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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.

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# Author: Randal S. Olson (randalolson.com / @randal_olson)
# Uses Tableau's Tableau20 color scheme

figure.figsize: 12, 7
figure.edgecolor: white
figure.facecolor: white

lines.linewidth: 2.5
lines.markeredgewidth: 0
lines.markersize: 10

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# Author: Randal S. Olson (randalolson.com / @randal_olson)
# Uses Tableau's Tableau10 color scheme

figure.figsize: 12, 7
figure.edgecolor: white
figure.facecolor: white

lines.linewidth: 2.5
lines.markeredgewidth: 0
lines.markersize: 10

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"""
Minimal character-level demo. Written by Andrej Karpathy (@karpathy)
BSD License
"""
import numpy as np

# data I/O
data = open('data.txt', 'r').read() # should be simple plain text file
chars = list(set(data))
print '%d unique characters in data.' % (len(chars), )

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"""A stripped-down MLP example, using Theano.

Based on the tutorial here: http://deeplearning.net/tutorial/mlp.html

This example trims away some complexities, and makes it easier to see how Theano works.

Design changes:

* Model compiled in a distinct function, so that symbolic variables are not in run-time scope.
* No classes. Network shown by chained function calls.

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# CamTracker.py - track a colourful object with a webcam mounted atop a servo
# Running on a Raspberry Pi, Raspbian Wheezy OS
# (c) Sakari Kapanen, 2013

import cv2
import numpy as np
from RPIO import PWM

# the HSV range we use to detect the colourful object
Hmin = 159

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    def Adam(cost, params, lr=0.0002, b1=0.1, b2=0.001, e=1e-8):
        updates = []
        grads = T.grad(cost, params)
        i = theano.shared(floatX(0.))
        i_t = i + 1.
        fix1 = 1. - b1**(i_t)
        fix2 = 1. - b2**(i_t)
        lr_t = lr * (T.sqrt(fix2) / fix1)
        for p, g in zip(params, grads):
            m = theano.shared(p.get_value() * 0.)

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1. General Background and Overview

• Probabilistic Data Structures for Web Analytics and Data Mining : A great overview of the space of probabilistic data structures and how they are used in approximation algorithm implementation.
• Models and Issues in Data Stream Systems
• Philippe Flajolet’s contribution to streaming algorithms : A presentation by Jérémie Lumbroso that visits some of the hostorical perspectives and how it all began with Flajolet
• Approximate Frequency Counts over Data Streams by Gurmeet Singh Manku & Rajeev Motwani : One of the early papers on the subject.
• [Methods for Finding Frequent Items in Data Streams](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.187.9800&rep