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ebolyen/upgma.ipynb

Last active August 29, 2015 14:01
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UPGMA Compare
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upgma.ipynb
{
"metadata": {
"name": "UPGMA comparison"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": "Comparison of UPGMA from PyCogent and SciPy/scikit-bio\n========================================================"
},
{
"cell_type": "code",
"collapsed": false,
"input": "from cogent.cluster.UPGMA import UPGMA_cluster\nfrom cogent.core.tree import PhyloNode\nfrom scipy.cluster.hierarchy import average as scipy_upgma\nfrom skbio.core.tree import TreeNode, DistanceMatrix\nfrom StringIO import StringIO\nimport numpy as np\nimport math",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The following matrix is taken from http://www.southampton.ac.uk/~re1u06/teaching/upgma/\nas an example of the correct procedure and result of UPGMA"
},
{
"cell_type": "code",
"collapsed": false,
"input": "matrix = np.array([[0, 19, 27, 8, 33, 18, 13],\n [19, 0, 31, 18, 36, 1, 13],\n [27, 31, 0, 26, 41, 32, 29],\n [8, 18, 26, 0, 31, 17, 14],\n [33, 36, 41, 31, 0, 35, 28],\n [18, 1, 32, 17, 35, 0, 12],\n [13, 13, 29, 14, 28, 12, 0]],\n np.core.numerictypes.sctype2char(float))",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Here is the UPGMA of the above matrix as calculated by PyCogent:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "pycogent_newick = str(UPGMA_cluster(matrix.copy(), map(PhyloNode, 'abcdefg'), 99999999))\nprint pycogent_newick",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "((((a:4.0,d:4.0):3.875,((b:0.5,f:0.5):5.75,g:6.25):1.625):6.3125,c:14.1875):4.03125,e:18.21875);\n"
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Here is a linkage matrix created by running UPGMA from SciPy:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "# First we need to get the upper triangle from the matrix\ndef get_upper_triangle(matrix):\n m = matrix.copy()\n num_entries = len(matrix)\n top_triang = []\n offset = 1 # we skip the first diag with 1\n for i in range(0, num_entries):\n for j in range(offset, num_entries):\n dist = m[i][j]\n top_triang.append(dist)\n offset +=1\n return np.array(top_triang)\n\ns_upgma = scipy_upgma(get_upper_triangle(matrix))\nprint s_upgma",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "[[ 1. 5. 1. 2. ]\n [ 0. 3. 8. 2. ]\n [ 6. 7. 12.5 3. ]\n [ 8. 9. 16.5 5. ]\n [ 2. 10. 29. 6. ]\n [ 4. 11. 34. 7. ]]\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": "Here is the linkage matrix formatted as a Newick string using scikit-bio:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "skbio_newick = str(TreeNode.from_linkage_matrix(s_upgma, 'abcdefg'))\nprint skbio_newick",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "(e:17.0,(c:14.5,((a:4.0,d:4.0):4.25,(g:6.25,(b:0.5,f:0.5):5.75):2.0):6.25):2.5);\n"
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": "The following is what we expect:\n--------------------------------\n\n<img src=\"http://www.southampton.ac.uk/~re1u06/teaching/upgma/upgma16.PNG\">\n\nTo compare:"
},
{
"cell_type": "code",
"collapsed": false,
