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Learning Spatially Localized, Parts- Based Representation
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Abstract In this paper, we propose a novel method, called local non-negative matrix factorization (LNMF). This gives a set of bases which not only allows a non-subtractive representation of image but also manifests localized features.
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Introduction The case of N*M image pixels, each taking a value in {0,1, …,255};there is a huge number of possible configurations: Subspace analysis helps to reveal dimensional structures if patterns observed in high dimensional spaces.
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Introduction (PCA) Principal Component Analysis (PCA) Dimension reduction is achieved by discarding least significant components. PCA is unable to extract basis components manifesting localized features.
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Introduction (NMF) Non-negative matrix factorization (NMF) NMF 特殊的地方在於其對矩陣分解過程的非負限制。這限制會使得能 得到更好的反應原始數據的局部特徵。 http://www.cse.nsysu.edu.tw/seminar/97/20081024.pdf
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Method (NMF) NMF: Constrained Non-Negative Matrix Factorization Let a set of training images be given as an n* matrix X. A basis image by n*m matrix B. H is the matrix of m* coefficients of weights. Dimension reduction is achieved when m<n. Kullback – Leibler divergence
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Method (LNMF) LNMF: Given the existing constrains for all i, we wish that should be as small as possible. Imposed by =min. Different bases should be as orthogonal as possible, so as to minimize redundancy. Imposed by. Only components giving most important information should be retained. Imposed by.
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Experiments Data Preparation The set of the 10 images for each person is randomly partitioned into training subset of 5 images and a test set of the other 5. The training set is then used to learn basis components, and the test set for evaluate.
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Experiments Learning Basis Components
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Experiments Reconstruction
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Experiments Face Recognition
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Experiments Face Recognition
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