Continuum Direction Vectors in High Dimensional Low Sample Size Data

This dissertation consists of three parts regarding High Dimensional Low Sample Size (HDLSS) data analysis. Dimension reduction techniques in high dimensional space, based on a small number of direction vectors, will be the common theme. In the first part of the dissertation, Continuum Regression, originally proposed by Stone and Brooks (1990), will be understood as a family of methods for searching among direction vectors. Continuum Regression includes three popular methods- Ordinary Least Squares, Partial Least Squares, and Principal Component Regression - as special cases. The novel use of Continuum Regression in HDLSS settings will be illustrated by an application to microarray experiments. In the second part of the dissertation, we will extend the Continuum Regression idea to the challenging case of paired HDLSS data. The extended method, Continuum Canonical Correlation, is proposed, as a family of methods for searching direction vectors over two high dimensional spaces simultaneously. The last part of the dissertation studies the HDLSS asymptotic behavior of the maximum covariance direction vectors over two data spaces, i.e., the singular vectors of the sample cross-covariance matrix. We find some conditions under which consistency and strong inconsistency of the singular vectors in HDLSS is observed

Proto-Model of an Infrared Wide-Field Off-Axis Telescope

We develop a proto-model of an off-axis reflective telescope for infrared wide-field observations based on the design of Schwarzschild-Chang type telescope. With only two mirrors, this design achieves an entrance pupil diameter of 50 mm and an effective focal length of 100 mm. We can apply this design to a mid-infrared telescope with a field of view of 8 deg X 8 deg. In spite of the substantial advantages of off-axis telescopes in the infrared compared to refractive or on-axis reflective telescopes, it is known to be difficult to align the mirrors in off-axis systems because of their asymmetric structures. Off-axis mirrors of our telescope are manufactured at the Korea Basic Science Institute (KBSI). We analyze the fabricated mirror surfaces by fitting polynomial functions to the measured data. We accomplish alignment of this two-mirror off-axis system using a ray tracing method. A simple imaging test is performed to compare a pinhole image with a simulated prediction.Comment: 14 pages, 16 figure

ON SEMIDEFINITE LINEAR FRACTIONAL OPTIMIZATION PROBLEMS (Study on Nonlinear Analysis and Convex Analysis)

Recently, semidefinite optimization problems have been intensively studied since many optimization problems can be changed into the problems and the problems are very tractable ([5]). In this paper, we review the duality results for semidefinite linear fractional optimization problems in the paper ([3] On duality theorems for semidefinite linear fractional optimization problems, Journal of Nonliner and Convex Analysis, volume 20, 2019, 1907-1912)

Kernel continuum regression

The continuum regression technique provides an appealing regression framework connecting ordinary least squares, partial least squares and principal component regression in one family. It offers some insight on the underlying regression model for a given application. Moreover, it helps to provide deep understanding of various regression techniques. Despite the useful framework, however, the current development on continuum regression is only for linear regression. In many applications, nonlinear regression is necessary. The extension of continuum regression from linear models to nonlinear models using kernel learning is considered. The proposed kernel continuum regression technique is quite general and can handle very flexible regression model estimation. An efficient algorithm is developed for fast implementation. Numerical examples have demonstrated the usefulness of the proposed technique

Recycling Studies for Swine Manure Slurry Using Multi Process of Aerobic Digestion (MPAD)

This study was carried out to investigate the feasibility of Multi Process of Aerobic Digestion (MPAD) for recycling of swine manure slurry as fertilizer. MPAD consisted of three kinds of difference process which are thermophilic aerobic oxidation (TAO) system, lime solidification system, and reverse osmosis (R/O) membrane system. TAO system was studied well previously for decade. The chemical composition of the lime-treated solid fertilizer was as like that organic matter 17.4%, moisture 34.1%, N 0.9%, P 1.7%, K 0.3%, Ca 12.7%, and which was expected to be useful as acid soil amendment material. The concentrated liquid material produced by R/O membrane system was also expected as a good fertilizer for crops production and soil fertility improvement.OtherShinshu University International Symposium 2010 : Sustainable Agriculture and Environment : Asian Networks II 　信州大学国際シンポジウム2010 : 持続的農業と環境 : アジアネットワークII ― アジアネットワークの発展をめざして―. 信州大学農学部, 2010, 71-77conference pape