From 6c82f33b0c8c2eaf24a54f1c772e25c4a97310c0 Mon Sep 17 00:00:00 2001
From: Adrian Englhardt <adrian.englhardt@kit.edu>
Date: Tue, 7 Apr 2020 14:41:55 +0200
Subject: [PATCH] Add gamma initialization with mean criterion.

---
 README.md                                    |    20 +-
 examples/svdd_parametrization.ipynb          | 33264 +++++++++--------
 src/SVDD.jl                                  |     2 +
 src/init_strategies/strategies_gamma.jl      |    41 +
 test/init_strategies/init_strategies_test.jl |     3 +-
 5 files changed, 18651 insertions(+), 14679 deletions(-)

diff --git a/README.md b/README.md
index 7bea9a6..6b36905 100644
--- a/README.md
+++ b/README.md
@@ -46,7 +46,9 @@ The packages includes the following strategies to initialize parameters.
 * _Gauss Kernel gamma_
   * Rule of Scott [3]
   * Rule of Silverman [4]
-  * Wang data shifting [5]
+  * Mean criterion [5]
+  * Modified mean criterion [6]
+  * Wang data shifting [7]
   * Fixed Gamma
 * _Cost parameters C_
   * Rule of Tax [1]
@@ -67,15 +69,13 @@ This package is developed and maintained by [Holger Trittenbach](https://github.
 
 ## References
 
-[1] Tax, David MJ, and Robert PW Duin. "Support vector data description." Machine learning 54.1 (2004): 45-66.
-
-[2] Görnitz, Nico, et al. "Toward supervised anomaly detection." Journal of Artificial Intelligence Research 46 (2013): 235-262.
-
-[3] Scott, David W. Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons, 2015.
-
-[4] Silverman, Bernard W. Density estimation for statistics and data analysis. Routledge, 2018.
-
-[5] Wang, Siqi, et al. "Hyperparameter selection of one-class support vector machine by self-adaptive data shifting." Pattern Recognition 74 (2018): 198-211.
+[1] Tax, David MJ, and Robert PW Duin. "Support vector data description." Machine learning 54.1 (2004): 45-66.<br>
+[2] Görnitz, Nico, et al. "Toward supervised anomaly detection." Journal of Artificial Intelligence Research 46 (2013): 235-262.<br>
+[3] Scott, David W. Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons, 2015.<br>
+[4] Silverman, Bernard W. Density estimation for statistics and data analysis. Routledge, 2018.<br>
+[5] Chaudhuri, Arin, et al. "The mean and median criteria for kernel bandwidth selection for support vector data description." 2017 IEEE International Conference on Data Mining Workshops (ICDMW). IEEE, 2017.<br>
+[6] Liao, Yuwei, et al. "A new bandwidth selection criterion for using SVDD to analyze hyperspectral data." Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIV. Vol. 10644. International Society for Optics and Photonics, 2018.<br>
+[7] Wang, Siqi, et al. "Hyperparameter selection of one-class support vector machine by self-adaptive data shifting." Pattern Recognition 74 (2018): 198-211.
 
 [docs-master-img]: https://img.shields.io/badge/docs-master-blue.svg
 [docs-master-url]: https://englhardt.github.io/SVDD.jl/latest
diff --git a/examples/svdd_parametrization.ipynb b/examples/svdd_parametrization.ipynb
index 3f96a88..221422f 100644
--- a/examples/svdd_parametrization.ipynb
+++ b/examples/svdd_parametrization.ipynb
@@ -12,13 +12,15 @@
     "    - Fixed Gamma\n",
     "    - Rule of Thumb Scott [3]\n",
     "    - Rule of Thumb Silverman [4]\n",
-    "    - Wang data shifting [5]\n",
+    "    - Mean Criterion [5]\n",
+    "    - Modified Mean Criterion [6]\n",
+    "    - Wang data shifting [7]\n",
     "* Cost Parameter C\n",
     "    - Fixed C\n",
     "    - Rule of Tax [1]\n",
     "    - Binary Search\n",
     "* Combined C and Gamma\n",
-    "    - Wang data shifting [5]\n",
+    "    - Wang data shifting [7]\n",
     "    \n",
     "We apply these strategies with the standard SVDD [1] on a small example data set.\n",
     "\n",
@@ -26,7 +28,9 @@
     "[2] Görnitz, Nico, et al. \"Toward supervised anomaly detection.\" Journal of Artificial Intelligence Research 46 (2013): 235-262.<br>\n",
     "[3] Scott, David W. Multivariate density estimation: theory, practice, and visualization. John Wiley & Sons, 2015.<br>\n",
     "[4] Silverman, Bernard W. Density estimation for statistics and data analysis. Routledge, 2018.<br>\n",
-    "[5] Wang, Siqi, et al. \"Hyperparameter selection of one-class support vector machine by self-adaptive data shifting.\" Pattern Recognition 74 (2018): 198-211."