"input": "print \"ScyPy/skbio: \" + skbio_newick\nprint \"PyCogent \" + pycogent_newick",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "ScyPy/skbio: (e:17.0,(c:14.5,((a:4.0,d:4.0):4.25,(g:6.25,(b:0.5,f:0.5):5.75):2.0):6.25):2.5);\nPyCogent ((((a:4.0,d:4.0):3.875,((b:0.5,f:0.5):5.75,g:6.25):1.625):6.3125,c:14.1875):4.03125,e:18.21875);\n"
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": "I believe the above discrepancy is a result of PyCogent's UPGMA algorithm mutating the matrix after each iteration effectively taking a running average between two clusters rather than maintaining a reference to the original matrix and calculating the average distance of all original elements.\n\nFortunately we can demonstrate a correlation using Greg Caporaso's dataset in his [book](https://github.com/gregcaporaso/An-Introduction-To-Applied-Bioinformatics/):"
},
{
"cell_type": "code",
"collapsed": false,
"input": "soil_dm_str = 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15197110076\t0.687342919183\t0.759480157455\nGB2.141732\t0.770994532905\t0.71206229417\t0.747001448824\t0.632045389698\t0.874000155512\t0.734445360388\t0.854646046721\t0.862470516065\t0.826204667726\t0.695879701421\t0.634899737912\t0.675452873053\t0.849515947701\t0.668264491098\t0.688543055343\t0.753568917792\t0.733058031358\t0.673653230302\t0.701916751581\t0.728078250552\t0.846225316004\t0.784083591095\t0.768804971837\t0.861268828623\t0.837943721195\t0.687593993656\t0.778750962915\t0.810168353197\t0.659605362215\t0.884111307714\t0.617102771113\t0.676800645518\t0.701954495981\t0.841850450134\t0.695534295702\t0.670386730768\t0.744835907608\t0.771160684122\t0.777042889592\t0.684411624551\t0.781727738939\t0.677240404892\t0.848591531374\t0.742799484469\t0.741760647444\t0.721351153488\t0.86161053667\t0.898995474904\t0.679145677822\t0.637913550416\t0.809092958293\t0.859539159625\t0.630375026126\t0.867329265308\t0.662347151758\t0.863526620261\t0.699873653053\t0.83752164786\t0.808653858523\t0.730544700821\t0.86735641637\t0.757584274262\t0.848556995076\t0.730858546781\t0.733001692069\t0.819622339098\t0.85655782029\t0.729948790326\t0.745086529527\t0.754114996833\t0.677000003005\t0.776229191185\t0.69956122176\t0.905900693941\t0.748039824524\t0.741279835045\t0.856836960687\t0.645054411855\t0.813446372063\t0.865617583214\t0.828326828857\t0.689473981688\t0.75227643219\t0.875368467518\t0.715197110076\t0.0\t0.756571233406\t0.819053773522\nCL2.141671\t0.713860366658\t0.700396287442\t0.829163370451\t0.745395557492\t0.803646149281\t0.721950100873\t0.732598123492\t0.79780306402\t0.75773899141\t0.681958043459\t0.784995003277\t0.761509560089\t0.778526897193\t0.776245244538\t0.746855720937\t0.695651663401\t0.651169888444\t0.756546671436\t0.689915792303\t0.751563116106\t0.757698941496\t0.81521784111\t0.72246988506\t0.766678118035\t0.779913619543\t0.721905945293\t0.629557344015\t0.729317687442\t0.775284115744\t0.809585278998\t0.752867926027\t0.765915147902\t0.797341731143\t0.779371890673\t0.75355544013\t0.763336486511\t0.678168586188\t0.693450677791\t0.845666360765\t0.73562906966\t0.749605300872\t0.734576179976\t0.77040933545\t0.840375768701\t0.712626943013\t0.697185267367\t0.787297088617\t0.839673548631\t0.768325279187\t0.764218460162\t0.69649557949\t0.797925934359\t0.784459699516\t0.78240093762\t0.