The idea is. With lots of data representing a signal you want to use. You might get lots of different values for the same x coordinate. That is. More than one y value for the x coordinate.

Then I thought why reduce a signal to a function of statisitical points. With some least square method for some line. I mean. We have computers capabable of taking advantage of as many data points we can sample.

Still to make some size reduction my idea is to store all the data in some kind of fourier series. That is. With multiple values y for some x coordinate. Not making some statistical reduction to get a function.

This information I imagine could be useful for a machine learning algorithm.

An example would be a camera photo. Where you will have multiple colors for some of the pixels. Not reducing the pixel color to one color. Just storing all the colors that the pixel got from the sensor. I think this could be taking advantage of in machine learning.

Since there are several statistical methods available. Some will be better than others for the particular problem. However my hope is that machine learning will find the best method possible. And since machine learning evolves its better to store all the data for future improvements.

Another idea would be to keep the value of one of the multiple values in every multivalued point. So that in a lossy fourier based compression. Each of the “choice values” makes a good contribution to the signal. By good. I mean it does not add to some ?high frequency noise.