From 3296a36b846187093831ed07bd7df67073c04e0f Mon Sep 17 00:00:00 2001 From: shawk masboob <masboob.shawk@gmail.com> Date: Fri, 21 Feb 2020 13:24:21 -0500 Subject: [PATCH] removing temp files --- .DS_Store | Bin 8196 -> 0 bytes .Rhistory | 0 Models/.DS_Store | Bin 6148 -> 0 bytes ...Graph_Theory_ShawkMasboob-checkpoint.ipynb | 100 ------------------ ...ROJECT_Auto_Documentation-checkpoint.ipynb | 6 -- ...-PROJECT_Auto_Documentation.cpython-37.pyc | Bin 2050 -> 0 bytes .../__pycache__/TDA_Prediction.cpython-37.pyc | Bin 1852 -> 0 bytes .../__pycache__/TDA_Regression.cpython-37.pyc | Bin 2033 -> 0 bytes Reports/.DS_Store | Bin 6148 -> 0 bytes Topological_ML/.DS_Store | Bin 6148 -> 0 bytes .../Untitled1-checkpoint.ipynb | 6 -- .../__init__.py-checkpoint.ipynb | 6 -- .../__pycache__/TDA_Prediction.cpython-37.pyc | Bin 1874 -> 0 bytes .../__pycache__/__init__.cpython-37.pyc | Bin 259 -> 0 bytes 14 files changed, 118 deletions(-) delete mode 100644 .DS_Store delete mode 100644 .Rhistory delete mode 100644 Models/.DS_Store delete mode 100644 Models/.ipynb_checkpoints/0207-REPORT-Graph_Theory_ShawkMasboob-checkpoint.ipynb delete mode 100644 Models/.ipynb_checkpoints/0214-PROJECT_Auto_Documentation-checkpoint.ipynb delete mode 100644 Models/__pycache__/0214-PROJECT_Auto_Documentation.cpython-37.pyc delete mode 100644 Models/__pycache__/TDA_Prediction.cpython-37.pyc delete mode 100644 Models/__pycache__/TDA_Regression.cpython-37.pyc delete mode 100644 Reports/.DS_Store delete mode 100644 Topological_ML/.DS_Store delete mode 100644 Topological_ML/.ipynb_checkpoints/Untitled1-checkpoint.ipynb delete mode 100644 Topological_ML/.ipynb_checkpoints/__init__.py-checkpoint.ipynb delete mode 100644 Topological_ML/__pycache__/TDA_Prediction.cpython-37.pyc delete mode 100644 Topological_ML/__pycache__/__init__.cpython-37.pyc diff --git a/.DS_Store b/.DS_Store deleted file mode 100644 index 942fd30a9f40b152c4f4b81765b733297b33664c..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 8196 zcmeHMzmL-}6n?&zo?8S|2#Jna*g7<DaJL|ZQU)ZD5IMmBsFz$y8!3sSCZ)P7MfoFG z;J;zy4?qkzAQpCJ7M_35%cVb#38B`O?9a8|v-`eJb@E&QAnlQ70yF@CV&z!Bh|Pk+ z=XsqgTWaJgB0+zE01|hc#BRXcIcq(j8PE)91~dbj0nNbwzyLn8d7(?5`*K#dngPwg zMl!(92LmfdOJOEa939w*6acY|!=hjx^8n#vD6|x25``<SDYFNnT!~6Ch;+w!gPS8- z3Nwk)9f))XqIM=KLm^^!^fQDx5KE$NH3OP~c?NjyUV+EJz=K{PfB)>pfuE$U)>pDs zDqpB<Q(B|7OSM<_fQ{|cNk>WB8NT43o;c~iRsDU&f?3~jpZUFUw|?zDi&DprdPCvt zdp$IH`P`2@Hg2;~<RxMqTTW0~rPXe|F`4X`x0}XIb8p%-CcC?>rm=JD&U9L(*Ke42 zA0C89$CJ0ycOPV2M4b(Ar4Z-GVvs@Kv=3Pr=j_gq5VB53U1HE*?|*!${QPvUxJJml zb8X_m>V4kW!zf@;AJ^vJeH)&l2r-H=g!If+%34WL2y=lL1&h2KVd>k6l4H*5RFLIX z3nVG5QxN4c?4uxDlmKfVd^iLL`(6CiJj&g6t(8P8gI*xmO8dNg@#~ZCO1^V^PR0CN zp9Rvc+@m0L?l90@&A|FIP?8}wc>e!j`ThU;6QLv23~Vq1q};JPZ6x5&`*V>Co@*Oe z53usW?J|kN1sjo$BZ_n!arTEH_6;=UK9<5vB937B_ZI=PmpA?V7YgWR6B+mo?s-yu diff --git a/.Rhistory b/.Rhistory deleted file mode 100644 index e69de29..0000000 diff --git a/Models/.DS_Store b/Models/.DS_Store deleted file mode 100644 index 5008ddfcf53c02e82d7eee2e57c38e5672ef89f6..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 6148 zcmeH~Jr2S!425mzP>H1@V-^m;4Wg<&0T*E43hX&L&p$$qDprKhvt+--jT7}7np#A3 zem<@ulZcFPQ@L2!n>{z**<q8>++&mCkOWA81W14cNZ<zv;LbK1Poaz?KmsK2CSc!