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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. Outline. Introduction Group Coding Dictionary Learning

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group sparse coding

Group Sparse Coding

SamyBengio, 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

outline
Outline
  • Introduction
  • Group Coding
  • Dictionary Learning
  • Results and Discussion
introduction
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
dictionary construction
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
problem statement
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 m’th group
    • the subscript m is removed for single group operation.
  • Sub goals
    • Encoding ( )
    • Learning a good dictionary from a set of training groups
group coding
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 .
group coding7
Group coding
  • Define
  • Optimum for p=1
  • Optimum for p=2
dictionary learning
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
dictionary learning9
Dictionary Learning
  • In this paper p=2
  • Define auxiliary variables
  • Define vector (appearing in the gradient of objective function)
  • Similar to the argument in group coding, one can obtain
experimental setting
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.