In [23]:

    

import numpy as np  #Importing required modules and libraries

from math import *
from numpy import linalg

import matplotlib.pyplot as plt


    

In [24]:

    

train_data = np.genfromtxt('ex2data1.txt',delimiter=',')
y = train_data[:,-1]
print "Target Values:-"
print y
X= train_data[:,0:2]
m = len(y)
X= np.insert(X,0,np.ones(m),axis = 1)
alpha = 0.005


    

    




Target Values:-
[ 0.  0.  0.  1.  1.  0.  1.  1.  1.  1.  0.  0.  1.  1.  0.  1.  1.  0.
  1.  1.  0.  1.  0.  0.  1.  1.  1.  0.  0.  0.  1.  1.  0.  1.  0.  0.
  0.  1.  0.  0.  1.  0.  1.  0.  0.  0.  1.  1.  1.  1.  1.  1.  1.  0.
  0.  0.  1.  0.  1.  1.  1.  0.  0.  0.  0.  0.  1.  0.  1.  1.  0.  1.
  1.  1.  1.  1.  1.  1.  0.  0.  1.  1.  1.  1.  1.  1.  0.  1.  1.  0.
  1.  1.  0.  1.  1.  1.  1.  1.  1.  1.]

In [25]:

    

def sigmoid(z):
    return 1/(1+np.exp(-z))


    

In [26]:

    

def calcost(hypothesis,y):
	sum  = (np.dot(y,np.log(hypothesis))) + np.dot((1-y),np.log(1-hypothesis))
	return -sum/m


    

In [27]:

    

theta = np.array([0,0,0])
prod = np.dot(X,theta.transpose())
hypothesis = sigmoid(prod)
oldcost = calcost(hypothesis,y)
diff = hypothesis - y


    

In [28]:

    

while True:
    theta = theta - (alpha/m)*(np.dot(diff.transpose(),X))
    prod = np.dot(X,theta.transpose())
    hypothesis = 1/(1 + np.exp(-prod))
    diff = hypothesis - y
    newcost = calcost(hypothesis,y)
    print newcost
    if abs(newcost-oldcost) <= 0.001*oldcost:
        break
    else:
        oldcost = newcost


    

    




