How to classify parametric curves? I am working on a project which aims at determining whether a patient has cervical issues or not, based on a certain movement (for instance, turning the head from left to right and so on).

For each patient, I have one or more sets of coordinates acquired with a VR headset. One problem is, all the patients are assumed healthy and I cannot compare their data with patients who actually have cervical issues. 

I am currently working with two coordinates at a time, not the three, and I am considering two approaches: the first is to use approximation (splines...), the second is to use concave hulls. I am a bit more inclined to use hulls and I thought that I could calculate the distance between two hulls A and B as follows: area(A\B)+area(B\A). Note that the curves are parametric.

I have two questions:  


Is it possible to "classify" patients using a data set that only consists of healthy patients? Or to find a "descriptor" for them ?  
If so, or assuming I can get data on unhealthy patients, what tools can I use to classify the curves? I did not find anybody who worked on a similar problem.
Whenever you have skewed dataset, it means that you know some classes better than some others. In such cases it means that the data is your knowledge and there are learning algorithms for such occasions.

Consider an important fact here. Suppose that you have feature vectors of conditions of a nuclear company and they describe whether the company is in danger of nuclear radiation or not. In such case it is clear that it does not happen a lot that you have infected companies so most of your data have label of healthy condition. You have so much knowledge about the healthy class but you don't know much about the infected class because you don't have much data consequently you don't know its distribution and you can not estimate it well. Whenever your data is skewed, it means that e.g. you have 1 million feature vectors of negative class and 5 feature vectors of positive class. Now suppose that you change the feature vectors. In such cases you have imbalanced data-set or you just have the data samples of some classes without some other, you can use anomaly detection.


  In data mining, anomaly detection (also outlier detection) is the identification of items, events or observations which do not conform to an expected pattern or other items in a dataset. Typically the anomalous items will translate to some kind of problem such as bank fraud, a structural defect, medical problems or errors in a text. Anomalies are also referred to as outliers, novelties, noise, deviations and exceptions.