Can correlation matrix be used as features in machine learning classification Can I use correlation between the training data as features, and if possible how will I test the test data with the model coefficients
I will try to explain more
If the training data are
X = [X1, X2,....., Xn]
and Xi = [Xi1,Xi2,....., Xi100]

where X are the training data and Xi is one sample of the data
and
K = [Xcorr1,1 ... Xcorr1,n
     ...      ...   ...
     Xcorrn,1 ... Xcorrn,n]

K will be something like that
K = [1 .2 .3 .4
     .2 1 .5 .6
     .3 .5 1 .7
     .4 .6 .7 1]

Can I will use this K to train my model ?
If it is possible How will I test my test data which will be
X = [X1, X2,....., Xn]

 A: I think I may now understand the proposed algorithm, and it seems reasonable, but I don't think it is the way I would go about it.
The correlation in question is not the usual Pearson correlation, but the sort used in signal processing, which is related to convolutions and autocorrelations:

(source: Wikipedia)
This function describes the similarities between the signals at different spatial distances.
As I understand it, the idea is to compute the correlation functions between the test signal and each of the training signals and compute a weighted sum, which will hopefully (if the genetic algorithm worked well) would pick out parts of the correlation function that contain discriminative information.  So the feature is actually a similarity metric based on the correlation function.
This means the features of the new dataset are measures of the similarity between the test signals and each of the training signals.  To generate the features for the test cases, it should be sufficient to just compute the covariance function between each test signal and each training signal and compute the weighted sums as before.
However, I think there is a much simpler approach.  Just compute the covariance function between the signal and all of the training signals and just concatenate them together to make one very long vector and then use that as the input to a support vector machine.  The performance bounds for the SVM don't depend on the dimensionality of the input vector, so provided you tune the regularisation parameter properly, over-fitting shouldn't be a problem and the SVM will identify the correct weightings for each lag in the correlation functions for you.  As you can use the dual formulation of the SVM, there will be one parameter per training signal, rather than one for each element of the feature vector, which in this case will be reasonably efficient.  This is likely to be much more effective than a GA, where there is little or no control over over-fitting.
A: Of course can and should are different things. Of course you can take either the upper or lower triangle of the correlation matrix and train a machine learning model that takes them as input. While opinions, first principles, and guesswork might be helpful/misleading, the should part will become apparent from the performance of the models you try on such a feature space.
Using such a feature space as the correlations will average out lots of details about the original dataset. And correlation is itself translation-invariant and absolute-scale invariant, which also loses information, but z-score standardization is common (and often useful) anyway.
If you are predicting some variables from the correlation matrix in the training set, you will have to compute the corresponding correlation matrix for the test set as well.
My advice is to do a few tests to see how well it works.

The OP has clarified that they are not computing the usual Pearson correlation matrix, but rather a cross correlation. I quickly cooked up an example with correlation in the usual sense. For brevity I omit otherwise important aspects of machine learning such a cross validation. I may return to give a cross-correlation example in the future.
First import some modules and set a seed value for reproducibility.
import numpy as np
from sklearn.svm import SVC

np.random.seed(0)


Then let's define some population covariance matrices for three classes. I later assume that the mean vectors are the zero vector since the Pearson correlations are translation invariant anyway.
cov1 = np.eye(3)
cov2 = np.ones((3,3))
cov3 = [[1,-1,0],
        [-1,1,-1],
        [0,-1,1]]

covs = [cov1, cov2, cov3]

Now let's construct a $3000 \times 3$ matrix (1000 per population) whose rows are the $m=10$ samples and whose columns are the off-diagonal correlations. The sampling assumes a trivariate Gaussian distribution for each population. I apologize that the code is needlessly complicated due to stream-of-consciousness coding.
sample_corrs = []

k = 1000
m = 10

for i in range(k):
    sample = [np.random.multivariate_normal(
            np.zeros(3),
            cov=covi,
            size=10
            ) for covi in covs]

    sample_corrs += [np.corrcoef(X_i.T)[np.triu_indices(3, 1)] for X_i in sample]

y = np.array([0,1,2] * k)
sample_corrs = np.array(sample_corrs)

Then train a support vector machine classifier (using a radial basis function as the kernel by default).
model = SVC()
model.fit(sample_corrs, y)

And check the accuracy on the training set.
>>> print(np.mean(model.predict(sample_corrs) == y))
0.934

So it appears you can discriminate populations based on their sample correlation matrices, at least in this idealized example.
I'll skip doing the cross-validation and hyperparameter tuning here since my goal here was just to show that some sort of model could be trained on a correlation matrices to predict a class.

Performing dimensionality reduction via principal component analysis on the $3000 \times 3$ matrix gives the following projection in 2D.

A: I don't see it, unless you have something like multiple multivariate time series and take the correlation matrix of the univariate time series (think multiple speech signals that you want to classify as being English or Spanish). (Let's ignore the time dependence and say that we're just going to slug through the calculation.)
In such a situation, that could be a feature extraction method. For each time series, you reduce the time series to a matrix, and then you use the matrix entries to predict the outcome. This even could result in different-length time series having the same number of features. I have my doubts that this will preserve the valuable information needed to make accurate predictions, but maybe there could be situations where this works.
However, if you just have a regular data frame (such as all of the time series concatenated together) and take the covariance matrix, you will wind up with one correlation matrix and a bunch of outcomes.
set.seed(2022)
N <- 1000
p <- 10
X <- matrix(rnorm(N*p, 0, 1), N, p)
y <- X %*% rnorm(p, 0, 1) + rnorm(N, 0, 1)
features <- corr(X)
L <- lm(y ~ features)

You don't have feature values corresponding to each outcome, so this code fails.
