I never thought of application of higher mathematics and statistics in the very fascinating manner to get the best possible insights in the most complex cases. It is going to be the next hot trend in the big data analysis in Finance, Supply chain management, Banking, Healthcare, Sales and others.
There has been a trend of using knowledge of every field including computer science, physics to get insights in terms of business needs and opportunities. Computational geometry has been fascinating as well as thought-provoking and that is why it has been used by many business leaders and investors. Envisage this computational geometry being coupled with algebraic topology as it can enhance the quality of analysis in an incredible manner. You can think of contours, silhouettes, surfaces made for data, by data and of data.
Now, conjure up a picture when someone attempts to apply beauty of machine learning, data mining, probability and statistics in this data silhouettes, contours, surfaces. Incredible insights can be expected from it. In terms of mathematics, a set of data points is to be replaced by simplicial complexes(indexed by proximity parameter),thereafter, analyse it via persistent homology and then encode it into persistence diagram.
It is meant to solve the most complex problems any business-leader or any researcher faces. Professionals and would-be-professionals from the field of Big Data Analytics, Artificial Intelligence, Robotics, Structural biology and Computer- vision are being allured by topological data analysis. Recently, R addicts and python addicts have developed packages to do this marvelous analysis. Come, be part of it.