Pio Raffaele Fina PRFina

Quick List of Resources for Topological Data Analysis with Emphasis on Machine Learning

This is just a quick list of resourses on TDA that I put together for @rickasaurus after he was asking for links to papers, books, etc on Twitter and is by no means an exhaustive list.

Survey Papers

Both Carlsson's and Ghrist's survey papers offer a very good introduction to the subject

Topology and Data by Gunnar Carlsson
Barcodes: The Persistent Topology of Data by Robert Ghrist

Other Papers and Web Resources

Extracting insights from the shape of complex data using topology A good introductory paper in Nature on the Mapper algorithm.

	import numpy as np
	N=10
	K=5
	array = np.arange(100)

	windows = np.lib.stride_tricks.sliding_window_view(array, N)
	strides = windows[::K]

	print(strides)

	# fake data
	true1 = 100.0
	predicted1 = 90.0
	# 2 order of magnitude bigger
	true2 = true1 * 100.0
	predicted2 = predicted1 * 100.0

	np.sqrt(mean_squared_log_error([true1],[predicted1])) # => 0.10426101032440993
	np.sqrt(mean_squared_log_error([true2],[predicted2])) # => 0.10534940571943174