773979887967\t0.782306077586\t0.693960004203\t0.765860544383\t0.860081326243\t0.715520474708\t0.782664039728\t0.732265197025\t0.801505220155\t0.702009156586\t0.823135630763\t0.734859452185\t0.771993470771\t0.702695024981\t0.816809984731\t0.811763294725\t0.684700821115\t0.717361093102\t0.756004682491\t0.849322421317\t0.746125579708\t0.723754219342\t0.795333572811\t0.725113726775\t0.740004286817\t0.779943436613\t0.758895935123\t0.694967963846\t0.643700638144\t0.802850934476\t0.687342919183\t0.756571233406\t0.0\t0.739202954285\nSK1.141669\t0.673966462302\t0.784531402763\t0.84125975609\t0.802090919047\t0.757202316601\t0.7312195981\t0.683121159457\t0.755930422531\t0.723513824746\t0.737931920496\t0.821181930555\t0.823124060588\t0.755217446253\t0.82191314658\t0.816435570277\t0.702129776343\t0.703262973651\t0.814004504088\t0.753669878145\t0.803409848127\t0.77377147222\t0.811811506882\t0.790669441712\t0.729267507328\t0.679808173491\t0.786178142443\t0.702153083184\t0.656183111229\t0.823802643262\t0.763273198585\t0.791789365256\t0.815177493712\t0.841684348216\t0.701138200838\t0.767966829765\t0.821362691168\t0.74459360168\t0.715329224577\t0.84387524155\t0.789672553182\t0.79599170556\t0.802285642218\t0.663088580062\t0.861461411726\t0.659512110227\t0.678818668805\t0.73039256079\t0.781965790877\t0.824930354978\t0.801021957759\t0.667803314634\t0.760561506299\t0.806981994218\t0.736833908955\t0.82626469244\t0.778301060805\t0.805009332868\t0.776666452051\t0.863537928291\t0.713350692266\t0.731933317937\t0.716594089061\t0.733506706792\t0.796756728962\t0.836501727494\t0.643385919151\t0.772000300991\t0.788380579067\t0.836449672179\t0.834159376\t0.762304956908\t0.681262319968\t0.802222279629\t0.778005573478\t0.750758368474\t0.801738612034\t0.732038610247\t0.766520804916\t0.626363378258\t0.747546118326\t0.702813350242\t0.752509290936\t0.74110563838\t0.736200970813\t0.759480157455\t0.819053773522\t0.739202954285\t0.0\"\"\"",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 19
},
{
"cell_type": "code",
"collapsed": false,
"input": "soil_dm = DistanceMatrix.from_file(StringIO(soil_dm_str))\nprint soil_dm",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "88x88 distance matrix\nIDs:\nIT2.141720, HI3.141676, MD2.141689, CA1.141704, PE5.141692, CO1.141714, ...\nData:\n[[ 0. 0.72577309 0.84042375 ..., 0.77099453 0.71386037\n 0.67396646]\n [ 0.72577309 0. 0.81429344 ..., 0.71206229 0.70039629\n 0.7845314 ]\n [ 0.84042375 0.81429344 0. ..., 0.74700145 0.82916337\n 0.84125976]\n ..., \n [ 0.77099453 0.71206229 0.74700145 ..., 0. 0.75657123\n 0.81905377]\n [ 0.71386037 0.70039629 0.82916337 ..., 0.75657123 0. 0.73920295]\n [ 0.67396646 0.7845314 0.84125976 ..., 0.81905377 0.73920295 0. ]]\n"
}
],
"prompt_number": 40
},
{
"cell_type": "code",
"collapsed": false,
