I first caught wind of Active Matter through the work of one of my favorite researchers, Tamas Vicsek, whose intellectual bling includes a fractal bearing his name. My understanding of this sprawling sub-domain of physics is that we can study the activity of individuals agents and systems as though studying something like hydrodynamics, kinematics, and non-equilbrium statistical phsyics. Crowds become streams. Flocks become rivers. Networks of agents become oceans.

I’d like to overview Pearson’s r, touch upon Kendall and Spearman, and then dive into MIC. Pearon’s r This is what people typically think of when they think of correlation. It measures the linear relationship between two variables. If you plot (x, y) pairs and look for a line of best fit to describe their relationship, a $\rho = 1$ would be all the points on a line with a positive slope, and likewise a $\rho = -1$ would be all the points on a line with a negative slope.

Sometimes we want to perform an operation on an agent/vector/particle based on what we know about its neibhors. Here are contenders for measuring the nearness of any two points in an n-dimensional real vector space with fixed cartesian coordinates, and strategies for using these distances to calculate neighors: Distance Euclidean As the name suggests, this is the square root of the sum of squares for each corresponding input pair of our points.

PSO Approach A paper was brought to my attention today (Particle Swarm Optimization for Outlier Detection) presenting a novel application of PSOs in outlier detection, and I wanted to write about it to see if I can find my way to some context in operations intelligence (i.e. possibly anomaly detection in log files?). As the authors established the outlier problem, I realized that I carry with me a distance measurement bias when I think about classifying outliers.