Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Atomic Decomposition by Basis Pursuit
SIAM Review
Support vector machine learning for interdependent and structured output spaces
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Robust Face Recognition via Sparse Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Sampling theorems for signals from the union of finite-dimensional linear subspaces
IEEE Transactions on Information Theory
Greed is good: algorithmic results for sparse approximation
IEEE Transactions on Information Theory
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Using image hierarchies for visual categorization has been shown to have a number of important benefits. Doing so enables a significant gain in efficiency (e.g., logarithmic with the number of categories [16,12]) or the construction of a more meaningful distance metric for image classification [17]. A critical question, however, still remains controversial: would structuring data in a hierarchical sense also help classification accuracy? In this paper we address this question and show that the hierarchical structure of a database can be indeed successfully used to enhance classification accuracy using a sparse approximation framework. We propose a new formulation for sparse approximation where the goal is to discover the sparsest path within the hierarchical data structure that best represents the query object. Extensive quantitative and qualitative experimental evaluation on a number of branches of the Imagenet database [7] as well as on the Caltech-256 [12] demonstrate our theoretical claims and show that our approach produces better hierarchical categorization results than competing techniques.