Djemel Ziou

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Learning of Data Collections in High-dimensional
Spaces Without Supervision

• Djemel Ziou
• NSERC/Bell Canada Chair in personal imaging
  Computer Science dept.
• Université de Sherbrooke
• Quebec, Canada

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Content

• Visual collection management
• Machine learning
• Image segmentation
• Content based image suggestion

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Visual collection management
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Motivations
NSF 2007, B. Efron 2002.
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Reactive Access to Collections

• Text-based image retrieval
• Text keywords extracted from Web pages
  containing the image, figure captions,

Short term need User queries an information
retrieval system

• Content-based image retrieval
• Visual appearance color, shape, texture, regions
  of interest,

• Limitations
• Query, features, similarity, indexing,

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Proactive Access To Collections
Predict the buyers needs
Suggestion
Suggestion rules

• Collaboration Users conformity to groups ?
  Opinions of other users
• 2. Content Conformity to himself
• Items with same tags (keywords)

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Machine Learning
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Introduction

• Representation of stimulus

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Introduction

• Data

• Generative learning

Under certain assumptions (structural, MAP)

• Discriminative learning

Unlike generative learning, 1) provides no
information about x (
) 2) Discriminative learning cannot be used
with unlabelled data (C must be observed).
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Discriminative Learning Bayesian Logistic
Regression Ksantini, Ziou, Colin, Dubeau. IEEE
Trans. On PAMI, 2008
Maximizing the conditional Log-Likelihood.
where
There are several drawbacks (high-dimension,
separability, )
Bayesian formulation
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Variational approximation and Jensens inequality
lead to
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Generative learning case of finite mixture of
pdfs

• Finite mixture model.

Problems pdf, estimation, model selection,
Which Pdf?
Gaussian, Gamma, , same or different pdfs for
populations.
Mixture of different Pdfs for SAR images El Zaart
and Ziou, Int J. Remote Sensing 2007

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The Generalized Dirichlet Distribution
Generalized Dirichlet distribution (GDD)
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Multi-dimensionality is Omnipresent

• Multidimensional data
• Image Descriptors 128 000 features (128 Sift
  features x 1000 interest points).
• Faces 128x128 pixels 16384 features/face
• Text terms in a corpus 10 000

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High-Dimensional data
Bouguila and Ziou. IEEE Trans. On PAMI, 2007
Boutemedjet, Bouguila and Ziou. IEEE Trans. On
PAMI, 2009
If is GDD (
)
If d1
for d2D
Each is a Beta
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Feature Selection

• Mixture model before and after transformation

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Feature Selection Model
Boutemedjet, Bouguila and Ziou. IEEE Trans. On
PAMI, 2009

• Relevance Criterion marginal independence of Xl
  from the class label Z
• Label Xl with hidden Bernoulli variable ?l, such
  that ?l0 when Xl ?l,
• General definition ?l mixture of K ?kl
• e.g. distribution of background in object
  images.
• Label Xl in the mixture ?l by hidden multinomial
  variable
• Approximation
• New mixture model Generalized Dirichlet (GD) with
  selection of independent features

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Unsupervised Learning using the MML Principle
Bouguila and Ziou. IEEE Trans. On TKDE, 2007
Paradigm
Send
Encode
Decode
What is the minimum message length?

• is the number of parameters being
  estimated and equal to M (2D1).
• is the prior probability.
• is the Fisher information
  (determinant of the Hessian matrix).
• Problems ? And ?

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Unsupervised Learning MML
Boutemedjet, Bouguila and Ziou. IEEE Trans. On
PAMI, 2009

• Fisher Information
• E.g.
• Prior distribution
• E.g.
• Message Length of the data set

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Optimization of MML

• Expectation Maximization (EM) algorithm
• E-step expected posterior probabilities
• M-step

2x2 matrix
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Object image categorization

• Goal Identify categories and irrelevant
  features
• Challenge Intra-class variability inter-class
  similarity
• Existing Supervised, K-NN with Euclidian
  distance
• Collection 2688 images, 8 classes
• Features
• Scale Invariant Feature Transform (SIFT)
  1.5.106
• descriptors 128-D (2 GB)
• Visual vocabulary 700 visual words
• Probabilistic Latent Semantic Indexing (pLSI)
• P(zI) hidden aspects defined on simplex ?
• Non-Euclidian

Challenging problem in computer vision
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Results
Feature Selection improves the accuracy of image
categorization
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Image segmentation and object tracking
M.S. Allili and Ziou, Int. J. of Computer
Mathematics, 2007.M.S. Allili and Ziou, J.
Neurocomputing, 2008.
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Problem formulation of segmentation
Active contour based approach
Variational formulation
Final contour
Initial Contour
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Proposed approach
Statistical Model selection
Contrast estimation

