KDComp is a MATLAB project designed for computing kernel dictionaries and related matrices used in signal processing. The project includes functions for calculating kernel dictionaries (KD), RkkD matrices, TD matrices, and a testing script to evaluate the performance of these computations.
This function computes the KD matrix.
KD = CalculateKD(Dic, Nd, sigma, Ruu)
Dic: Dictionary matrix.
Nd: Dimension of the dictionary.
sigma: Standard deviation.
Ruu: Autocorrelation matrix.This function computes the RkkD matrix.
RkkD = CalculateRkkD(Dic, Nd, sigma, Ruu)
Dic: Dictionary matrix.
Nd: Dimension of the dictionary.
sigma: Standard deviation.
Ruu: Autocorrelation matrix.This function computes the TD matrix.
TD = CalculateTD(KDvec, Cv, Nd)
KDvec: Vectorized KD matrix.
Cv: Covariance matrix.
Nd: Dimension of the dictionary.Explanation:
1. Function Definition:
• function TD = CalculateTD(KDvec, CvD, Nd): Defines the function CalculateTD that takes KDvec, CvD, and Nd as inputs and computes the transformation matrix TD.
2. Vectorized Inner Product Method:
• TD = reshape(KDvec' * reshape(CvD', [], 1), Nd, Nd);
• reshape(CvD', [], 1): Converts the matrix CvD into a column vector.
• KDvec' * reshape(CvD', [], 1): Computes a vectorized inner product.
• reshape(..., Nd, Nd): Reshapes the resulting vector into an Nd \times Nd matrix TD, representing the transformation matrix.
3. Benefits of Vectorization:
• Efficiency: Avoids the inefficiencies of nested loops, using MATLAB’s optimized matrix operations.
• Scalability: Particularly advantageous for larger values of Nd, where traditional methods would be slower.
4. Uncommented Traditional Approach (for Reference):
• Provided as commented-out code, it demonstrates a nested loop method for computing TD. This approach is typically slower and less efficient compared to the vectorized method shown.
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The MATLAB file Fix_dic_test.m implements a Kernel Least Mean Square (KLMS) algorithm using a Gaussian kernel with a fixed uniform dictionary. The code involves several key components: parameter initialization, input signal generation, filter operation, theoretical model computation, and result plotting.
To use KDComp, clone the repository to your local machine:
git clone https://github.com/czichiy/KDComp.gitMake sure you have MATLAB installed on your system.