1 / 16

Proximal Methods for Sparse Hierarchical Dictionary Learning

This paper presents proximal methods for sparse hierarchical dictionary learning, addressing structured sparsity and its applications in various tasks. The authors explore dictionary learning in scenarios where the structure of the data is essential for effective feature selection. They also compare traditional methods like Lasso and Group Lasso with the proposed hierarchical structure. Experimental results showcase the performance of the learned dictionaries on natural image patches and text documents, demonstrating their utility in both regression and classification tasks.

antoinette-jaydin
Télécharger la présentation

Proximal Methods for Sparse Hierarchical Dictionary Learning

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Proximal Methods for Sparse Hierarchical Dictionary Learning Rodolphe Jenatton, Julien Mairal, Guillaume Obozinski, Francis Bach Presented by Bo Chen, 2010, 6.11

  2. Outline • 1. Structured Sparsity • 2. Dictionary Learning • 3. Sparse Hierarchical Dictionary Learning • 4. Experimental Results

  3. Structured Sparsity • Lasso (R. Tibshirani.,1996) • Group Lasso (M. Yuan & Y. Lin, 2006) • Tree-Guided Group Lasso (Kim & Xing, 2009)

  4. Tree-Guided Structure Example Multi-task: Tree Regularization Definition: Kim & Xing, 2009

  5. Tree-Guided Structure Penalty Introduce two parameters: Rewrite the penalty term, if the number of tasks is 2. (K=2): Generally: Kim & Xing, 2009

  6. In Detail Kim & Xing, 2009

  7. Some Definitions about Hierarchical Groups

  8. Hierarchical Sparsity-Inducing Norms

  9. Dictionary Learning • If the structure information is introduced, the difference • between dictionary learning and group lasso: • Group Lasso is a regression problem. Each feature has its own physical • meaning. The structure information should be meaningful and correct. • Otherwise, the ‘structure’ will hurt the method. • In dictionary learning, the dictionary is unknown. So the structure information • will be a guide to help learn the structured dictionary.

  10. = Optimization • Proximal Operator for Structure Norm Fix the dictionary D, the objective function: Transformed to a proximal problem: Proximal operator with the structure penalty:

  11. Learning the Dictionary Updating D 5 times in each iteration, Updating A,

  12. Experiments : Natural Image Patches • Use the learned dictionary from training set to impute the missing values in testing samples. Each sample is a 8x8 patch. • Training set: 50000; Testing set: 25000 • Test 21 balanced tree structures of depth 3 and 4. Also set the number of the nodes in each layer.

  13. Learned Hierarchical Dictionary

  14. Experiments : Text Documents Key points:

  15. Visualization of NIPS proceedings Documents: 1714 Words: 8274

  16. Postings Classification Training set: 1000; Testing set: 425; Documents: 1425; Words:13312 Goal: classify the postings from the two newsgroups, alt.atheism and talk.religion.misc.

More Related