+    "[5] Chaudhuri, Arin, et al. \"The mean and median criteria for kernel bandwidth selection for support vector data description.\" 2017 IEEE International Conference on Data Mining Workshops (ICDMW). IEEE, 2017.<br>\n",
+    "[6] Liao, Yuwei, et al. \"A new bandwidth selection criterion for using SVDD to analyze hyperspectral data.\" Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIV. Vol. 10644. International Society for Optics and Photonics, 2018.<br>\n",
+    "[7] Wang, Siqi, et al. \"Hyperparameter selection of one-class support vector machine by self-adaptive data shifting.\" Pattern Recognition 74 (2018): 198-211."
    ]
   },
   {
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@@ -4215,7 +4219,7 @@
    "source": [
     "## Gamma Parameter\n",
     "\n",
-    "SVDD.jl implements multiple strategies to choose gamma independent of C.\n",
+    "SVDD.jl implements multiple strategies to choose $\\gamma$ (gamma) independent of C.\n",
     "\n",
     "### Rule of Thumb"
    ]
@@ -4224,10 +4228,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Scott and Silverman proposed two rule of thumbs that infer $gamma$ from the size $n$ and dimensionality $d$ of the data set.\n",
+    "Scott and Silverman proposed two rule of thumbs that infer $\\gamma$ from the size $n$ and dimensionality $d$ of the data set. Both rules first calculate the kernel bandwidth $s$ and then set $\\gamma = 1 / (2 * s^2)$.\n",
     "\n",
-    "$\\gamma_{\\text{scott}} = n^{{-1}/({d+4})}$<br>\n",
-    "$\\gamma_{\\text{silverman}} = (n(d+2)/4)^{{-1}/({d+4})}$"
+    "$s_{\\text{scott}} = n^{{-1}/({d+4})}$<br>\n",
+    "$s_{\\text{silverman}} = (n(d+2)/4)^{{-1}/({d+4})}$"
    ]
   },
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    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Both rule of thumbs result in the same value for $\\gamma$."
+    "Both rule of thumbs result in the same value for $\\gamma$, due to $d = 2$ and $(d+2)/4 = 1$."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Mean criterion"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "The mean criterion includes the variance of the data in the kernel bandwidth $s$ calculation. Here, $\\sigma_j^2$ indicates the variance in each dimension. The parameter $\\delta$ controls the distance to the identity matrix.\n",
+    "The SVDD allows manual configuration of the $\\delta$ parameter. Additionally, we implement the recommended value $\\delta = \\sqrt{2}*10^{-6}$.\n",
+    "\n",
+    "$s = \\sqrt{\\dfrac{2n*\\sum_{j=1}^d\\sigma_j^2}{(n-1)\\ln\\left(\\dfrac{n-1}{\\delta^2}\\right)}}$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "metadata": {},
+   "outputs": [
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+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "init_strategy = SVDD.SimpleCombinedStrategy(SVDD.MeanCriterion(),\n",
+    "                                            SVDD.FixedCStrategy(0.01))\n",
+    "train_and_plot_svdd(dummy_data, init_strategy, solver)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Kadke et al. propose a modified mean criterion which automatically selects the value $\\delta$ based on the data set size in [].\n",
+    "\n",
+    "$ϕ = \\dfrac{1}{\\ln\\left(N - 1\\right)}$<br>\n",
+    "$δ = -0.14818008 * ϕ^4 + 0.284623624 * ϕ^3 - 0.252853808 * ϕ^2 + 0.159059498 * ϕ - 0.001381145$\n",
+    "\n",
+    "The kernel bandwidth is the calculated as with the original mean criterion (see previous block)."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "metadata": {},
+   "outputs": [
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+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "init_strategy = SVDD.SimpleCombinedStrategy(SVDD.ModifiedMeanCriterion(),\n",
+    "                                            SVDD.FixedCStrategy(0.01))\n",
+    "train_and_plot_svdd(dummy_data, init_strategy, solver)"
    ]
   },
   {
@@ -8645,12 +12569,12 @@
     "\n",
     "The wang data shifting strategy first generates pseudo inliers and outliers. Then, it tunes the kernel parameter in a second step to optimize prediction quality on this generated test data.\n",
     "\n",
-    "*Note:* We made some changes compared to the original algorithm proposed in [5], for details see [here](https://github.com/englhardt/SVDD.jl/blob/master/src/init_strategies/strategies_gamma.jl#L49)."
