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I know the benefits of using cnns(reduced size weight matrices). Is it a good idea to convert a input vector(which is not a image) into a matrix and apply cnn's. What I understand is that it should not be done because this would enforce some relationship between input vector value which actually doesn't exist.

Am I correct or there is some way we can apply cnn's to reduce computation?

If cnn's can't be applied what could be the method for reducing computation for very high dimensional input

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This is a job for dimensionality reduction techniques. PCA is a simple and intuitive method that you should probably try first. If you find it is insufficient or ineffective, you could try using an autoencoder.

As you said, using a CNN would imply a locational relationship between variables. If such a relationship does not exist, the CNN could have difficulty finding suitable weights. It is possible that forcing the CNN to link seemingly unrelated variables could help the model generalize better or reveal underlying structure that you cannot perceive, but there are other problems that you will run into. For example, CNNs generally use pooling layers as a form of nonlinear dimensionality reduction. However, if your variables are completely independent and unrelated, you would simply be throwing away possibly critical information using this down-sampling technique.

So while it might be feasible to use a CNN, you should probably use the right tool for the job.

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