Energy functional
Euler-Lagrange PDE
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Topology change (Level sets)
Experimental results
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Object tracking in video
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CBIS as a Model Selection Problem
Boutemdjet and Ziou, IEEE Trans. on multimedia,
2008.
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Suggestion Criteria

• Data
• Users Uu1,u2,,UNu
• Contexts Ee1,e2,,eNe
• Images X x1,x2,,xNx
• Ratings of user on images
• D(u(i),e(i),x(i),r(i)),i1,,N,
• Data modeling principle
• Similar users prefer visually and semantically
  similar products
• Suggestion consumers need highly rated and
  less redundant products

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Data model p(u,e,x,r)

• Rating model data ? Each Quadruplet (u,e,v,x)
  is a random vector
• Discover user/image classes (z,c) and Label
  (u,e,v,x) with 2 hidden variables z user class,
  c image class
• All variables except x are discrete multinomial
  distributions, xGD
• Parameters
• Diversity Penalize predicted ratings for
  consumed images Xue
• Consumed images become irrelevant
  Nue(u,e,xtue,r-),t1,..,Nue
• Update T from Nue
• New data are handled.

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Algorithm
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Results Mean Absolute Error (MAE)

• PCC Pearson Correlation Coefficients (P. Resnick
  et al., CSCW 1994)
• Aspect Model (T. Hofmann, ACM TOIS 2004)
• Flexible Mixture Model (L. Si R. Jin, ICML
  2003)
• User Rating Profile (B. Marlin, NIPS 2004)
• V-FMM No contextual information, ESingleton
• V-GD-FMM No Feature Selection

PCC Aspect FMM URP V-FMM V-GD-FMM I-VCC D-VCC
Avg. MAE 1.327 1.201 1.145 1.116 0.890 0.754 0.712 0.645
Std. Deviation 0.040 0.051 0.036 0.042 0.038 0.027 0.022 0.014
Improvement () 0.00 9.49 13.71 15.90 32.94 43.18 51.62 55.84
Feature Selection improves the rating prediction
accuracy
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• Thank you

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References

• M. S. Allili, D. Ziou. Object tracking in videos
  using adaptive mixture models and active
  contours. Neurocomputing 7, pp. 2001-2011, 2008.
• M. S. Allili, D. Ziou Automatic colour-texture
  image segmentation using active contours. Int. J.
  Comput. Math. 84(9) 1325-1338, 2007.
• S. Boutemedjet, Djemel Ziou. A Graphical Model
  for Context-Aware Visual Content Recommendation.
  IEEE Trans. on Multimedia 10, pp. 52-62, 2008.
• S. Boutemedjet, N. Bouguila, and D. Ziou (In
  press). A Hybrid Feature Extraction Selection
  Approach for High-Dimensional Non-Gaussian Data
  Clustering. IEEE Trans. on Pattern Analysis and
  Machine Intelligence, 2009.
• N. Bouguila and D. Ziou High-Dimensional
  Unsupervised Selection and Estimation of a Finite
  Generalized Dirichlet Mixture Model Based on
  Minimum Message Length. IEEE Trans. on Pattern
  Analysis and Machine Intelligence, 2007.
• R. Ksantini, D. Ziou, B. Colin, F. Dubeau.
  Weighted Pseudometric Discriminatory Power
  Improvement Using a Bayesian Logistic Regression
  Model Based on a Variational Method. IEEE Trans.
  Pattern Anal. Mach. Intell. 30(2) 253-266, 2008.
• D. Ziou, T. Hamri, S. Boutemedjet. A hybrid
  probabilistic framework for content-based image
  retrieval with feature weighting. Pattern
  Recognition 42(7) 1511-1519, 2009.
• M. L. Kherfi, D. Ziou. Relevance feedback for
  CBIR a new approach based on probabilistic
  feature weighting with positive and negative
  examples. IEEE Trans. on Image Processing 15(4)
  1017-1030 2006.
• M.-F. Auclair-Fortier, D. Ziou. A Global Approach
  for Solving Evolutive Heat Transfer for Image
  Denoising and Inpainting. IEEE Trans. Image
  Processing, 152558-2574, 2006.
• A. F. El Ouafdi, D. Ziou, and H. Krim. A smart
  stochastic approach for manifolds smoothing.
  Comput. Graphic Forum 27, pp. 1357-1364, 2008.

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