Support Vector Machines are a class of learning algorithms initially defined for discrimination, that is, predicting a binary qualitative variable. They were then generalized to the forecast of a quantitative variable. They are based on the search for the optimal margin hyperplane which, where possible, classifies or separates the data correctly while being as far as possible from all observations. The Support Vector Regression (SVR) uses mostly the same principles as the SVM, maintaining all the main features that characterize the algorithm (maximal margin).
In comparison to the multilinear regression, in some specific cases the training of a SVR (especially when using a nonlinear kernel) can be slower than the training of the multiple linear regression. But generally, SVRs are very much appreciated for providing a practical and efficient way to build accurate predictive models.
DIAMOND MINING
Let’s consider we have the intuition that the price of diamonds found at some location in the ground is in correlation with – at this same location – the ground pressure and the concentration of an imaginary mineral called Paleonium. We decide to build a dataset (see bottom) containing 1000 observations whose columns A, B, C are the concentration in g/m^3 of Paleonium found, the ground pressure in kg/cm^2 and the price of diamonds in dollars/carats. We use Support Vector Regression to check if this correlation exists and, if so, build the related predictive model. And finally, we show the observations and the predictions in a 3D graph that helps to get a visual impression of the correctness of the model.
Here is the script in Python.
And here, the script in R.
Paleonium,Pressure,Price
17,6567,2810.280298
59,5253,1986.967089
123,9715,2083.132087
182,2073,2236.340285
133,6400,1903.323339
41,17016,1616.17379
40,19145,747.1934265
35,17180,1718.235458
146,14121,2044.434408
120,17102,1147.952682
10,15626,2764.488398
55,8206,2260.401395
19,2774,2370.507571
133,11326,2100.963239
164,4474,2102.081487
116,7899,2072.629049
80,16750,1357.632882
12,2067,2312.198021
15,13560,2825.173862
12,5155,2750.317255
78,19223,261.5642451
33,19013,1026.591739
147,18590,970.1210764
24,10289,2746.858643
127,6448,1838.903265
159,13153,2421.623121
4,15075,2958.40444
142,17497,1296.027888
160,3615,1984.402182
192,11931,3144.528479
134,11112,2054.92462
66,3710,1643.396725
24,16793,2156.561488
187,17740,2065.204409
189,19592,1027.804504
178,17487,2009.225825
59,5934,1997.788906
36,16191,1946.592441
187,7771,2945.545098
190,2299,2498.391415
85,11731,1945.373232
69,10701,2056.777155
6,13056,3051.385525
43,16902,1721.802983
160,19785,271.8181622
170,16788,1934.197709
71,9927,2190.616456
138,15214,1906.124486
152,15189,1921.497186
66,7019,1947.260916
172,17995,1644.276479
117,9274,1992.62961
166,15747,2197.187116
171,16684,1959.008017
128,19197,336.1845834
166,2849,1968.790341
169,2896,2110.652095
44,9171,2524.538539
45,7375,2321.539449
108,15243,1701.990586
62,18168,984.4439225
102,10905,1897.912961
180,13215,2733.394337
186,17524,2049.416491
128,13271,1959.903639
89,7690,1947.312141
56,8990,2253.015915
96,5340,1647.990343
114,7347,1863.816172
95,752,1452.890876
9,10079,3090.473057
60,295,1641.135886
67,14207,1975.763427
66,14892,1793.220118
28,9835,2665.405715
191,10484,3169.22792
165,8894,2567.898136
174,5045,2432.257042
19,16847,2245.996881
103,3240,1408.417384
198,2068,2761.966793
28,17267,1814.179973
146,1830,1547.1445
173,17541,1898.420072
165,3983,2197.596984
113,5299,1677.604953
117,1343,1341.918676
36,19811,241.0555242
136,7231,2135.45046
172,7502,2643.045404
51,19966,-2.278363643
145,19990,-83.18709232
172,67,2296.620664
37,5199,2149.707548
50,13556,2128.117068
183,16371,2345.169979
84,2646,1285.065638