"input": "soil_id_str = \"IT2.141720\tHI3.141676\tMD2.141689\tCA1.141704\tPE5.141692\tCO1.141714\tDF3.141696\tPE1.141715\tSP2.141678\tCO3.141651\tSA2.141687\tCM1.141723\tLQ2.141729\tSR2.141673\tCR1.141682\tVC1.141722\tIE2.141655\tRT2.141710\tCC1.141721\tTL2.141706\tPE6.141700\tHI1.141693\tPE7.141734\tBF1.141647\tMP2.141695\tKP1.141713\tCL3.141664\tSK3.141716\tSF1.141728\tPE4.141683\tBP1.141702\tSB1.141730\tSF2.141677\tSN1.141681\tSA1.141670\tKP3.141658\tIE1.141648\tCL1.141697\tMD5.141688\tSR1.141680\tHI2.141672\tMT1.141719\tTL3.141709\tSV1.141649\tCO2.141657\tMT2.141698\tHF1.141663\tCF2.141679\tRT1.141654\tGB1.141665\tDF1.141684\tPE2.141725\tCA2.141685\tCF1.141675\tGB5.141668\tLQ3.141712\tDF2.141726\tLQ1.141701\tMD4.141660\tIT1.141711\tBF2.141708\tSN3.141650\tTL1.141653\tAR3.141705\tJT1.141699\tBZ1.141724\tHI4.141735\tAR2.141703\tSV2.141666\tMD3.141707\tKP4.141733\tHJ2.141717\tSR3.141674\tCF3.141691\tSK2.141662\tAR1.141727\tBB2.141659\tGB3.141652\tHJ1.141718\tPE3.141731\tMP1.141661\tSP1.141656\tCL4.141667\tHF2.141686\tVC2.141694\tGB2.141732\tCL2.141671\tSK1.141669\"\nsoil_ids = soil_id_str.split(\"\\t\")",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 41
},
{
"cell_type": "code",
"collapsed": false,
"input": "skbio_tree = TreeNode.from_linkage_matrix(scipy_upgma(soil_dm.condensed_form()), soil_ids)\nskbio_tt_dm = skbio_tree.tip_tip_distances()\nskbio_tt_dm.to_file(\"skbio_tt_dm.txt\")\nprint skbio_tt_dm.data",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "[[ 0. 0.7630057 0.7630057 ..., 0.81986874 0.81986874\n 0.81986874]\n [ 0.7630057 0. 0.6491661 ..., 0.81986874 0.81986874\n 0.81986874]\n [ 0.7630057 0.6491661 0. ..., 0.81986874 0.81986874\n 0.81986874]\n ..., \n [ 0.81986874 0.81986874 0.81986874 ..., 0. 0.63979378\n 0.63979378]\n [ 0.81986874 0.81986874 0.81986874 ..., 0.63979378 0. 0.61956525]\n [ 0.81986874 0.81986874 0.81986874 ..., 0.63979378 0.61956525 0. ]]\n"
}
],
"prompt_number": 67
},
{
"cell_type": "code",
"collapsed": false,
"input": "pycogent_tree = UPGMA_cluster(soil_dm.data.copy(), map(PhyloNode, soil_ids), 1e305)\npycogent_tt_dm = pycogent_tree.tipToTipDistances()\nDistanceMatrix(pycogent_tt_dm[0], [n.Name for n in pycogent_tt_dm[1]]).to_file(\"pycogent_tt_dm.txt\")\nprint pycogent_tt_dm[0]",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "[[ 0. 0.63979378 0.63979378 ..., 0.83809269 0.83809269\n 0.83809269]\n [ 0.63979378 0. 0.61956525 ..., 0.83809269 0.83809269\n 0.83809269]\n [ 0.63979378 0.61956525 0. ..., 0.83809269 0.83809269\n 0.83809269]\n ..., \n [ 0.83809269 0.83809269 0.83809269 ..., 0. 0.69230269\n 0.72027191]\n [ 0.83809269 0.83809269 0.83809269 ..., 0.69230269 0. 0.72027191]\n [ 0.83809269 0.83809269 0.83809269 ..., 0.72027191 0.72027191 0. ]]\n"
}
],
"prompt_number": 86
},
{
"cell_type": "code",
"collapsed": false,
"input": "!compare_distance_matrices.py --method=mantel -i skbio_tt_dm.txt,pycogent_tt_dm.txt -o mantel_out -n 9999",
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 91
},
{
"cell_type": "code",
"collapsed": false,
"input": "!cat mantel_out/mantel_results.txt",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "# Number of entries refers to the number of rows (or cols) retained in each\r\n# distance matrix after filtering the distance matrices to include only those\r\n# samples that were in both distance matrices. p-value contains the correct\r\n# number of significant digits.\r\nDM1\tDM2\tNumber of entries\tMantel r statistic\tp-value\tNumber of permutations\tTail type\r\nskbio_tt_dm.txt\tpycogent_tt_dm.txt\t88\t0.88388\t0.0001\t9999\ttwo sided\r\n"
}
],
"prompt_number": 92
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
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