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This is an important problem, with a lot of work done on it already.The t-SNE algorithm (t-distributed Stochastic Neighbor Embedding) is an algorithm for representing a clustered high-dimensional set of points as a 2-dimensional set which tends to respect the clustering. t-SNE works well in many situations. There are open-source implementations in R, Matlab/Octave, and Cuda, and probably others. After you encode your data as a set of vectors, it is relatively easy to run it through through a t-SNE module. Then you can color the points according to whether they are in Group A or B.Here is an example of t-SNE on a set of images:In this example, most images of faces were clustered in the bottom. Most images of airplanes were clustered on the right. These came out of the t-SNE algorithm even without labeling the images.You are unlikely to do better if you only spend a little time working from first principles.

Let us assume our data looks something like this:If we apply PCA to this data, the first principle component would give the direction of maximum variance (the direction along which most of the data is aligned):If we project our data on this principle component, all the clusters in the data would fall on top of each other and we lose cluster information completely.On the other hand, if we apply t-SNE to this data, we get a lower dimensional representation that pretty much preserves all the cluster information. It would look something like this:Now coming back to the question. Even when t-SNE preserves local information which we can lose with PCA, I can think of three reasons why PCA is better suited for dimensionality reduction as compared to t-SNENew data: PCA is a transformation that rotates basis vectors in the same feature space. So new data can be projected along these new basis vectors. t-SNE on the other hand is a non-parametric algorithm and it does not learn a mapping function from the higher to lower dimensions, so projecting new data onto the lower dimension is a problem.Non-deterministic solution: t-SNE minimizes the KL divergence between the joint probabilities of higher dimensional data and the corresponding lower dimensional embedding. Since this might not always be a convex function, t-SNE can lead to different solutions for different runs. PCA on the other hand is deterministic. The set of eigenvectors you obtain for a dataset are always the same.Loss of global information about data: PCA uses eigenvectors as basis vectors of the feature space to successively capture maximum variance in data. t-SNE, on the other hand tries to preserve local information while converting data to a lower dimensional embedding, but does not accurately capture the global properties of data.So even though t-SNE is an excellent candidate for visualizing high dimensional data, it is not an ideal algorithm for dimensionality reduction.

Before we deployed for a 30 day combat operation we were given a plastic box with compartments that contained pills. Some of the pills helped to combat the problem; if you had a runny nose and prone to sneezing you’d take the correct pill and you couldn’t sne even if you wanted, if you had the runs you’d take what we called the ‘cork’, when you returned to the A-Site and couldn’t poop we’d take what we called the ‘brown bomber’ and to facilitate our ability to survive with only 2 to 3 hours of sleep every night we were given 30 Amphetamines one per night we refered to them as ‘grasshoppers’ when you returned to the A-Site after 30 days you’d be jumpy.