68,4436,1802.646366
189,13387,2960.547352
99,19852,-377.1419123
125,660,1508.455517
200,8634,3401.65637
13,11386,3100.888376
19,9760,2895.94968
62,18943,702.7753315
70,2004,1515.126568
83,3504,1579.375331
113,16274,1473.566676
112,19161,244.5772182
34,8770,2644.419902
194,9479,3211.686956
181,18334,1642.031863
162,11652,2504.238515
154,9865,2514.749367
20,18182,1800.604772
89,3294,1357.184529
77,298,1498.785478
135,624,1487.183112
151,2042,1691.989345
121,1188,1452.213251
16,19222,1214.592273
94,19883,-226.8989096
74,8534,2040.623717
127,16121,1625.330048
61,797,1511.199606
186,3770,2465.644241
168,9718,2556.961529
134,18377,866.3163467
68,3769,1562.637285
49,10273,2288.11687
20,13796,2738.640639
91,8277,2062.281408
70,14521,1918.332239
14,15976,2516.12294
115,11314,2048.448657
24,19060,1144.755092
146,11132,2370.914188
65,6279,1960.275667
71,3040,1559.381761
60,11810,2226.081869
100,5288,1742.162729
75,17418,1225.20717
27,3700,2278.946774
76,15798,1514.512283
39,17464,1680.624702
149,15096,2046.191453
84,7644,1990.47597
179,14943,2511.279816
22,4469,2393.329107
12,3024,2462.933397
128,261,1575.68936
0,6135,3114.897791
99,3194,1503.533717
143,3068,1735.176192
195,16319,2755.934858
130,13557,1980.30053
10,2879,2475.961417
97,8859,1903.752804
159,6752,2355.659765
200,17183,2541.238942
73,1659,1397.475255
113,18631,526.0403977
170,11182,2640.489613
23,859,2148.897585
45,2217,1736.403166
190,4745,2856.847903
59,3648,1697.728731
120,7558,2029.109143
99,17566,1075.507337
180,12190,2933.572919
81,12644,2034.794825
63,18077,1103.104669
18,4516,2569.864448
92,14056,1838.168373
28,15104,2410.011418
4,15109,3006.061596
32,13000,2588.785564
53,17004,1453.532416
2,16025,2838.39769
161,2328,1804.325154
37,17726,1490.025397
152,17544,1362.796257
39,1370,1774.126368
39,16720,1878.992719
125,9330,2005.562132
148,19049,700.6940254
135,19015,527.7912619
122,18179,829.9605805
179,12988,2741.947626
59,13658,2032.926229
145,6718,2094.309147
149,14119,2198.237337
68,18009,1113.458703
16,19329,1208.635581
159,19776,293.9020071
160,19436,657.0924942
14,2732,2500.941056
67,11877,2191.838156
4,12607,3199.822477
179,17539,1978.903479
164,90,2089.914084
114,13675,1848.776175
72,7705,1968.652602
93,5061,1736.968837
166,19970,271.077945
141,4170,1763.399831
190,10743,3234.944907
79,14023,1880.718212
111,18167,779.5932762
39,6888,2316.02839
67,13305,1911.099449
179,3923,2372.242814
34,15161,2254.112718
25,13913,2649.236122
166,10396,2593.719423
178,3304,2195.119336
91,11071,2075.203217
28,15629,2243.93259
79,15616,1571.271242
66,3322,1636.060108
148,8126,2363.934868
173,7659,2674.472279
83,9246,2095.039834
56,14935,1851.793103
124,1411,1439.885251
23,18166,1598.634789
94,5124,1718.302866
197,12515,3318.015178
17,10768,2955.056336
119,7113,1871.923872
82,18636,677.4220465
86,16114,1458.948596
164,8759,2487.029579
74,19448,111.7682371
28,18035,1518.727624
157,3487,1999.399775
121,5263,1688.759008
28,13364,2504.247963
79,16213,1474.64832
154,17413,1483.90236
108,8275,1875.76384
56,18837,648.2549543
104,16183,1511.644991
145,673,1680.142866
123,12556,2012.236456
73,2710,1433.818173
151,12552,2339.417509
21,9005,2793.136616
48,512,1730.816669
165,13248,2402.78405
183,18727,1532.998192
144,6331,2183.842484
80,8972,2117.888505
58,7300,2094.407209
116,13172,1820.913664
125,14508,1710.941475
117,17172,1222.458053
65,2777,1439.400086
71,3276,1609.370489
182,19280,1076.619407
48,165,1923.265876
130,12806,1963.893767
28,17524,1810.602046
151,6741,2233.407567
172,4789,2293.760742
165,2002,1806.25541
200,11403,3396.196289
79,5256,1712.870073
23,17912,1848.805218
95,18449,766.2371794
77,6513,1969.864208
47,2899,1711.178076
94,7093,1950.028547
158,10680,2545.187698
20,14451,2539.43654
26,9519,2803.058213
158,8198,2509.560215
