We propose an original sequential learning algorithm, SBA that enables the SVM to efficiently learn from only a small subset of the input data set. The principle is based on sequentially adding convex hull points of the binary classes to a small subset. The SVM is trained on the current training pool and its result is used to find the data which is wrongly classified and furthest away from the current optimal hyperplane. This point is added to the training pool and the SVM is retrained on it. The iteration stops when no more such points are found. A formal proof of strict convergence is provided and we derive a geometric bound on the training time. It will be explained how SBA can be extended to handle non-linearly and non-separable class distributions. Experimental trials on some well known data sets verify the speed advantage of our method coupled to any SVM over that of that SVM used and the core vector machine

LDA (linear discriminant analysis) and its variants are popular for image-based classification problems such as face recognition. However, their performance is inherently unstable when the samples are sparse. We propose a new type of discriminant analysis called MMDA (margin-maximization discriminant analysis), which derives features by maximizing the average margin between the classes. The method does not require S/sub W/ (within-class scatter matrix) to be non-singular and well-conditioned as it does not involve its inverse term, and the features can be directly derived from the input space. A computational trick has also been proposed for MMDA to handle high-dimensional data. We conducted intensive tests on ORL and UMIST face databases, and the results show that MMDA is a good replacement of LDA for the sparse sample problem.

Subspace methods have been widely used for face recognition possibly because of their robustness and simplicity. Due to high dimensionality of image space, these methods are likely to encounter computational problem when having to deal with very large number of face training samples. In this paper, a new subspace approach called the spectral-face analysis is developed to overcome this. It handles pixel information in matrix form rather than as vectors, and in so doing, keeps the basis computation invariant to the size of the training samples. Two types of statistics are implemented for the spectral-face analysis: the “covariance face” and the “error face”. As they employ smaller vector space, the recognition rates are, as expected, not as good as conventional subspace methods such as PCA and LDA. To improve the performance, we extend the spectral-face methodology by some “stacking” technique, the sole purpose being to increase the vector space dimension. Extensive tests have been carried out on the ORL face database with good and interesting results. Application of LDA to the spectral-face analysis also showed marked improvements.

Subspace methods have been widely used for face recog- nition possibly because of their robustness and simplicity. Due to high dimensionality of image space, these methods are likely to encounter computational problem when hav- ing to deal with very large number of face training sam- ples. In this paper, a new subspace approach called the spectral-face analysis is developed to overcome this. It han- dles pixel information in matrix form rather than as vectors, and in so doing, keeps the basis computation invariant to the size of the training samples. Two types of statistics are im- plemented for the spectral-face analysis: the "covariance face" and the "error face". As they employ smaller vector space, the recognition rates are, as expected, not as good as conventional subspace methods such as PCA and LDA. To improve the performance, we extend the spectral-face methodology by some "stacking" technique, the sole pur- pose being to increase the vector space dimension. Exten- sive tests have been carried out on the ORL face database with good and interesting results. Application of LDA to the spectral-face analysis also showed marked improvements.