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KDComp

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.

Files Overview

file 1. CalculateKD

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.

file 2. CalculateRkkD

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.

file 3. CalculateTD

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.

...

File 4. Fix_dic_test

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.

Installation

To use KDComp, clone the repository to your local machine:

git clone https://github.com/czichiy/KDComp.git

Make sure you have MATLAB installed on your system.