143,2523,1682.14258
116,10575,1953.728912
50,6211,2116.600602
13,12363,3014.719203
74,11034,1985.992823
22,4422,2516.864474
119,4832,1620.10947
156,4706,1962.098184
25,10656,2785.432227
162,12927,2406.967508
55,6482,2018.726184
11,19619,1126.577164
128,17486,1257.259915
59,6572,2103.554119
38,6127,2303.906362
195,3573,2793.868075
156,17486,1460.99933
143,16189,1771.227888
24,1017,2171.605086
12,7008,2970.943223
1,9555,3379.071759
160,16295,2007.208468
55,1169,1640.146862
26,9339,2850.132663
32,871,1947.407438
92,9222,1951.494286
79,15885,1463.412718
88,13376,1785.785816
67,15749,1759.846104
127,1775,1401.595086
71,18870,642.9717523
17,14312,2767.056407
77,1481,1364.042329
46,8981,2341.230785
141,16552,1562.441438
55,13619,2173.987185
6,4960,2893.292196
90,9036,1906.006531
145,1077,1506.417327
145,1026,1653.758051
84,15238,1537.134581
88,8225,1927.65992
107,4609,1577.581379
194,16837,2547.443204
68,8630,2184.025718
199,3082,2804.593017
194,8530,3208.797434
91,13552,1828.252423
78,13652,1915.20201
115,19138,347.5404547
112,2826,1431.818202
72,11427,2026.597512
167,14416,2438.063701
118,14568,1743.985672
145,15392,1904.169758
168,18711,1187.532216
71,9450,2149.387084
176,12247,2698.160311
145,12020,2271.114119
143,10882,2321.080501
119,16141,1490.721999
49,7435,2365.614316
66,9411,2141.586052
181,5383,2565.859983
20,6206,2655.123993
70,13064,1903.223236
3,1124,2668.877108
67,878,1476.290642
27,13362,2550.07801
191,6577,3111.355774
38,14139,2367.186848
105,15311,1579.198005
62,13006,1985.688262
142,8636,2136.576828
186,9237,2992.322152
96,4741,1656.784037
150,10314,2400.399907
176,18087,1744.062831
103,225,1403.134639
74,12897,2058.593451
46,1902,1733.073312
184,2911,2316.968063
16,2208,2220.510032
93,1146,1280.827487
4,18726,1896.737111
12,17495,2193.78366
48,6123,2115.228501
110,17022,1245.284908
11,16298,2545.509754
31,7581,2587.359685
116,19,1526.401144
14,8999,3091.347139
125,1644,1469.664364
68,8264,2160.850549
143,16112,1636.626566
36,10388,2597.80518
150,4109,1948.515376
128,6096,1944.047393
14,17212,2273.871083
104,19914,-282.8914864
162,15297,2045.05443
69,16031,1525.084725
103,13553,1762.902771
188,10455,3091.189001
145,275,1760.862075
82,17521,1044.944008
199,17896,2387.203395
8,16152,2561.610814
97,17387,1055.639812
159,9613,2424.288685
75,13821,1790.972265
91,3761,1449.337625
131,4982,1756.412999
16,8170,3056.563367
8,14676,2789.533858
185,1620,2312.035866
126,1230,1398.598053
100,9858,1902.71321
178,15166,2389.242506
29,12080,2707.850577
172,1348,1990.341883
157,10443,2420.608661
138,8595,2204.418494
103,19175,237.891061
5,4648,2847.363436
127,7261,1988.096903
156,7299,2349.595272
117,17686,1024.920629
145,9529,2290.043309
43,7598,2439.334147
102,6998,1903.529286
72,2291,1410.58685
134,16131,1673.987507
24,2177,2180.364838
142,1304,1525.858311
51,13800,2045.057405
135,1316,1422.498026
168,8203,2567.14089
16,13658,2896.902574
69,19255,297.1043475
86,4853,1677.432696
41,4632,2114.159307
81,5091,1690.278454
47,5937,2105.664808
116,15702,1545.111322
166,14422,2289.349008
144,8917,2287.841471
14,6342,2905.044579
23,2327,2126.49473
197,10586,3296.212916
14,14956,2677.695507
137,12143,2181.45685
31,2950,2117.780755
91,12294,1984.599161
4,16330,2611.645192
117,11564,1942.315592
78,6013,1883.248965
105,1011,1288.792598
162,16447,1963.250034
81,2647,1436.107996
167,13470,2422.90669
30,10561,2789.894821
189,6685,2967.366234
193,4826,2895.864575
68,548,1559.244697
48,18696,859.5557237
132,257,1556.129463
80,6263,1836.192518
182,2876,2370.793424
91,13732,1853.297468
160,9551,2487.487226
90,2231,1351.045911
139,7799,2206.549636
91,11360,1994.203616
33,9028,2631.433769
195,18937,1662.383259
54,13828,2016.395781
18,170,2442.633742
127,13880,1917.172536
183,10705,2902.37707
2,2458,2635.109972