( z0ynLxE!0092;Krf2c+FF_Fe*7ECH>lEfg7;MkzE(HCqgga^y>{tEnwC%0;vJ&^%eQ zLs35+`xjp>T0<F0fCPF1$Cyrb|F7^5{eNG?83~ZUUlGt@xh*qZDeu<Z%US-OSsOPv j)R!Z4KLME7ReXlK;d!wEw5GODWMKRea10D2@KpjYNUI8I diff --git a/Models/.ipynb_checkpoints/0207-REPORT-Graph_Theory_ShawkMasboob-checkpoint.ipynb b/Models/.ipynb_checkpoints/0207-REPORT-Graph_Theory_ShawkMasboob-checkpoint.ipynb deleted file mode 100644 index 9cc6b8c..0000000 --- a/Models/.ipynb_checkpoints/0207-REPORT-Graph_Theory_ShawkMasboob-checkpoint.ipynb +++ /dev/null @@ -1,100 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# <center>Graph Theory within Topological Data Analysis</center>\n", - "\n", - "<center>by Shawk Masboob</center>" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Graph theory utilizes limited topological thought (i.e. it can be considered a subset of topology). Topological objects consist of nodes, edges, and faces. In graph theory, these objects arise through natural geo-spatial data (cell tower data, election data, etc.) or through artificial construction (social complexity theory, political relations theory, etc.). Some application of graph theory involve using graphs modeling relations and processes in physical, biological, and social and information systems. Graph theory is also used to represent computer networks. \n", - "\n", - "Graph theory and topology are related in that graphs are a 1-simplicial complex. A simplicial complex is a finite collection of simplices. [1]. A simplex is a generalized triangle in any arbitrary dimension where the 0-simplex is a point, the 1-simplex is a line segment, the 2-simplex is a triangle, the 3-simplex is a tetrahedron, the 4-simplex is a 5-cell, and so on. The figure below provides a simple example of simplices." - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "|  | \n", - "|:--:| \n", - "|__Figure 1.__ From left to right: a point (vertex), a line segment (an edge), a triangle, and a tetrahedron.\n", - "Image Source: [1] |" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The shift from the 1-simplicial complex and the 2-simplicial complex provides a simple demonstration of the relationship between graph theory and topology. It is challenging to discuss concepts within topology without implicitly referencing properties of graph theory. \n", - "\n", - "As mentioned above, there are many applications within graph theory. These same applications can be done using topology, specifically topological data analysis (TDA). TDA seeks to analyze datasets using various techniques from topology. It is beneficial to convert the data points with simplicial complexes based on some distance metric. A simple way of converting data points into a global object is to use each point as the vertices of a graph and to let the edges of the graph be determined by proximity. [2]. The graph at this stage (1-simplex), while capturing connectivity within the data, fails to capture higher order features beyond clustering. [2]. Moving up the “simplicial scales†allows the researcher to see other interesting features that may not be so obvious when using a standard graph. The Cech Complex and the Rips Complex are the two most common methods used to “fill in†the higher dimensional simplices. [2] Figure 2 demonstrates the process of converting a dataset into a higher order simplicial complex. " - ] - }, - { - "attachments": {}, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "|  | \n", - "|:--:| \n", - "|__Figure 2.