How to arrange learning by sample?

Question

Machine learning

Good afternoon.
The following task is set: there is a sample with 300 fields. It represents people with cancer. Fields - results of analyses. It is necessary for new people with passed tests to determine whether they have oncology.
To begin with, I plan to use the principal components method to reduce the dimensionality of the sample. What to do after, I do not know.
If there were two samples - sick / healthy, then this would be a classification task. But what if there is only one sample? How to compare the new values ​​of the vector with the original sample?
There is an idea to use a genetic algorithm in this case. But everything remains at the level of the idea.
What algorithm would you use to solve this problem?
Thanks in advance for your reply.

Answer 1

When I was in bachelor's degree, I had a similar problem. I ended up soldering the Gaussian (read, ellipse) around the sample (there were points on the plane) and everything that fell into the ellipse was sick, and everyone who was not, respectively, was not. It even gave good accuracy.
Another simple option is to throw some kind of Gaussian on each point from your training data, "add" them all together to get some kind of strange distribution, which, in fact, will give you the area in which your data is located. Even some probability can be predicted. Probably, if you think about it, you can bring a more or less beautiful theory under this.
If you look for how this is implemented in a normal way, then the following is immediately googled: www.researchgate.net/publication/221654469_Learnin...
isites.harvard.edu/fs/docs/icb.topic274302.files/D...
You can also dig into the One-Class SVM. Haven't done it myself, but it might work for you. The implementation is in libSVM.
In general, look towards one-class classification. There is plenty to choose from. Someone even defended his doctoral thesis - homepage.tudelft.nl/n9d04/thesis.pdf.
In general, keep it up.