Solving the small sample size problem in face recognition using generalized discriminant analysis

The goal of face recognition is to distinguish persons via their facial images. Each person's images form a cluster, and a new image is recognized by assigning it to the correct cluster. Since the images are very high-dimensional, it is necessary to reduce their dimension. Linear discriminant analysis (LDA) has been shown to be effective at dimension reduction while preserving the cluster structure of the data. It is classically defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be nonsingular restricts its application to datasets in which the dimension of the data does not exceed the sample size. For face recognition, however, the dimension typically exceeds the number of images in the database, resulting in what is referred to as the small sample size problem. Recently, the applicability of LDA has been extended by using the generalized singular value decomposition (GSVD) to circumvent the nonsingularity requirement, thus making LDA directly applicable to face recognition data. Our experiments confirm that LDA/GSVD solves the small sample size problem very effectively as compared with other current methods.     

A stochastic realization algorithm via block LQ decomposition in Hilbert space

A stochastic realization problem of a stationary stochastic process is re-visited, and a new stochastically balanced realization algorithm is derived in a Hilbert space generated by second-order stationary processes. The present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block Hankel matrix derived by a “block LQ decomposition”. Extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification.     

基于奇异值分解和神经网络的个性化信息模式识别

随着信息资源的持续增长，信息获取系统为特定用户提供特定信息服务的需求越来越重要。该文提出了基于奇异值分解和神经网络的个性化信息模式识别的方法，可以方便地获取用户信息需求的特征，并且利用这些特征信息完成个性化的信息识别和匹配，即实现个性化信息的模式识别，进而实现信息的个性化获取和管理。该文中的算法实现简单，可以方便地应用到目前的一些信息管理、服务系统中。     

非透视3点问题的解析解

由于在机器人导航等领域新的图像装置不符合透视规则,无法运用传统的透视位置估计方法,采用吴氏零点分解方法,给出非透视3点问题的解析解.利用新图像装置的几何条件,建立了非透视3点方程系统.     

蒸汽压法测定导热油热分解温度的研究

根据克拉贝龙—克劳修斯方程，建立了国内外文献未见报道的测定导热油热分解温度的试验装置和试验方法，测定了大量国内外导热油的热分解温度，数据表明该法具有准确、简单、实用、省时、省力等优点     

Catalytic decomposition of HCFC22 (CHClF2)

The catalytic decomposition of CHClF₂ was studied over various acidic metal oxides in a fixed-bed reactor. The Cr₂O₃ZrO₂ exhibited the highest activity. The presence of water vapor in the reaction system suppresses the transformation of oxides to fluorides, progresses the formation of CO₂, and it improves the catalysts life.     

大规模电力系统不对称短路的分块射影解法

本文把网络的分块射影法用于大规模电力系统不对称短路的分析计算。研究表明：该方法对短路计算是可行的。一旦求出了射影张量，即可重复用于后续的计算，只需改变故障所在的那一个子网络的射影张量。本文提出的网络分块射影算法为大规模电力系统的分析计算提供了一条崭新的途径。     

利用独立分量分析法去除地震噪声

 独立分量分析（ICA）作为盲源分离（BSS）的一种新方法,是分解观测数据中独立信息的有力工具。以往的ICA算法一般假设噪声可以忽略不计，而实际的观测数据中又常常包含一些加性噪声。对于加性噪声的影响不能忽略的情况下，改进的ICA算法首先利用非零时间滞后协方差，应用两步特征值分解法(EVD)可成功地去除部分加性噪声的影响；再利用ICA算法就能更好地分离出原信号。本文通过对地震理论模型和实际资料的试验，说明改进的ICA算法能够有效地克服加性噪声对常规ICA算法的影响，能够分离出地震资料中的有效信号，从而实现利用独立分量分析压制地震资料噪声的目的。     

一次国际设计竞赛的尝试--多维住宅设计

在后工业时代，建筑设计已经冲破了西方思维所惯用的二元对立方式的约束，呈现出日新月异的景象，建筑表皮的创作尤为突出。这个住宅设计是从四维分解到四维连续的一种大胆尝试，并引入拓扑学的基本方法处理动态空间。