# Image classification by sparse coding Feature learning problem Given a 14×14 ima

## Image classification by sparse coding Feature learning problem Given a 14×14 ima

Watson, Mac, On-Air Personality has reference to this Academic Journal, PHwiki organized this Journal Image classification by sparse coding Feature learning problem Given a 14×14 image patch x, can represent it using 196 real numbers. Problem: Can we find a learn a better representation as long as this Unsupervised feature learning Given a set of images, learn a better way to represent image than pixels.

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First stage of visual processing in brain: V1 Schematic of simple cell Actual simple cell Green: Responds to white dot. Red: Responds to black dot. [Images from DeAngelis, Ohzawa & Freeman, 1995] Gabor functions. Also used in image compression in addition to denoising. The first stage of visual processing in the brain (V1) does edge detection. Learning an image representation Sparse coding (Olshausen & Field,1996) Input: Images x(1), x(2), , x(m) (each in Rn x n) Learn: Dictionary of bases f1, f2, , fk (also Rn x n), so that each input x can be approximately decomposed as: s.t. ajs are mostly zero (sparse) Use to represent 14×14 image patch succinctly, as [a7=0.8, a36=0.3, a41 = 0.5]. I.e., this indicates which basic edges make up the image. [NIPS 2006, 2007] Sparse coding illustration Natural Images Learned bases (f1 , , f64): Edges x » 0.8 f36 + 0.3 f42 + 0.5 f63 [0, 0, , 0, 0.8, 0, , 0, 0.3, 0, , 0, 0.5, ] = [a1, , a64] (feature representation) Test example Compact & easily interpretable

More examples Represent as: [0, 0, , 0, 0.6, 0, , 0, 0.8, 0, , 0, 0.4, ] Represent as: [0, 0, , 0, 1.3, 0, , 0, 0.9, 0, , 0, 0.3, ] Method hypothesizes that edge-like patches are the most basic elements of a scene, in addition to represents an image in terms of the edges that appear in it. Use to obtain a more compact, higher-level representation of the scene than pixels. [Evan Smith & Mike Lewicki, 2006] Digression: Sparse coding applied to audio Digression: Sparse coding applied to audio [Evan Smith & Mike Lewicki, 2006]

Sparse coding details Input: Images x(1), x(2), , x(m) (each in Rn x n) L1 sparsity term (causes most s to be 0) Alternating minimization: Alternately minimize with respect to fis (easy) in addition to as (harder). Solving as long as bases Early versions of sparse coding were used to learn about this many bases: 32 learned bases How to scale this algorithm up Sparse coding details Input: Images x(1), x(2), , x(m) (each in Rn x n) L1 sparsity term Alternating minimization: Alternately minimize with respect to fis (easy) in addition to as (harder).

Goal: Minimize objective with respect to ais. Simplified example: Suppose I tell you: Problem simplifies to: This is a quadratic function of the ais. Can be solved efficiently in closed as long as m. Algorithm: Repeatedly guess sign (+, – or 0) of each of the ais. Solve as long as ais in closed as long as m. Refine guess as long as signs. Feature sign search (solve as long as ais) The feature-sign search algorithm: Visualization Starting from zero (default) Current guess: The feature-sign search algorithm: Visualization 1: Activate a2 with + sign Active set ={a2} Starting from zero (default) Current guess:

The feature-sign search algorithm: Visualization 1: Activate a2 with + sign Active set ={a2} Starting from zero (default) Current guess: The feature-sign search algorithm: Visualization 2: Update a2 (closed as long as m) Starting from zero (default) 1: Activate a2 with + sign Active set ={a2} Current guess: The feature-sign search algorithm: Visualization 3: Activate a1 with + sign Active set ={a1,a2} Starting from zero (default) Current guess:

The feature-sign search algorithm: Visualization 4: Update a1 & a2 (closed as long as m) Starting from zero (default) 3: Activate a1 with + sign Active set ={a1,a2} Current guess: Be as long as e feature sign search 32 learned bases With feature signed search

Recap of sparse coding as long as feature learning Relate to histograms view, in addition to so sparse-coding on top of SIFT features. Input: Images x(1), x(2), , x(m) (each in Rn x n) Learn: Dictionary of bases f1, f2, , fk (also Rn x n). SIFT descriptors x(1), x(2), , x(m) (each in R128) R128. Training time Sparse coding recap x » 0.8 f36 + 0.3 f42 + 0.5 f63 [0, 0, , 0, 0.8, 0, , 0, 0.3, 0, , 0, 0.5, ] Much better than pixel representation. But still not competitive with SIFT, etc. Three ways to make it competitive: Combine this with SIFT. Advanced versions of sparse coding (LCC). Deep learning. Combining sparse coding with SIFT Input: Images x(1), x(2), , x(m) (each in Rn x n) Learn: Dictionary of bases f1, f2, , fk (also Rn x n). SIFT descriptors x(1), x(2), , x(m) (each in R128) R128. Test time: Given novel SIFT descriptor, x (in R128), represent as

Putting it together Relate to histograms view, in addition to so sparse-coding on top of SIFT features. Feature representation Learning algorithm x(1) a(1) x(2) x(3) a(2) a(3) or Learning algorithm Suppose youve already learned bases f1, f2, , fk. Heres how you represent an image. E.g., 73-75% on Caltech 101 (Yang et al., 2009, Boreau et al., 2009) K-means vs. sparse coding Centroid 1 Centroid 2 Centroid 3 K-means Represent as: K-means vs. sparse coding Centroid 1 Centroid 2 Centroid 3 K-means Represent as: Basis f1 Sparse coding Represent as: Basis f2 Basis f3 Intuition: Soft version of k-means (membership in multiple clusters).

K-means vs. sparse coding Rule of thumb: Whenever using k-means to get a dictionary, if you replace it with sparse coding itll often work better.

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