Finding patterns in data I am probably looking for a definition.
Imagine we have 10 variables, but we are not interested in some kind of linear relation (nor quadratic or with any curve to it). What I would like is a way to find "clusters" , patterns or combinations (whatever you want to call it). For instance, given 10 variables, let's say two (or more) people have extremely similar scores, though they are both not necessarily high nor low. I'm under the impression that this information is lost to us, while in fact this could be an interesting finding.
Is there a name for trying to distinguish such interesting data patterns?
Any suggestions are welcome (also for the title).
 A: You definitely wan't to do some kind of clustering, but there are so many algorithms now a days, it's hard to suggest one without knowing more about the data (what types of variables and number of records, for example). Can you give some more information? Such as more about the data structure, or what kind of patterns you are looking for (maybe an example of how scores can be similar but one high and one low; do you mean similar variance?)
I don't think PCA is a good choice, as it only finds linear relationships(which you specifically mentioned you aren't looking for), and doesn't deal well with multicollinearity if it is present. It seems like the question asker is looking for a more robust method than using the eigenvalues of a correlation/covariance matrix.
A: It sounds like you are trying to cluster your data. Principle Component Analysis is an easy way to find clusters within your data, regardless of their relative high/low quality (there are many R packages for this).  k-means clustering is an established algorithm as well.
You might look at the general Wikipedia article.
A: Been comparing clustering algorithms kcluster, PCA, and TSNE for a while now. I would suggest TSNE its a great algorithm that beats PCA on one research benchmark in a specific real dataset like a twitter feed same with MNIST dataset.
Summary of process: First, t-SNE constructs a probability distribution over pairs of high-dimensional objects in such a way that similar objects have a high probability of being picked, whilst dissimilar points have an extremely small probability of being picked. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the Kullback–Leibler divergence between the two distributions with respect to the locations of the points in the map. Note that whilst the original algorithm uses the Euclidean distance between objects as the base of its similarity metric, this should be changed as appropriate.
Comparison to KCluster: The difference between kcluster and tsne is that you don't have to set on how many cluster it should have in the hyper parameter its allocated automatically. the only down side of this is its slow as it computes everything.
Preview/References:
Here's a web demo: https://cs.stanford.edu/people/karpathy/tsnejs/
Here's the blog version: http://karpathy.github.io/2014/07/02/visualizing-top-tweeps-with-t-sne-in-Javascript/
