Browsing by Subject "Pattern recognition"

Now showing 1 - 2 of 2
  • Thumbnail Image
    Item
    Numerical linear algebra techniques for effective data analysis.
    (2010-09) Chen, Jie
    Data analysis is a process of inspecting and obtaining useful information from the data, with the goal of knowledge and scientific discovery. It brings together several disciplines in mathematics and computer science, including statistics, machine learning, database, data mining, and pattern recognition, to name just a few. A typical challenge with the current era of information technology is the availability of large volumes of data, together with ``the curse of dimensionality''. From the computational point of view, such a challenge urges efficient algorithms that can scale with the size and the dimension of the data. Numerical linear algebra lays a solid foundation for this task via its rich theory and elegant techniques. There are a large amount of examples which show that numerical linear algebra consists of a crucial ingredient in the process of data analysis. In this thesis, we elaborate on the above viewpoint via four problems, all of which have significant real-world applications. We propose efficient algorithms based on matrix techniques for solving each problem, with guaranteed low computational costs and high quality results. In the first scenario, a set of so called Lanczos vectors are used as an alternative to the principal eigenvectors/singular vectors in some processes of reducing the dimension of the data. The Lanczos vectors can be computed inexpensively, and they can be used to preserve the latent information of the data, resulting in a quality as good as by using eigenvectors/singular vectors. In the second scenario, we consider the construction of a nearest-neighbors graph. Under the framework of divide and conquer and via the use of the Lanczos procedure, two algorithms are designed with sub-quadratic (and close to linear) costs, way more efficient than existing practical algorithms when the data at hand are of very high dimension. In the third scenario, a matrix blocking algorithm for reordering and finding dense diagonal blocks of a sparse matrix is adapted, to identify dense subgraphs of a sparse graph, with broad applications in community detection for social, biological and information networks. Finally, in the fourth scenario, we visit the classical problem of sampling a very high dimensional Gaussian distribution in statistical data analysis. A technique of computing a function of a matrix times a vector is developed, to remedy traditional techniques (such as via the Cholesky factorization of the covariance matrix) that are limited to mega-dimensions in practice. The new technique has a potential for sampling Guassian distributions in tera/peta-dimensions, which is typically required for large-scale simulations and uncertainty quantifications./
  • Thumbnail Image
    Item
    Spatial-frequency bandwidth requirements for pattern vision.
    (2010-07) Kwon, MiYoung
    Visual resolution is an important factor which affects human pattern recognition. Dealing with degraded visual resolution is relevant to both normally sighted and visually impaired individuals. This thesis describes three studies that address human pattern recognition under conditions of low resolution and its linkage to real life visual activities such as reading. Deficiencies of pattern recognition in peripheral vision might result in higher bandwidth requirements, and may contribute to the functional problems of people with central-field loss. In the first study (Chapter 2), we asked whether there are differences in spatial-frequency requirements between central and peripheral vision for pattern recognition. Critical bandwidths (i.e., the minimum low-pass filter bandwidth yielding 80% recognition accuracy) were measured for letter and face recognition. We found that critical bandwidths increased from central to peripheral vision for both letter and face recognition, demonstrating that peripheral vision requires higher bandwidth for pattern recognition than central vision. In the second study (Chapter 3), we asked how letter recognition is possible with severe reduction in the spatial resolution of letters. We addressed the question by testing the hypothesis that when spatial resolution is severely limited, the visual system relies increasingly on contrast coding for letter recognition. The size of the gap between contrast thresholds for detecting and recognizing letters was used as a marker for the extent of reliance for contrast coding. We found that as spatial resolution for rendering letters decreases, the system relies more on contrast differences. Letters are the fundamental building blocks of text. Besides single letter recognition, it has been proposed that the visual span, the number of letters that can be recognized without moving the eyes, imposes a limitation on reading speed. In the third study (Chapter 4), we investigated whether the bandwidth requirement for reading speed can be accounted for by the bandwidth requirement for letter recognition. We found that bandwidth limitations on reading performance appear to be closely associated with bandwidth limitations on the visual span, and also to a bandwidth limitation on letter recognition. Together, these three studies provide us with a better understanding of spatial-frequency requirements for pattern vision.