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0.768559810713
2.6213403707
0.477751261961
1.46059354123
1.50128465655
4.75859554039
0.623036206496
1.45059656838
4.64009121493
0.555083488279
1.30657074889
4.29034644588
0.38597278556
0.840603236162
2.86839086304
0.359903536254
0.896284727385
1.73901138557
5.1964252985
0.922072033151
1.73426043819
5.17385942974
0.907220276978
1.71613213083
5.12946164195
0.876471070657
1.68940340777
5.07088283473
0.836049121546
1.65222164886
4.99434257087
0.78409320725
1.59787024299
4.88569669104
0.712710149841
1.50808827648
4.70240495145
0.600501404676
1.32267931941
4.27847774997
0.391717621745
0.795693708582
2.65851588519
0.457396028849
1.2983608735
1.62557342872
4.97714802122
0.768399345425
1.61361088883
4.94384963311
0.747346153026
1.57979612002
4.87015454547
0.700116417824
1.51154061225
4.72646930808
0.612094624568
1.36396294822
4.39299990564
0.437713976593
0.951430763104
3.21091527843
0.26497388373
0.377213213414
0.824634991064
2.81920967281
0.37917926929
1.00267320143
1.75758823073
5.22613573371
0.944120363031
1.74005595293
5.18354312589
0.914204883713
1.71883980655
5.13421267354
0.879769863533
1.69126328144
5.0741446289
0.838236948098
1.65389484671
4.99712206032
0.785902218671
1.59966905069
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0.714481705132
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0.388395241219
0.790062456727
2.64005323335
0.465742475075
1.34035996235
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0.724015589657
1.56365415684
4.84714401982
0.683930726306
1.49984766006
4.70947620296
0.600649514399
1.35345337377
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0.427367872424
0.931459745132
3.14924614377
0.275559394849
0.4399784199
1.02595842513
3.49087427102
0.226491975939
0.225176168111
0.236991543187
0.313274399852
0.645113285461
2.1941397799
0.782756693603
2.69574209897
0.437909548595
1.32292023019
1.62064949573
5.00351522738
0.780705825582
1.66838995336
5.0778063958
0.835000323874
1.69428165458
5.10891311553
0.859250857568
1.6948394048
5.09580272504
0.851619906069
1.677047159
5.05180896027
0.822018721294
1.64412528238
4.9817384862
0.774940133822
1.59153284332
4.87488433236
0.705192474115
1.50102707799
4.68787776074
0.591559371754
1.30886986475
4.24274188285
0.377111704763
0.75330322592
2.50348057508
0.543119326205
1.67966702259
1.26797664782
4.17117577105
0.343847218566
0.680819357992
2.26717107909
0.711327734387
2.38734348464
0.621550073603
2.04243553582
0.906395008332
3.09062029382
0.285022253669
0.521930211207
1.26033103822
4.17845307608
0.339207599173
0.704786788677
2.39033059666
0.621927068758
2.06997228537
0.883975835037
3.02729558317
0.301123494097
0.623605113489
1.47476389922
4.7009134453
0.587212069302
1.39384700639
4.50933058272
0.483583849243
1.1467190611
3.85345157947
0.25457392626
0.353983896964
0.898128963507
1.7407343042
5.20000779134
0.923939151392
1.73562787804
5.17772910882
0.909333709509
1.71802593571
5.1343912143
0.879374590642
1.69226344373
5.07711767456
0.839877948719
1.65636560562
5.0021436122
0.788946525244
1.60385873733
4.89609090382
0.719075017926
1.51760522945
4.71950265623
0.610188192016
1.34226269138
4.32225166582
0.409174521267
0.85292400438
2.85908291978
0.364292228133
0.86262776443
1.69635830954
5.0976851557
0.852835111067
1.67733618112
5.05149203035
0.821691137931
1.64340559451
4.97939002055
0.7732628691
1.5894330714
4.86950437324
0.701664863293
1.49598180386
4.67550961437
0.584392370375
1.29490761696
4.20505870464
0.362937259661
0.707755346152
2.3321290484
0.657816353105
2.15011532235
0.804345781587
2.71101555396
0.427005336141
1.18973459751
1.68788173255
5.08881859123
0.845676605913
1.67840960597
5.05887022325
0.826133158042
1.6520755835
4.99991464804
0.786616420794
1.60729630723
4.90729610409
0.725660768883
1.53132144005
4.75117421169
0.628342386052
1.3797932591
4.41454433822
0.449158290363
0.973689168826
3.26919405691
0.255109582125
0.323451026542
0.626942709952
2.0747848387
0.875252448297
2.98674103571
0.313667105776
0.677959908792
1.54891804467
4.84745393291
0.678652323666
1.53475146207
4.80866719391
0.655798681764
1.48720192886
4.69997283268
0.591387158013
1.36389564838
4.41206818679
0.441012010314
0.996959869964
3.37444972064
0.23656498569
0.260630255881
0.39198379672
1.0918910404
1.73870388476
5.19386456043
0.919370022474
1.73187336098
5.16914774133
0.903006031107
1.71346587964
5.12455110066
0.872242714422
1.6866238748
5.06529184718
0.831508219771
1.64877947917
4.98645783014
0.778208401883
1.59228671534
4.87201313595
0.703443353376
1.49635251792
4.67302428777
0.583153160068
1.29072392749
4.19079950628
0.357939084704
0.690620132958
2.26473727925
0.707392557468
2.34060917369
0.650445869105
2.1289369185
0.821521171818
2.77560963184
0.395651973276
1.05013604326
1.73336195859
5.16387358862
0.900043635741
1.70533121057
5.10326190404
0.857752489949
1.67160805954
5.03208103865
0.808984754491
1.6249075116
4.93686569801
0.745430423891
1.55213113055
4.78902576472
0.65167304416
1.41579527327
4.49335654663
0.487368378887
1.07255299459
3.57646625594
0.237544046825
0.231113355081
0.235521756496
0.279170097335
0.530095702011
1.29718314514
4.27500221775
0.372972308535
0.840410820077
2.88076449375
0.349861474871
0.887973321215
1.73310827723
5.18317767875
0.91138520335
1.72817381932
5.16177697842
0.897538753974
1.71022681216
5.1179772097
0.867448163342
1.68311973024
5.05815239508
0.826432558502
1.64432467353
4.97733199391
0.771956185702
1.58558121281
4.85799908949
0.694396967616
1.48380845294
4.64512806434
0.567287627911
1.25897734555
4.10676396301
0.329545895308
0.593639573648
1.88526145884
1.04891551283
3.52704538165
0.231006370673
0.2248627408
0.221234179242
0.219936800435
0.223993831965
0.252720186757
0.392948182398
1.1347732241
1.72885812074
5.18722608468
0.912124531688
1.74142596715
5.19685065826
0.921342584921
1.73156854357
5.16787875047
0.901825787781
1.71247726119
5.12240136183
0.870457981136
1.68540438511
5.06268994
0.829464643219
1.64723065438
4.9829520113
0.775637286349
1.58987648259
4.86628408947
0.699595401305
1.49149823094
4.6610757805
0.576187223961
1.27763906582
4.15465018314
0.345070650287
0.64888797706
2.10363909263
0.840035772606
2.82764965119
0.372761806965
0.92829458359
1.72056781007
5.1354300907
0.879902746484
1.68978020712
5.06969683301
0.834424603773
1.65031332628
4.98782976739
0.778986147957
1.5926365788
4.87073589078
0.702498208396
1.49487209629
4.6672089421
0.579724436171
1.28420984535
4.17047197895
0.350537772664
0.667527350722
2.17501098909
0.777541224949
2.60097863581
0.481190309192
1.42502629149
1.50842665991
4.7336549544
0.61239201552
1.39337353155
4.47062709899
0.470092438851
1.06938883228
3.59000963814
0.231202903969
0.228899542311
0.243635314288
0.328827062506
0.79637218177
1.68370789696
5.10102510427
0.850568339688
1.70451045864
5.1244380345
0.86955146977
1.70042061868
5.10405450726
0.856737204818
1.68007286405
5.05557016556
0.823979544233
1.64566078277
4.98206435228
0.774595342433
1.59141585217
4.87070120215
0.702031829618
1.49738783039
4.67423322979
0.583291256616
1.2944370567
4.19762432139
0.359616719075
0.701231989511
2.30521532066
0.672818790819
2.20582003748
0.751619463261
2.51164793207
0.532592202293
1.65437550681
1.28449068355
4.20669696414
0.355061961837
0.729833005387
2.449655205
0.572771237331
1.84105853271
1.09437589197
3.67881965916
0.232525322093
0.251244619555
0.371166052558
0.837639478172
2.86715514872
0.353703391953
0.910755295294
1.73500948021
5.18008120322
0.909380021501
1.7221806354
5.14618605376
0.886374939015
1.70061124496
5.09636986361
0.852147721289
1.66984669639
5.02991211658
0.806865498606
1.6251491635
4.93753589621
0.745329630907
1.55427655581
4.79234787803
0.653220437437
1.42087727398
4.50235787737
0.491320033772
1.08608016239
3.61370837383
0.237722006655
0.236904216944
0.26786269162
0.425446592499
1.24549950419
1.65428622104
5.03838557042
0.807480760589
1.66499207727
5.04511055363
0.814167422876
1.65560256255
5.01556750543
0.795348645021
1.62701276322
4.95146285933
0.753180560928
1.57418280548
4.84078517161
0.682160604983
1.47515736723
4.62977844776
0.557408027586
1.24755027673
4.07736892531
0.318778287525
0.564591653284
1.77425693172
1.15733026795
3.84914179953
0.258432591498
0.352664515829
0.86717425354
1.70380618746
5.11379470256
0.862853806362
1.68802360899
5.07344781284
0.835797942941
1.65852350685
5.00873225451
0.792155875364
1.61207298018
4.91231144454
0.72854271395
1.53478959464
4.75248866255
0.628792588576
1.38124258406
4.40993046754
0.446569039459
0.969727129055
3.24796954802
0.255613253525
0.333694415111
0.665565860642
2.21615084257
0.744681838458
2.51115301563
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0.805408234564
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0.411588321705
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0.851836815873
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4.76001320729
0.631957743713
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4.45326847548
0.465523398958
1.03087285593
3.44799107649
0.234545464948
0.234413265508

