How do feature selection on a sparse matrix?
You can do a dimentionality Reduction as your matrix is Sparse. I would suggest to use PCA. PCA will reduce your 1500 input into k dimensional input of your choice with as much information retained as possible . Here k is a hyperparameter that you need to tune and fine the best one.
Another Approach is LASSO classfier which is a linear model with L1 regularization. This model will perform automatic feature selection and zero out the weight of feature that is not needed. But your input columns must be independent.