+    "*Note:* We made some changes compared to the original algorithm proposed in [7], for details see [here](https://github.com/englhardt/SVDD.jl/blob/master/src/init_strategies/strategies_gamma.jl#L92)."
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 12,
    "metadata": {},
    "outputs": [
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+   "execution_count": 14,
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-       "  1590.56,1207.23 1593.02,1201.96 1595.35,1188.83 1594.71,1175.71 1591.98,1162.58 1590.56,1157.81 1587.86,1149.45 1583.47,1136.33 1579.74,1123.2 1577.16,1110.07 \n",
-       "  1575.91,1096.95 1575.86,1083.82 1576.51,1070.7 1576.84,1057.57 1574.81,1044.44 1570.25,1036.23 1566.92,1031.32 1550.53,1018.19 1549.94,1017.83 1530.99,1005.06 \n",
-       "  1529.62,1004.09 1516.19,991.937 1509.31,983.82 1505.72,978.81 1497.25,965.684 1488.99,952.61 1488.96,952.557 1479.73,939.431 1470.86,926.304 1468.68,922.559 \n",
-       "  1462.88,913.178 1457.53,900.051 1454.93,886.925 1454.47,873.799 1455.3,860.672 1456.48,847.546 1456.92,834.419 1455.45,821.293 1450.95,808.166 1448.37,803.451 \n",
-       "  1442.59,795.04 1430.55,781.913 1428.05,779.021 1417.87,768.787 1410.34,755.66 1416.1,742.534 1428.05,736.255 1441.37,729.408 1448.37,727.022 1468.53,716.281 \n",
-       "  1468.68,716.205 1484.6,703.155 1488.99,698.621 1495.01,690.028 1501.61,676.902 1506.2,663.775 1509.31,652.671 1509.8,650.649 1512.93,637.522 1516.2,624.396 \n",
-       "  1519.86,611.269 1523.94,598.143 1528.36,585.016 1529.62,581.416 1532.75,571.89 1537.34,558.764 1542.66,545.637 1549.26,532.511 1549.94,531.375 1556.62,519.384 \n",
-       "  1564.59,506.258 1570.25,496.916 1572.36,493.131 1578.56,480.005 1583.18,466.878 1586.21,453.752 1588.03,440.625 1589.3,427.499 1590.56,416.882 1590.84,414.373 \n",
-       "  1593.1,401.246 1596.21,388.12 1599.43,374.993 1601.58,361.867 1601.27,348.74 1597.05,335.614 1590.56,326.752 1585.87,322.487 1570.25,313.86 1549.94,309.933 \n",
-       "  1529.62,312.172 1509.31,320.56 1506.51,322.487 1492.74,335.614 1488.99,341.085 1484.66,348.74 1479.8,361.867 1476.12,374.993 1472.28,388.12 1468.68,397.638 \n",
-       "  1467.37,401.246 1461.59,414.373 1454.94,427.499 1448.37,439.527 1447.78,440.625 1440.85,453.752 1433.48,466.878 1428.05,475.329 1424.88,480.005 1414.38,493.131 \n",
-       "  1407.74,499.781 1400.39,506.258 1387.42,515.786 1381.73,519.384 1367.11,527.764 1357.74,532.511 1346.8,537.918 1329.57,545.637 1326.48,547.049 1306.17,555.339 \n",
-       "  1295.75,558.764 1285.85,562.073 1265.54,566.695 1245.22,569.006 1224.91,569.052 1204.6,566.499 1184.28,560.258 1181.31,558.764 1163.97,548.534 1160.46,545.637 \n",
