My Masters Thesis investigated Topological Data Analysis(TDA), which is essentially the study of the shape of data. I decided to attempt to apply TDA to financial markets, in particular cryptocurrency since the market was always open and there are no restrictions to wash sales. 

The theory relies on two aspects. First, the use of a Moving Average Point Cloud, which is the space of all intersections of moving averages. The intersection of two moving averages is a common technical trading signal. This point cloud is embedded in a plane where each quadrant(1-4) can be regarded as a market state: Future Bear, Bear, Future Bull, Bull. 

The second aspect is the use of Topology, where by two different point clouds are compared using topology. That is, two point clouds are similar if one can deform one into another without 'teariing' the points apart, although stretching and twisting are allowed. Alternatively, one can look at a more temporal aspect of the point cloud by treating it as a point in a high dimensional space, and then the sequence of point clouds as the topological space of interest. Both approaches give insight into the state and evolution of the system. You can read more by clicking the below research link.