# Machine learning with 2D matrix input and numerical output (regression)

I am working on a data science project on chemistry. My main expertise is in chemistry, and this is my first time working with statistical learning/machine learning. I am trying to test various different methods to see which one works. In my case, the input is a 2D matrix like the one shown below. And the output has to be a real number (it will be in the range -30 to +30).

$$\text{input =}\begin{bmatrix} 2.56&1&2&0 \\ 0&1.98&1&1 \\ 1&0&3.47&2 \\ 0&1&0&1.67 \end{bmatrix} \,\,\text{ output = }\mathrm{-3.7}$$

I have a dataset, with a 2D matrix input for each point, and the corresponding target output value for that point. I am supposed to train a learning model (regression or something similar) on the dataset. I am mainly considering regression models from scikit-learn, but I am open to using other packages (and other learning models such as CNN's).

The problem is that I don't know how to feed the 2D matrix into the learning model. The regression models assume a 1D array input for each datapoint. I could flatten the 2D array into 1D as suggested in some answers on this site, but the adjacency of elements is one of the most important pieces of information that I think will be lost when I flatten it. (What I mean is that there is important information in the closeness of two different elements in the matrix)

What are some of the good ways to handle a 2D matrix input for a machine learning model?

The technical details of what the numbers in matrix mean, are not important for my question. I am trying to understand the general methods of dealing with a 2D input for a statistical model.

If you go for a CNN (with only one "color" channel), which sounds like a good idea, you don't need to do much except glueing multiple observations together across an additional dimension. So for training a CNN with Keras, the input would be a n × 4 x 4 x 1 array and the output a one-dimensional vector of length n.

For less flexible modeling techniques like a random forest, an old trick with complex input is to derive a couple of meaningful features and use these as input:

• largest value on diagonal
• mean value on diagonal
• standard deviation on diagonal
• largest value off diagonal
• ...

This is an alternative to just flatten the numbers. However, if your sample is very large, then flattening is not a bad approach either.

• Thanks! Could you please explain what the 'one colour channel' CNN means? I have never heard that before. Also, do you think it is reasonable to diagonalize the 2D matrix and then take the diagonal values as input (I have seen this in a couple of research papers)? Jan 1 at 22:02