Can anyone tell me how does curve fitting models like polynomial fit,linear fit help in classification of some data ,That is using CFTOOL?Just curious in knowing..what are things or parameters we should be looking at ?

Was just trying some models on some data, am a noob in using cftool... had gone through various articles on this...got to know some few things here and there... but Am still confused,how will it help in classifying some data ?

Answer 1

[John D'Errico]

This is not really a MATLAB question, but it does show confusion about how to use a specific toolbox. Anyway, I think you are approaching this from the wrong end of the horse. And we all know what comes from the wrong end of a horse. :)

You don't use a curve fitting tool to classify data. You use a curve fitting tool when you have a model that you want to fit to some data.

So first, you need to postulate some model. Then you can fit the model to some data. At the end, you may decide if the model fit poorly. If it exhibits lack of fit, etc. Then you might return to the initial step, and see if you can think of a better model.

In general, it is best if physical principles can be used to postulate the model. That makes it more likely the model might fit well.

For example, suppose I had some population data. Single species, bacteria growing in a petri dish. I might then postulate an exponential growth rate curve. THEN use a curve fitting tool to fit the model.

But, suppose I see the population does not grow continuously, but it stops after a while, or crashes? Now we might decide the model simply does not fit the data. In fact, more complex models, probably models that are derived from the solution to a valid ODE would be good. Fit that model next.

[L K]

Ok. But the thing i had in my mind is, suppose if am having different sets of data like contaminated with something and a pure product. Can i use these models on it to classify these two,this is what is going actually in my mind...Is it the right thing ?

[John D'Errico]

Again, start with the model. Don't use the data to infer some choice of model. That will lead to overfitting, just finding some random model that happens to fit through your data points.

But suppose you have a model for some process, where the model includes a "term" in it for a contaminant in some amount. Estimate the parameters of the model. Tools often provide some sort of confidence estimate around the parameters. Does the estimate of the amount of the contaminant include zero as a possibility within those limits? If so, then you should probably infer the contamination is not really there. It might just be random noise in your data. So this might drive you to get better data, with lower noise, or just get more data. Now you might be able to decide if the contamination is real, or just spurious noise.

So you might use such a model to decide that a contaminant is possibly present or not. But the point is to start with a model that allows it.

Alternatively, you might start with a model that allows no contaminant. Does the model have clear lack of fit? If so, then you need to expand the model, or choose a better one. A problem is that lack of fit is not something you can always test for, as opposed to the other case. Lack of fit is something best identified by your eyes.

Off to play bridge now. (I do have my priorities in line.) I'll look back in this afternoon in case this did not answer your question.

[John D'Errico]

Ok, back...

There are curve fitting tools that claim to find the model for any set of data, just from the shape of the curve. They just fit all sorts of models to the data, and the one that works best is proclaimed the model. Personally, I don't like that approach. While it may get lucky, it will tend to overfit the data. It will convince someone that a specific model is the correct one for their curve, when in fact, there is no such conclusion that can be drawn.

Only the source of the data really understands what they have. I once was asked to help model some curves. In talking to the scientists who were generating the data, I learned that their data was good enough that if there was a bump or a sharp corner in it, they needed to see that in the model. Those features were critically important.

The point is, you need to understand your data, the expected error, any characteristics about it. Finally, you need to understand the source of the data to be able to intelligently choose a model for it.

So use curve fitting tools by making the decisions, instead of letting them make the decisions for you, hoping the computer can get it right. Computers are stupid gits, good at doing what they are told, but terribly poor at making intelligent decisions.

[L K]

Ok, But which curve fitting tools you are talking about?I meant exactly what you said ,I have a data and i have curve on it, but i want to find a model for it,so Using cftool would help?