Learning Convolutional Feature Hierarchies for Visual Recognition Koray Kavukcuoglu, Pierre Sermanet, Y-Lan Boureau, Karol Gregor, Michael Mathieu, Yann LeCun NIPS 2010 Presented by Bo Chen

Outline 1. Drawbacks in the Traditional Convolutional Methods 2. The Proposed Algorithm and Some Details 3. Experimental Results 4. Conslusions

Convolutional Sparse Coding Negative: 1. The representations of whole images are highly redundant because the training and the inference are performed at the patch level. 2. The inference for a whole image is computationally expensive.

Solutions 1. Introducing Convolution Operator 2. Introducing Nonlinear Encoder Module

Learning Convolutional Dictionaries 1. The Boundary Effects Due to Convolutions Apply a mask on the derivatives of the reconstruction error: where mask is a term-by-term multiplier that either puts zeros or gradually scales down the boundaries. 2. Computational Efficient Derivative

Learning an Efficient Encoder 1. A New Smooth Shrinkage Operator: 2. To aid faster convergence, use stochastic diagonal Levenberg-Marquardt method to calculate a positive diagonal approximation to the hessian.

Patch Based vs Convolutional Sparse Modeling The convolution operator enables the system to model local structures that appear anywhere in the signal. The convolutional dictionary does not waste resources modeling similar filter structure at multiple locations. Instead, it Models more orientations, frequencies, and different structures including center-surround filters, double center-surround filters, and corner structures at various angles.

Multi-Stage Architecture The convolutional encoder can be used to replace patch-based sparse coding modules used in multistage object recognition architectures. Building on the previous findings, for each stage, the encoder is followed by and absolute value rectification, contrast normalization and average subsampling. Absolute Value Rectification: a simple pointwise absolute value function applied on the output of the encoder. Contrast Normalization: reduce the dependencies between components (feature maps). When used in between layers, the mean and standard deviation is calculated across all feature maps with a 9 × 9 neighborhood in spatial dimensions. Average Pooling: a spatial pooling operation that is applied on each feature map independently.

Experiments 1: Object Recognition Using Caltech 101 Dataset Preprocess: 1. 30/30 training/testing; 2. Resize: 151x143; 3. Local Contrast Normalization Unsupervised Training: Berkeley segmentation dataset Architecture: First Layer: 64 9x9; Pooling: 10 × 10 area with 5 pixel stride. Second Layer: 256 9x9, where each dictionary elementis constrained to connect 16 dictionary elements from the first layer; 6 × 6 area with stride 4.

Recognition Accuracy One Layer Two Layers Ours: 65.8% (0.6)

Pedestrian Detection(1) Original dataset: positive=2416; negative=1218 Augmented: positive= 11370 (1000); negative=9001(1000) Layer-1: 32 7x7; Layer-2: 64 7x7; Pooling: 2x2

Pedestrian Detection(2)

Conclusions 1. Convolutional training of feature extractors reduces the redundancy among filters compared with those obtained from patch based models. 2. Introduced two different convolutional encode functions for performing efficient feature extraction which is crucial for using sparse coding in real world applications. 3. The proposed sparse modeling systems has been applied through a successful multi-stage architecture on object recognition and pedestrian detection problems and performed comparably to similar systems.