In [29]:

    

print "Values of theta:- ",theta
prod = np.dot(X,theta.transpose())
predicted = sigmoid(prod)
print "The predicted values are as follows:- "
print predicted


    

    




Values of theta:-  [-17.62979105   0.165549     0.1287347 ]
The predicted values are as follows:- 
[  1.35474929e-01   9.43427431e-04   9.02779324e-02   9.69060197e-01
   9.94253691e-01   5.13473879e-02   9.92686734e-01   6.86454867e-01
   9.98019350e-01   8.75690229e-01   9.59336571e-01   2.18974362e-01
   9.97105204e-01   9.98395333e-01   2.14892486e-01   9.42086344e-01
   6.44335211e-01   4.08032435e-01   9.97602906e-01   7.75328358e-01
   2.76552745e-01   9.96620932e-01   4.85973009e-02   1.87978112e-03
   9.84474131e-01   8.43523084e-01   8.04665276e-01   9.41596178e-01
   2.84111507e-01   5.51150260e-02   8.70387591e-01   9.79233141e-01
   2.93872102e-01   4.81181828e-01   1.41018639e-01   1.34322905e-01
   6.71022402e-01   9.68025502e-01   5.25835915e-01   9.23713401e-02
   9.70941787e-01   4.46131653e-02   9.98415988e-01   7.74736526e-01
   3.62666751e-02   3.48228889e-01   9.85512184e-01   9.99939998e-01
   9.93963329e-01   9.99869889e-01   9.94247548e-01   9.98717125e-01
   9.50074221e-01   1.56858273e-02   5.24837829e-02   1.51706472e-01
   9.99389255e-01   5.17538267e-01   9.74688285e-01   9.87329618e-01
   9.97246586e-01   3.22035273e-03   3.68726980e-02   1.89007546e-03
   1.57019557e-01   2.10698042e-01   8.35356840e-01   5.58978812e-02
   9.99457590e-01   7.81045576e-01   1.30868484e-03   9.53346921e-01
   9.98812751e-01   8.56781777e-01   8.67252877e-01   9.99728979e-01
   8.29865593e-01   6.18424414e-01   1.04412818e-01   8.14916854e-01
   9.97707884e-01   9.81153638e-01   8.89653311e-01   3.79321865e-01
   9.99379629e-01   9.91199099e-01   3.74213659e-01   9.98508146e-01
   9.99602573e-01   2.42230843e-01   9.99622093e-01   9.99817631e-01
   2.05206154e-02   9.96406084e-01   9.56197644e-01   9.18338060e-01
   6.41039568e-01   9.99531493e-01   4.72698864e-01   9.98120515e-01]