Which is the best technique to identify from which category a sample belongs I'm a software developer and I'm facing a problem that I think should be solved through statistical techniques. 
We are developing software to classify some data. At the beginning of the project the founders of our company have interviewed about 5k people around the world about a few things they know/have. (Because it's top secret information I can't talk about, let's assume that we collect A, B and C). After some spent time on categorizing those people, they were able to identify some patterns on that data and segregate it into 8 categories. Now our software MVP helps people to identify, for a given sample data (A+B+C), which category it belongs. Good enough for a 3 months old startup.
Now, three developers were hired to improve the accuracy of our algorithm (including me). The current solution was made through "Ifs and Elses" on the source code, but it delivers A+B+C classifications with 60~70% of accuracy rate. I'm pretty confident that if we solve this classification through real math/statistics techniques it would have better results.
Our team have only the basics skills on statistics: Mean, StdDev, Variance, etc... After all, we just developers. After some research I discovered that there is a lot of techniques to solve this kind of problem (Classification Tree, Regressions, Persons'R, etc...).
Today, I'm here to ask you, math experts, what are the techniques I should really learn to solve this classification problem? We don't want to learn all about Stats and Discrete Math to solve this problem. It may take a year of more.
Thanks in advance.
 A: There are a number of techniques for this sort of classification, depending on the amount of data you have.  For 5k samples and assuming you have say ~100 attributes per sample, this is not a large data set.
You may want to do some exploration of the data using k-Means clustering which will create clusters of your data into similar items.  This might validate your 
earlier assumption/deduction that there are 8 clusters.
There is a technique that is popular these days called Random Forests.
While it is computationally more demanding it is relatively more forgiving in terms of data hygiene.  You can quickly pick up pointers and toy examples on Random Forests using Python, on www.kaggle.com
I am not sure if this is considered shameless self promotion or not but I have created a collection of self-learning materials in Data Science in the form of IPython Notebooks, available open source on github at http://learnds.com 
These are meant for developers who are familiar with Python to pick up a handful of useful techniques over a few weekends.  It is not exhaustive but will give you a sense of methodologies and tools needed.
Good luck!
Nitin
