This project aims to apply the NMF to detecting counterfeit notes. You are asked to produce a code-notebbok in Python-Jupiter. For some Python functions, you can use existing resources on the Internet, by naming your sources. There are several libraries like for example:
[login to view URL] (*).
1. Suppose we have a set of pictures where each one of them corresponds to one of the bills (true or false). After applying the wavelet transform to the banknote images, we obtain a matrix where each image is described by 4 characteristics: variance, asymmetry, kurtosis and entropy.
(a) Save this dataset in two variables: bank data for data and bank_labels for labels.
(b) Create two matrices A_false (as counterfeit notes) and A_free
(only real tickets).
(c) Then create two bank train dies (500 objects from A_vrais
and 600 objects from A_false) and bank_test (the rest).
(d) View the data in a separate figure using a
function of visualization of the archive (*) for example fit transform.
2. Apply the Semi-NMF to the bank_train matrix using the corresponding function of the archive (*) (example nmf). Save the prototype matrix obtained in W_train.
(a) Write a show clusters program to transform the resulting partition matrix to a real partition matrix I (On
look for a maximum element in each line and replace it
by 1. All other elements are replaced by 0.). calculate
the purity for the partition matrix obtained previously.
(b) Classify the objects saved in bank_test using the
matrix of prototypes W_train learned previously (H_test =
W_train-1 * bank_test). Warning! In case the matrix W_train
is a square matrix, we use the pseudo-inverse of
Moore-Penrose (look for the corresponding command in scikit-learn).
(c) Calculate the external indices (purity and entropy for the H_test partition matrix). For this, we use the purity and entropy command of scikit-learn.
(d) Calculate the internal indices (Davies and Bouldin DB Index,
the CH index of Calinsky and Harabsz, the KL index of Krzanowski and Lai and the Dunn index) for the partition matrix H_test.
For this, we use the matching command scikit-learn
(e) View the data with the labels.
3. Make the sequence of commands (2a) - (2e) with the classic NMF.
4. Apply Symmetric NMF to the K_test matrix.
(a) Calculate the Gram K test matrix using the command
corresapondant kernelRBF with σ = 1.
(b) Calculate the external and internal indices for the partition matrix.
(c) Visualize the data with the labels obtained?
(d) Make the sequence of commands (4a) - (4c) with the matrix of
Gram of a polynomial kernel with parameters [1; 0; 2].
5. Compare the results obtained.
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