The first decision point to visit when choosing an ML algorithm is the mode of the learning process: supervised, unsupervised, or reinforcement learning. These modes have very little overlap; in general an algorithm is either supervised or unsupervised but not both. This narrows your choices down by roughly half, and fortunately it is very easy to tell which mode of learning applies to your problem.
The difference between supervised and unsupervised learning is marked by whether or not you need labeled training examples to teach the algorithm. If all you have is data points, and not labels or categories to associate them with, then you are only able to perform unsupervised learning. You must therefore choose one of the unsupervised learning algorithms, such as k-means clustering, regressions, Principal Component Analysis (PCA), or singular value decomposition...