__ The bottom left image is the Cech Complex and the bottom right image is the Rips Complex.\n", - "Image Source: [2] |" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "As seen from Figure 2, any point cloud data can be converted into a higher order simplicial complex after selecting a specified proximity measure. \n", - "\n", - "A real-world example that combines graph theory and TDA is as follows: the human brain can be visualized using graph theory. However, the human brain is a very complex network that is hard to visualize. MAPPER (a Python TDA package) can be used to reduce the high-dimensional dataset without having to make many assumptions about the data. [3]. Doing so allows the researcher to visualize the data using some graph. \n", - "\n", - "TDA is used to understand complex and high dimensional data problems. The simple technique mentioned above is capable to pointing out the natural patterns within a dataset that a standard graph cannot. Graph theory is useful if one seeks construct a network. If one seeks to go beyond network construction and clustering, they ought to consider using TDA. That said, TDA is not independent of graph theory. There are some theoretical similarities and applications. As noted above, a graph is a 1-simplicial complex. " - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "---\n", - "# References\n", - "\n", - "[1] Edelsbrunner, Herbert. “Simplicial Complexes.†COMPUTATIONAL TOPOLOGY, www2.cs.duke.edu/courses/fall06/cps296.1/.\n", - "\n", - "[2] Ghrist, Robert. “Barcodes: The Persistent Topology of Data.†Bulletin of the American Mathematical Society, vol. 45, no. 01, 2007, pp. 61–76., doi:10.1090/s0273-0979-07-01191-3.\n", - "\n", - "[3] Saggar, M., Sporns, O., Gonzalez-Castillo, J. et al. Towards a new approach to reveal dynamical organization of the brain using topological data analysis. Nat Commun 9, 1399 (2018). https://doi.org/10.1038/s41467-018-03664-4" - ] - } - ], - "metadata": { - "anaconda-cloud": {}, - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.7.3" - } - }, - "nbformat": 4, - "nbformat_minor": 1 -} diff --git a/Models/.ipynb_checkpoints/0214-PROJECT_Auto_Documentation-checkpoint.ipynb b/Models/.ipynb_checkpoints/0214-PROJECT_Auto_Documentation-checkpoint.ipynb deleted file mode 100644 index 2fd6442..0000000 --- a/Models/.ipynb_checkpoints/0214-PROJECT_Auto_Documentation-checkpoint.ipynb +++ /dev/null @@ -1,6 +0,0 @@ -{ - "cells": [], - "metadata": {}, - "nbformat": 4, - "nbformat_minor": 2 -} diff --git a/Models/__pycache__/0214-PROJECT_Auto_Documentation.cpython-37.pyc b/Models/__pycache__/0214-PROJECT_Auto_Documentation.cpython-37.pyc deleted file mode 100644 index 07bd442147a3b679ee435f0f44f744bb0192657e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 2050 zcmah~!EWO=5EUiamSsEHF1mZ@i9ib!J|x}-MbR#TqPy7?O@VcSID65d1})ODYFQFU zDrp4wlzu_~qQBA4(6y)jLQkC;If)aXC=GIEBn~z2%?$l^FbEwO?9=am8h0G$FEs9k z56X8i&F`>CN3zsev4}B8y3+g2iCpQ+7D!LFWe21$1K9=HlA-K@Y|FkJfb7VfC{UgX zZdue-q3Yhk8Olc)^}z0t-6FdWcAxAv%4h)gfb39pR3CH~Ex9{!hR^<nxSS!Y11YR9 z%9<D-;9#411kwbsNcO9<cEHK4Mj?k$7HKXdxA_gf^X7A%uegbmWn%YIC3HqR$A92A zeB7lyIEt2kW}^>AX)`hlalKp#Gt2YY=$$f4n-?RPd757)u}G&Y5igQVP3gcSyBxjG zrAp1{)xj5E?wy^V{&;+JF@00oeEKer%azKkut}cn7dH(q46}tWFddHXGu;LmBSIW5 zOpJ<<J_iMmG7BkMJGU-#)(kLv)mPh?wGt`6&UGsP7kc#^HcN<_b`n9afs9t6lgtj? 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