# Nonparametric mixture model and clusters

I have a question about clusters that I am contemplating to treat with a nonparametric mixture approach (I think). I am working on the explanation of human comportment.
Each row of my database contains:

1. the ID of someone
2. some parameters of the environment X (example: the temperature, the wind, etc.)
3. a binary variable Y representing the person's reaction to the parameters (example: get sick or does not get sick because of the weather).

My idea (based on intuition and not on data) is that we can gather people in a finite number of groups so that in a group, people have the same reaction to temperature (some are easily sick, others are never sick...). In a given group, more formally, the law of Y conditional to the parameters X is the same.

I have no idea of the law of Y conditional to X. For the parameters X, I can do some hypothesis if necessary.

I would like to create some cluster of people "having more or less" the same reaction to parameter. Besides, I would like to predict the reaction of a given person to a given value of the parameters (even if this event has never happened in the database).

It seems to me that we can treat the problem like a nonparametric mixture model. As I don't have hypothesis on the conditional law of Y, I think I will have to create it with kernels method for instance. I have found this paper. Besides, it seems to me that, in this case, each row of observation $(X_i, Y_i)$ is not a simple realization of some random variable, but $X_i$ is a realization of a random variable, and $Y_i$ is a realization of a random variable conditional to $X_i$. I don't know if it makes a difference.

I have around 100000 rows. The vector $X_i$ has some discrete components, and others are continuous. I am wondering:

• Is my approach correct?
• Would you advise another point of view for this problem?

I would be very interested in any references about it.
Don't hesitate to ask me to reformulate the problem statement.

• Since you have labelled data it is simply a supervised classification problem and what you need is a binary classifier. Which classifier works "best" is a matter of personal taste and the specific problem. Definitely, I would try first some standard options (SVMs, decision trees etc.) before trying anything more exotic. – iliasfl Jul 6 '14 at 9:28
• Unless you are interested in the structure of the set, @iliasfl's comment is totally valid: classifier learning techniques will do well. Otherwise, you should use unsupervised learning. Before trying nonparametric models, you can try simpler EM algorithm for separating Gaussian mixture, or just k-means clustering, if you can estimate the number of clusters. Then, you may use its result for classification, or again classify raw data. – Roman Shapovalov Aug 5 '14 at 14:07