Group Sparse Coding

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Group Sparse Coding

• Samy Bengio, Fernando Pereira,
• Yoram Singer, Dennis Strelow
• Google
• Mountain View, CA
• (NIPS2009)

Presented by Miao Liu July-23-2010
Figures and formulae are directly copied from
the original paper
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Outline

• Introduction
• Group Coding
• Dictionary Learning
• Results and Discussion

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Introduction

• Bag-of-words document representations
• Encode document by a vector of the counts of
  descriptors (words)
• Widely used in text, image, and video processing
• Easy to determine a suitable word dictionary for
  text documents.
• For images and videos
• No simple mapping from the raw document to
  descriptor counts
• Require visual descriptors (color, texture,
  angles, and shapes) extraction
• Measure descriptors at appropriate locations
  (regular grids, special interest points, multiple
  scales)
• More carful design of dictionary is needed

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Dictionary Construction

• Unsupervised vector quantization (VQ), often
  k-means clustering
• Pro maximally sparse per descriptor occurrence
• Cons
• Does not guarantee sparse coding whole image
• Not robust w.r.to descriptor variability
• regularized optimization
• Encode each visual descriptor as a weighted sum
  of dictionary elements
• Mixed-norm regularizers
• Take into account the structure of bags of visual
  descriptors in images
• Presenting sets of images from a given category

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Problem Statement

• The main goal encode groups of instances (e.g.
  image patches) in terms of dictionary code words
  (some kind of average patches)
• Notations
• The mth group
• the subscript m is removed for single group
  operation.
• Sub goals
• Encoding ( )
• Learning a good dictionary from a set of
  training groups

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Group Coding

• Given and , group coding
  is achieved by solving
• where
• .
• is the
• balances fidelity and reconstruction
  complexity.
• Coordinate descent is applied to solve the above
  problem.
• Finally, compress into a single vector by
  taking p-norm of each .

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Group coding

• Define
• Optimum for p1
• Optimum for p2

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Dictionary Learning

• Good Dictionary should balances between
• Reconstruction error
• Reconstruction complexity
• Overall complexity relative to the given training
  set
• Seeking learning method facilitates both
• induction of new dictionary words
• removal of dictionary words that have low
  predictive power
• Applying
• Let
• Objective

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Dictionary Learning

• In this paper p2
• Define auxiliary variables
• Define vector (appearing in the gradient of
  objective function)
• Similar to the argument in group coding, one can
  obtain

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Experimental Setting

• Compare with previous sparse coding method by
  measuring impact on classification the PASCAL VOC
  (Visual Object Classes) 2007 dataset
• image from 20 classes, including people,
  animals, vehicles and indoor objects etc.
• around 2500 images for respective training and
  validation 5000 images for testing.
• Extract local descriptors based on Gabor wavelet
  response at
• Four orientations ( )
• Spatial scales and offsets (27 combination)
• The 27 (scale, offset) pairs were chosen by
  optimizing a previous image recognition task,
  unrelated to this paper.

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Results and Discussion
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Results and Discussion
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Results and Discussion