Say I'm building a neural network to fit some classifier of some sort. To make things concrete, let's take the example of predicting housing prices using features of houses.
What should I do if one or two of my features consist of many more numbers than the other features, or even all other features combined? For example, say I have a few housing features: size in sqft, age, median income of location. These are 3 numbers. And then I have another feature, height of the roof for each square foot of the house (it's a bit contrived for this example of course) for which I would have actually "size in sqft"-numbers for this feature. So now my feature vector looks like this:
X = [1500sqft, 34 years, $54,000, 10ft, 10.1ft, 10.3ft...1497 more numbers here...]
It seems that if I just naively put this into a neural net that the first 3 features would essentially be ignored since they only account for 3/1503 features. But they might actually be important. One try might be to simply average the "height of roof" feature over all of its elements to get an "average height of the roof" feature. That makes sense for this example, but what if sometimes I don't want to take this average? Are there any industry practices on what I might try if I ran into a problem like this?