163,13443,2478.588349
17,10708,2934.31674
12,3975,2547.320964
30,16185,2134.311294
177,1596,2227.722915
98,72,1614.453711
80,9890,1968.75645
156,9873,2505.089858
83,6435,1875.983653
56,18993,715.8261465
177,18122,1753.821096
97,2704,1294.733342
147,12388,2284.184112
83,12770,2014.804262
112,19002,308.1391221
70,6911,1997.555864
97,12058,1898.987242
66,11151,2222.668479
142,6544,2084.656103
105,14231,1823.356765
199,9054,3327.153591
103,19742,-251.2328879
116,13926,1754.630358
132,17724,1205.626814
37,12115,2533.190554
51,18250,1054.917531
196,14952,2914.325488
196,14113,3165.879554
91,13121,1861.609812
196,2645,2749.164837
139,4871,1836.408931
3,8600,3354.206274
112,18776,469.4255799
57,18371,973.823345
85,2522,1358.922501
26,16353,2176.165247
151,16530,1616.679107
26,17008,1993.366917
176,4013,2427.480637
173,4797,2476.471406
89,10005,1965.220693
65,6613,2108.587394
39,6206,2329.84555
193,1412,2581.807666
14,8068,3072.494537
20,2879,2306.01541
58,19323,483.8278969
48,13913,2100.515954
140,7254,2164.514293
113,11574,1947.790342
106,18626,644.7840742
10,7396,2970.377558
45,2393,1811.35837
17,11206,2906.750721
105,10708,1974.424158
21,12076,2791.872814
170,18607,1227.137288
54,9970,2258.138995
125,8780,2153.768241
35,700,2049.072077
56,1010,1678.881907
170,7193,2554.372873
88,17064,1140.53865
72,3675,1526.712269
103,17500,997.2405932
142,10468,2206.937572
74,17103,1369.9413
144,3678,1677.071984
96,9028,2014.831129
119,637,1377.528057
2,806,2663.121863
57,7995,2199.951603
30,9349,2775.342388
155,9587,2369.094198
185,1539,2350.83592
106,5290,1629.539178
182,13787,2767.742715
171,1402,2100.685091
54,1672,1594.908649
10,17399,2211.263724
89,8939,2013.199806
160,15224,2087.341945
9,14672,2858.050443
67,16497,1472.371799
4,14028,3122.998763
108,12389,2005.837064
81,14517,1669.159488
42,11425,2478.867349
181,17280,2101.117361
29,18162,1560.012149
182,14048,2723.974915
22,9319,2859.281952
195,19468,1301.602117
71,14796,1851.494073
107,10539,2085.839193
182,7887,2850.443488
60,11716,2085.801002
156,10751,2488.292465
166,721,2021.822366
199,17854,2236.630332
151,6353,2151.739858
194,2297,2619.993586
19,4189,2481.557885
183,17263,2093.076442
55,5078,1966.410357
148,5134,1959.380296
148,16723,1578.555989
163,3586,1934.030535
186,8520,3002.435159
192,14549,2843.06475
94,3150,1454.084682
147,17677,1260.439375
120,1157,1308.856936
56,18671,889.9348794
16,8995,2945.843742
173,4772,2347.112255
150,12084,2335.97518
1,1054,2788.446996
114,13575,1935.253446
53,6860,2214.365639
103,19301,175.9266276
73,3235,1476.26093
135,19717,36.59839188
158,13909,2295.903247
55,19953,-44.224648
160,14645,2285.618391
63,19430,217.1439863
90,849,1259.80127
91,16087,1383.244341
76,4554,1697.076321
10,3505,2565.178388
128,19963,-288.5051526
128,11839,2036.44098
194,8586,3280.095625
27,1984,1983.595975
13,7162,3031.748528
76,15937,1479.324192
164,10787,2670.132789
81,5807,1811.438345
112,4416,1553.650426
148,13448,2217.127361
137,11534,2118.345489
95,16589,1268.753619
104,5835,1794.563792
190,10157,3167.450939
188,3330,2438.696915
166,15,2125.552908
106,13486,1775.546672
177,5783,2532.102945
150,239,1752.036662
20,8366,2946.859721
104,13346,1828.469028
107,4561,1530.030128
34,15390,2246.261699
115,16173,1435.537851
144,361,1655.302221
53,9439,2239.908529
187,8672,2987.130392
103,15457,1470.054545
79,14311,1763.496656
121,10422,1985.229314
192,19104,1603.655554
62,13885,1964.36763
107,8695,1915.736915
4,11677,3240.603056
6,9248,3308.501829
8,17253,2266.321538
61,12823,2019.907391
44,19591,294.6157053
159,5154,2225.473198
119,7964,1919.396292
181,572,2382.836941
125,1965,1375.330539
50,14738,1986.951389
83,17901,966.4703731
31,15947,2070.938885
143,14049,2099.040842
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