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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.

	pragma solidity ^0.4.19;
	contract ERC721 {
	string constant private tokenName = "My ERC721 Token";
	string constant private tokenSymbol = "MET";
	uint256 constant private totalTokens = 1000000;
	mapping(address => uint) private balances;
	mapping(uint256 => address) private tokenOwners;
	mapping(uint256 => bool) private tokenExists;
	mapping(address => mapping (address => uint256)) private allowed;
	mapping(address => mapping(uint256 => uint256)) private ownerTokens;

	# Author: HJ van Veen <info@mlwave.com>
	# Description: Experiment to learn a tSNE transformer for new
	# test data with a multi-output GBM
	#
	# Idea first seen at lvdmaaten.github.io/tsne
	# > [...] it is not possible to embed test points in an existing
	# > map [...]
	# > A potential approach to deal with this would be to train
	# > a multivariate regressor to predict the map location from
	# > the input data.

	"""
	A bare bones examples of optimizing a black-box function (f) using
	Natural Evolution Strategies (NES), where the parameter distribution is a
	gaussian of fixed standard deviation.
	"""

	import numpy as np
	np.random.seed(0)

	# the function we want to optimize

	#!/usr/bin/env python
	"""
	Example of using Keras to implement a 1D convolutional neural network (CNN) for timeseries prediction.
	"""

	from __future__ import print_function, division

	import numpy as np
	from keras.layers import Convolution1D, Dense, MaxPooling1D, Flatten
	from keras.models import Sequential

	""" Trains an agent with (stochastic) Policy Gradients on Pong. Uses OpenAI Gym. """
	import numpy as np
	import cPickle as pickle
	import gym

	# hyperparameters
	H = 200 # number of hidden layer neurons
	batch_size = 10 # every how many episodes to do a param update?
	learning_rate = 1e-4
	gamma = 0.99 # discount factor for reward

	import pyeliza

	class Eliza:
	aliases = 'eliza'
	description = 'Virtual therapist'
	_therapist = pyeliza.eliza()

	def execute(self, expression, context):
	'''
	>>> from mock import Mock