Comparing Distance Measurements with Python and SciPy

At the core of cluster analysis is the concept of measuring distances between a variety of different data point dimensions. For example, when considering k-means clustering, there is a need to measure a) distances between individual data point dimensions and the corresponding cluster centroid dimensions of all clusters, and b) distances between cluster centroid dimensions and all resulting cluster member data point dimensions. While k-means, the simplest and most prominent clustering algorithm, generally uses Euclidean distance as its similarity distance measurement, contriving innovative or variant clustering algorithms which, among other alterations, utilize different distance measurements is not a stretch. It is thus a judgment of orientation and not magnitude: two vectors with the same orientation have a cosine similarity of 1, two vectors at 90 have a similarity of 0, and two vectors diametrically opposed have a similarity of -1, independent of their magnitude.