-       "  1146.35,532.511 1143.65,529.893 1133.68,519.384 1123.34,508.832 1120.77,506.258 1107,493.131 1103.03,489.346 1093.06,480.005 1082.71,469.024 1080.66,466.878 \n",
-       "  1070.14,453.752 1062.4,442.098 1061.34,440.625 1052.05,427.499 1042.08,415.305 1041.03,414.373 1021.77,401.374 1021.35,401.246 1001.46,396.472 981.142,397.824 \n",
-       "  971.781,401.246 960.828,406.424 950.732,414.373 940.514,424.39 937.719,427.499 926.118,440.625 920.2,446.572 911.664,453.752 899.886,462.398 891.779,466.878 \n",
-       "  879.572,474.13 867.906,480.005 859.258,486.713 851.729,493.131 847.975,506.258 856.032,519.384 859.258,521.856 878.419,532.511 879.572,533.049 899.886,541.548 \n",
-       "  909.488,545.637 920.2,550.904 934.707,558.764 940.514,563.429 949.57,571.89 955.72,585.016 955.592,598.143 953.817,611.269 955.495,624.396 960.828,633.379 \n",
-       "  962.707,637.522 974.299,650.649 981.142,656.048 989.357,663.775 1001.46,673.019 1006.05,676.902 1021.77,689.414 1022.5,690.028 1037.32,703.155 1042.08,707.868 \n",
-       "  1050.18,716.281 1061.7,729.408 1062.4,730.161 1074.21,742.534 1082.71,750.561 1088.72,755.66 1103.03,766.951 1105.66,768.787 1123,781.913 1123.34,782.239 \n",
-       "  1137.06,795.04 1143.65,805.754 1145.18,808.166 1148,821.293 1145.34,834.419 1143.65,837.125 1136.9,847.546 1123.34,858.922 1120.99,860.672 1103.03,870.502 \n",
-       "  1096.31,873.799 1082.71,879.677 1066.08,886.925 1062.4,888.558 1042.08,899.057 1040.47,900.051 1022.7,913.178 1021.77,914.068 1010.88,926.304 1002.24,939.431 \n",
-       "  1001.46,940.993 996.031,952.557 990.693,965.684 985.042,978.81 981.142,986.526 978.285,991.937 970.27,1005.06 961.335,1018.19 960.828,1019 951.813,1031.32 \n",
-       "  944.991,1044.44 941.988,1057.57 942.194,1070.7 943.937,1083.82 945.431,1096.95 945.576,1110.07 944.35,1123.2 942.565,1136.33 941.131,1149.45 \n",
+       "  1018.87,1280.72 1021.77,1277.88 1029.86,1267.59 1036.3,1254.47 1040.83,1241.34 1042.08,1237.53 1045.05,1228.21 1050.51,1215.09 1058.31,1201.96 1062.4,1196.42 \n",
+       "  1067.79,1188.83 1077.69,1175.71 1082.71,1168.96 1087.87,1162.58 1098.01,1149.45 1103.03,1142.77 1109.27,1136.33 1121.89,1123.2 1123.34,1121.72 1139.44,1110.07 \n",
+       "  1143.65,1107.13 1163.88,1096.95 1163.97,1096.9 1184.28,1088.55 1193.96,1083.82 1204.6,1078.97 1220.08,1070.7 1224.91,1068.63 1245.22,1061.72 1265.54,1058.46 \n",
+       "  1285.85,1059.67 1306.17,1064.7 1320.31,1070.7 1326.48,1074.49 1337.1,1083.82 1346.8,1095.05 1348.1,1096.95 1358.22,1110.07 1367.11,1117.23 1373.68,1123.2 \n",
