51
• /
• 1987

The condition that two hyper-ellipsoids have no points in common is derived using the simultaneous diagonalization of the two hyper-ellipsoids. It is observed that the simultaneous diagonalization is composed of rotation and extension followed by another rotation. An approximation to this condition in terms of the generalized distance is discussed.

• Journal of KIISE
• /
• v.42 no.2
• /
• pp.235-241
• /
• 2015

Locally linear embedding (LLE) [1] is a type of manifold algorithms, which preserves inner product value between high-dimensional data when embedding the high-dimensional data to low-dimensional space. LLE closely embeds data points on the same subspace in low-dimensional space, because the data points have significant inner product values. On the other hand, if the data points are located orthogonal to each other, these are separately embedded in low-dimensional space, even though they are in close proximity to each other in high-dimensional space. Meanwhile, it is well known that the facial images of the same person under varying illumination lie in a low-dimensional linear subspace [2]. In this study, we suggest an improved LLE method for face recognition problem. The method maximizes the characteristic of LLE, which embeds the data points totally separately when they are located orthogonal to each other. To accomplish this, all of the subspaces made by each class are forced to locate orthogonally. To make all of the subspaces orthogonal, the simultaneous Diagonalization (SD) technique was applied. From experimental results, the suggested method is shown to dramatically improve the embedding results and classification performance.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.15 no.4
• /
• pp.14-19
• /
• 1978

Here a method is shown to extract features from two multi-variable classes by using the coordinate systems transformed by one-class and mixture normalization algorithms. Some properties and implemented results of this technique are described. Also, comparision of these features with factor analysis results is performed. This method is thought to be more powerful one, in feature extraction sense, than factor analysis.

• Journal of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.507-528
• /
• 2006

In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

• Journal of the Korean Institute of Telematics and Electronics B
• /
• v.31B no.11
• /
• pp.97-108
• /
• 1994

A modified Karhunen-Loeve transformation technique using normalization and simultaneous diagonalization of two sample covariance matrices is proposed to separate the object from the background. The transformation technique for the separation of local data structure through maximizing the ratio of sample variances between two classes was identified as a promising one for a preprocessing of multi-variate signal processing algorithms using neighborhood operators including morphological filtering. To relate the separation quality of the proposed technique to a morphological measure, average height was defined by using morphological pattern spectrum. A practical implementation of the transformation technique was tested experimentally and the theoretical results were confirmed.