How to choose an overcomplete dictionary for dictionary learning in sparse coding?
Problem: I'm trying to understand how to choose the dictionary matrix in this paper http://yann.lecun.com/exdb/publis/pdf/gregor-icml-10.pdf. The paper is about Sparse Coding and trained Algorithms for solving the Lasso Problem. Experiments reported in the paper are conducted on datasets of natural image patches and handwritten digits.
Given is the Lasso problem (chapter 1.1 in the paper): $E_{W_d}(x,z) = dfrac12lvertlvert{x}-{W_d}{z}lvertlvert^2_2 + alphalvertlvert{z}lvertlvert_1$, where ${x}inmathbb{R}^n$ is a given input vector, ${z}inmathbb{R}^m$ is the sparse code vector and ${W_d}inmathbb{R}^{ntimes m}$ is a "dictionary matrix whose columns are the (normalized) basis vectors".
My question is: How does $W_d$ and these basis vectors look like, especially in the overcomplete case m > n? How do i choose these basis vectors and the dictionary $W_d$?
In the first Simulation (page 6, chapter 4. Results, first 2 paragraphs) they use a dataset of natural image patches (Screenshot of these 2 parapaghs: enter image description here).
They use image patches of size 10x10 pixels, randomly selected from the Berkeley image database. Therefore they use n = 100 for the input vectors x. For the number of columns in the dictionary they use m = 100 and m = 400 (4 times overcomplete). They then train this dictionary which resulted in gabor-like filters.
How do i choose/initialize this dictionary here before i start training it?
Any answer is appreciated!
optimization convex-optimization machine-learning signal-processing
asked Nov 24 at 18:50
Sorancon
113
add a comment |
Problem: I'm trying to understand how to choose the dictionary matrix in this paper http://yann.lecun.com/exdb/publis/pdf/gregor-icml-10.pdf. The paper is about Sparse Coding and trained Algorithms for solving the Lasso Problem. Experiments reported in the paper are conducted on datasets of natural image patches and handwritten digits.
Given is the Lasso problem (chapter 1.1 in the paper): $E_{W_d}(x,z) = dfrac12lvertlvert{x}-{W_d}{z}lvertlvert^2_2 + alphalvertlvert{z}lvertlvert_1$, where ${x}inmathbb{R}^n$ is a given input vector, ${z}inmathbb{R}^m$ is the sparse code vector and ${W_d}inmathbb{R}^{ntimes m}$ is a "dictionary matrix whose columns are the (normalized) basis vectors".
My question is: How does $W_d$ and these basis vectors look like, especially in the overcomplete case m > n? How do i choose these basis vectors and the dictionary $W_d$?
In the first Simulation (page 6, chapter 4. Results, first 2 paragraphs) they use a dataset of natural image patches (Screenshot of these 2 parapaghs: enter image description here).
They use image patches of size 10x10 pixels, randomly selected from the Berkeley image database. Therefore they use n = 100 for the input vectors x. For the number of columns in the dictionary they use m = 100 and m = 400 (4 times overcomplete). They then train this dictionary which resulted in gabor-like filters.
How do i choose/initialize this dictionary here before i start training it?
Any answer is appreciated!
optimization convex-optimization machine-learning signal-processing
asked Nov 24 at 18:50
Sorancon
113
add a comment |
Problem: I'm trying to understand how to choose the dictionary matrix in this paper http://yann.lecun.com/exdb/publis/pdf/gregor-icml-10.pdf. The paper is about Sparse Coding and trained Algorithms for solving the Lasso Problem. Experiments reported in the paper are conducted on datasets of natural image patches and handwritten digits.
Given is the Lasso problem (chapter 1.1 in the paper): $E_{W_d}(x,z) = dfrac12lvertlvert{x}-{W_d}{z}lvertlvert^2_2 + alphalvertlvert{z}lvertlvert_1$, where ${x}inmathbb{R}^n$ is a given input vector, ${z}inmathbb{R}^m$ is the sparse code vector and ${W_d}inmathbb{R}^{ntimes m}$ is a "dictionary matrix whose columns are the (normalized) basis vectors".
My question is: How does $W_d$ and these basis vectors look like, especially in the overcomplete case m > n? How do i choose these basis vectors and the dictionary $W_d$?
In the first Simulation (page 6, chapter 4. Results, first 2 paragraphs) they use a dataset of natural image patches (Screenshot of these 2 parapaghs: enter image description here).
They use image patches of size 10x10 pixels, randomly selected from the Berkeley image database. Therefore they use n = 100 for the input vectors x. For the number of columns in the dictionary they use m = 100 and m = 400 (4 times overcomplete). They then train this dictionary which resulted in gabor-like filters.
How do i choose/initialize this dictionary here before i start training it?
Any answer is appreciated!
optimization convex-optimization machine-learning signal-processing
asked Nov 24 at 18:50
Sorancon
113
Problem: I'm trying to understand how to choose the dictionary matrix in this paper http://yann.lecun.com/exdb/publis/pdf/gregor-icml-10.pdf. The paper is about Sparse Coding and trained Algorithms for solving the Lasso Problem. Experiments reported in the paper are conducted on datasets of natural image patches and handwritten digits.
Given is the Lasso problem (chapter 1.1 in the paper): $E_{W_d}(x,z) = dfrac12lvertlvert{x}-{W_d}{z}lvertlvert^2_2 + alphalvertlvert{z}lvertlvert_1$, where ${x}inmathbb{R}^n$ is a given input vector, ${z}inmathbb{R}^m$ is the sparse code vector and ${W_d}inmathbb{R}^{ntimes m}$ is a "dictionary matrix whose columns are the (normalized) basis vectors".
My question is: How does $W_d$ and these basis vectors look like, especially in the overcomplete case m > n? How do i choose these basis vectors and the dictionary $W_d$?
In the first Simulation (page 6, chapter 4. Results, first 2 paragraphs) they use a dataset of natural image patches (Screenshot of these 2 parapaghs: enter image description here).
They use image patches of size 10x10 pixels, randomly selected from the Berkeley image database. Therefore they use n = 100 for the input vectors x. For the number of columns in the dictionary they use m = 100 and m = 400 (4 times overcomplete). They then train this dictionary which resulted in gabor-like filters.
How do i choose/initialize this dictionary here before i start training it?
Any answer is appreciated!
optimization convex-optimization machine-learning signal-processing
optimization convex-optimization machine-learning signal-processing
asked Nov 24 at 18:50
Sorancon
113
asked Nov 24 at 18:50
Sorancon
113
edited Dec 3 at 11:37
asked Nov 24 at 18:50
Sorancon
113
asked Nov 24 at 18:50
Sorancon
113
asked Nov 24 at 18:50
Sorancon
113
113
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