Modern analytical instrumentation is capable of creating enormous and complex volumes of data. Analysis of large data volumes are complicated by lengthy analysis time and high computational demand. Incorporating real-time analysis methods that are computationally efficient are desirable for modern analytical methods to be fully utilized. The use of modern instrumentation in on-line pharmaceutical process validation, remote sensing, and astrobiology applications requires real-time analysis methods that are computationally efficient. Integrated sensing and processing (ISP) is a method for minimizing the data burden and sensing time of a system. ISP is accomplished through implementation of chemometric calculations in the physics of the spectroscopic sensor itself. In ISP, the measurements collected at the detector are weighted to directly correlate to the sample properties of interest. This method is especially useful for large and complex data sets. In this research, ISP is applied to acoustic resonance spectroscopy, near-infrared hyperspectral imaging and a novel solid state spectral imager. In each application ISP produced a clear advantage over the traditional sensing method. The limitations of ISP must be addressed before it can become widely used. ISP is essentially a pattern recognition algorithm. Problems arise in pattern recognition when the pattern-recognition algorithm encounters a sample unlike any in the original calibration set. This is termed the false sample problem. To address the false sample problem the Bootstrap Error-Adjusted Single-Sample Technique (BEST, a nonparametric classification technique) was investigated. The BEST-ISP method utilizes a hashtable of normalized BEST points along an asymmetric probability density contour to estimate the BEST multidimensional standard deviation of a sample. The on-line application of the BEST method requires significantly less computation than the full algorithm allowing it to be utilized in real time as sample data is obtained. This research tests the hypothesis that a BEST-ISP metric can be used to detect false samples with sensitivity > 90% and specificity > 90% on categorical data.

在處理具遺失值之類別資料時，傳統的方法是將資料捨棄，但是這通常不是明智之舉，這些遺失某些分類訊息的資料通常還是可以提供其它重要的訊息，尤其當這類型資料的個數佔大多數時，將其捨棄可能使得估計的變異數增加，甚至影響最後的決策。如何將這些遺失某些訊息的資料納入考慮，作出完整的分析是最近幾十年間頗為重要的課題。本文主要整理了五種分析這類型資料的方法，分別為單樣本方法、多樣本方法、概似方程式因式分解法、EM演算法，以上四種方法可使用在資料遺失呈隨機分佈的條件成立下來進行分析。第五種則為樣本遺失不呈隨機分佈之分析方法。 / Traditionally, the simple way to deal with observations for which some of the variables are missing so that they cannot cross-classified into a contingency table simply excludes them from any analysis. However, it is generally agreed that such a practice would usually affect both the accuracy and the precision of the results. The purpose of the study is to bring together some of the sound alternatives available in the literature, and provide a comprehensive review. Four methods for handling data missing at random are discussed, they are single-sample method, multiple-sample method, factorization of the likelihood method, and EM algorithm. In addition, one way of handling data missing not at random is also reviewed.

In this thesis, the expression variation problem in two-dimensional (2D) and three-dimensional (3D) face recognition is tackled. While discriminant analysis (DA) methods are effective solutions for recognizing expression-variant 2D face images, they are not directly applicable when only a single sample image per subject is available. This problem is addressed in this thesis by introducing expression subspaces which can be used for synthesizing new expression images from subjects with only one sample image. It is proposed that by augmenting a generic training set with the gallery and their synthesized new expression images, and then training DA methods using this new set, the face recognition performance can be significantly improved. An important advantage of the proposed method is its simplicity; the expression of an image is transformed simply by projecting it into another subspace. The above proposed solution can also be used in general pattern recognition applications. The above method can also be used in 3D face recognition where expression variation is a more serious issue. However, DA methods cannot be readily applied to 3D faces because of the lack of a proper alignment method for 3D faces. To solve this issue, a method is proposed for sampling the points of the face that correspond to the same facial features across all faces, denoted as the closest-normal points (CNPs). It is shown that the performance of the linear discriminant analysis (LDA) method, applied to such an aligned representation of 3D faces, is significantly better than the performance of the state-of-the-art methods which, rely on one-by-one registration of the probe faces to every gallery face. Furthermore, as an important finding, it is shown that the surface normal vectors of the face provide a higher level of discriminatory information rather than the coordinates of the points. In addition, the expression subspace approach is used for the recognition of 3D faces from single sample. By constructing expression subspaces from the surface normal vectors at the CNPs, the surface normal vectors of a 3D face with single sample can be synthesized under other expressions. As a result, by improving the estimation of the within-class scatter matrix using the synthesized samples, a significant improvement in the recognition performance is achieved.

In this thesis, the expression variation problem in two-dimensional (2D) and three-dimensional (3D) face recognition is tackled. While discriminant analysis (DA) methods are effective solutions for recognizing expression-variant 2D face images, they are not directly applicable when only a single sample image per subject is available. This problem is addressed in this thesis by introducing expression subspaces which can be used for synthesizing new expression images from subjects with only one sample image. It is proposed that by augmenting a generic training set with the gallery and their synthesized new expression images, and then training DA methods using this new set, the face recognition performance can be significantly improved. An important advantage of the proposed method is its simplicity; the expression of an image is transformed simply by projecting it into another subspace. The above proposed solution can also be used in general pattern recognition applications. The above method can also be used in 3D face recognition where expression variation is a more serious issue. However, DA methods cannot be readily applied to 3D faces because of the lack of a proper alignment method for 3D faces. To solve this issue, a method is proposed for sampling the points of the face that correspond to the same facial features across all faces, denoted as the closest-normal points (CNPs). It is shown that the performance of the linear discriminant analysis (LDA) method, applied to such an aligned representation of 3D faces, is significantly better than the performance of the state-of-the-art methods which, rely on one-by-one registration of the probe faces to every gallery face. Furthermore, as an important finding, it is shown that the surface normal vectors of the face provide a higher level of discriminatory information rather than the coordinates of the points. In addition, the expression subspace approach is used for the recognition of 3D faces from single sample. By constructing expression subspaces from the surface normal vectors at the CNPs, the surface normal vectors of a 3D face with single sample can be synthesized under other expressions. As a result, by improving the estimation of the within-class scatter matrix using the synthesized samples, a significant improvement in the recognition performance is achieved.