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Fast Inference in Sparse Coding Algorithms with Applications to Object Recognition (1010.3467v1)

Published 18 Oct 2010 in cs.CV and cs.LG

Abstract: Adaptive sparse coding methods learn a possibly overcomplete set of basis functions, such that natural image patches can be reconstructed by linearly combining a small subset of these bases. The applicability of these methods to visual object recognition tasks has been limited because of the prohibitive cost of the optimization algorithms required to compute the sparse representation. In this work we propose a simple and efficient algorithm to learn basis functions. After training, this model also provides a fast and smooth approximator to the optimal representation, achieving even better accuracy than exact sparse coding algorithms on visual object recognition tasks.

Citations (247)

Summary

  • The paper introduces the Predictive Sparse Decomposition (PSD) algorithm, which uses a learned nonlinear regressor to approximate sparse representations over 100x faster than traditional methods.
  • The experiments show that PSD achieves competitive recognition accuracy on MNIST and Caltech 101 while drastically reducing inference time.
  • The paper highlights PSD’s robustness under dynamic inputs, providing stable sparse representations ideal for real-time object recognition applications.

Analysis of "Fast Inference in Sparse Coding Algorithms with Applications to Object Recognition"

This paper introduces the Predictive Sparse Decomposition (PSD) algorithm, aiming to enhance the applicability of adaptive sparse coding methods in visual object recognition tasks by addressing computational inefficiencies. Sparse coding is instrumental in learning overcomplete sets of basis functions that enable the reconstruction of natural image patches. However, traditional sparse coding methods remain limited by the computational expense of determining sparse representations. PSD addresses these limitations by providing a fast and efficient approximation mechanism.

Algorithmic Innovations

The central contribution of the paper is the Predictive Sparse Decomposition method, which constructs a nonlinear regressor to predict sparse representations. The regressor, defined as F(Y;G,W,D)=Gtanh(WY+D)F(Y;G,W,D) = G \tanh(WY + D), is trained jointly with the basis functions, significantly reducing the complexity of sparse coding. The joint optimization uses a compound loss function that merges reconstruction error, sparsity constraint, and a predictive closeness term. This training strategy results in a regressor capable of rapid approximation, achieving a performance more than 100 times faster than exact methods such as the feature sign algorithm.

Experimental Results

The experiments demonstrate the algorithm's superiority in both recognition accuracy and computational efficiency. On the MNIST dataset, PSD achieves the highest recognition rates compared to PCA, RBM, and SESM, despite having the worst reconstruction errors, highlighting the effectiveness of its learned feature representation. In object recognition tasks using the Caltech 101 dataset, PSD's feed-forward inference achieves comparable or better recognition accuracy than exact sparse coding methods. The speed advantage of PSD is significant, offering an over 800-fold increase in feature extraction speed during inference—a critical factor in real-time applications.

Stability and Scalability

The paper also evaluates the stability of PSD compared to feature sign algorithms in dynamic conditions. By analyzing video sequences, PSD is shown to produce more consistent representations under changing inputs, attributed to the smooth and predictive nature of the trained regressor.

Implications and Future Work

The implications of this research are noteworthy in both theoretical and practical contexts. Theoretically, the paper introduces an efficient approximation mechanism for sparse coding that bridges the gap between computational tractability and representation effectiveness. Practically, the significant reduction in inference time without compromising accuracy renders PSD suitable for real-time applications in computer vision.

Future work may focus on extending the model convolutionally to exploit translation invariance, potentially reducing feature redundancy in the representation. Another avenue is the development of hierarchical models, which could be achieved by cascading PSD models to form deep architectures, as suggested by the authors.

In summary, this paper provides a robust method for fast sparse coding, paving the way for more efficient real-time object recognition systems. The Predictive Sparse Decomposition offers a promising advancement for leveraging sparse methods in computationally constrained environments.

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