Learning Spatially Localized, Parts-Based Representation

1
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 NM image pixels, each taking a value
  in 0,1,,255there 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)
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• http//www.cse.nsysu.edu.tw/seminar/97/20081024.pd
  f

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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 nm matrix B.
• H is the matrix of m coefficients of
  weights.
• Dimension reduction is achieved when mltn.
• KullbackLeibler 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