+       "  1387.42,1131.64 1394.46,1136.33 1407.74,1143.71 1416.84,1149.45 1428.05,1156.74 1435.55,1162.58 1448.37,1174.68 1449.31,1175.71 1459.9,1188.83 1468.68,1200.28 \n",
+       "  1470.02,1201.96 1482.43,1215.09 1488.99,1220.58 1501.78,1228.21 1509.31,1231.85 1529.62,1236.53 1549.94,1235.77 1570.25,1228.88 1571.31,1228.21 1585.88,1215.09 \n",
+       "  1590.56,1207.22 1593.01,1201.96 1595.35,1188.83 1594.71,1175.71 1591.98,1162.58 1590.56,1157.81 1587.86,1149.45 1583.47,1136.33 1579.73,1123.2 1577.15,1110.07 \n",
+       "  1575.9,1096.95 1575.84,1083.82 1576.5,1070.7 1576.82,1057.57 1574.8,1044.44 1570.25,1036.24 1566.92,1031.32 1550.54,1018.19 1549.94,1017.83 1531,1005.06 \n",
+       "  1529.62,1004.07 1516.2,991.937 1509.31,983.814 1505.72,978.81 1497.24,965.684 1488.99,952.627 1488.95,952.557 1479.72,939.431 1470.85,926.304 1468.68,922.582 \n",
+       "  1462.87,913.178 1457.52,900.051 1454.91,886.925 1454.45,873.799 1455.28,860.672 1456.45,847.546 1456.9,834.419 1455.42,821.293 1450.92,808.166 1448.37,803.509 \n",
+       "  1442.55,795.04 1430.5,781.913 1428.05,779.079 1417.82,768.787 1410.29,755.66 1416.05,742.534 1428.05,736.238 1441.35,729.408 1448.37,727.017 1468.53,716.281 \n",
+       "  1468.68,716.203 1484.59,703.155 1488.99,698.62 1495.01,690.028 1501.61,676.902 1506.2,663.775 1509.31,652.661 1509.8,650.649 1512.93,637.522 1516.19,624.396 \n",
+       "  1519.85,611.269 1523.93,598.143 1528.35,585.016 1529.62,581.398 1532.74,571.89 1537.33,558.764 1542.66,545.637 1549.25,532.511 1549.94,531.362 1556.61,519.384 \n",
+       "  1564.59,506.258 1570.25,496.907 1572.35,493.131 1578.56,480.005 1583.17,466.878 1586.21,453.752 1588.04,440.625 1589.31,427.499 1590.56,417.05 1590.86,414.373 \n",
+       "  1593.13,401.246 1596.24,388.12 1599.47,374.993 1601.61,361.867 1601.29,348.74 1597.06,335.614 1590.56,326.741 1585.87,322.487 1570.25,313.866 1549.94,309.948 \n",
+       "  1529.62,312.195 1509.31,320.595 1506.56,322.487 1492.8,335.614 1488.99,341.173 1484.71,348.74 1479.85,361.867 1476.17,374.993 1472.32,388.12 1468.68,397.721 \n",
+       "  1467.4,401.246 1461.61,414.373 1454.95,427.499 1448.37,439.535 1447.79,440.625 1440.85,453.752 1433.48,466.878 1428.05,475.324 1424.88,480.005 1414.38,493.131 \n",
+       "  1407.74,499.775 1400.38,506.258 1387.42,515.778 1381.72,519.384 1367.11,527.759 1357.74,532.511 1346.8,537.92 1329.59,545.637 1326.48,547.061 1306.17,555.358 \n",
+       "  1295.82,558.764 1285.85,562.098 1265.54,566.722 1245.22,569.034 1224.91,569.081 1204.6,566.525 1184.28,560.278 1181.27,558.764 1163.97,548.539 1160.46,545.637 \n",
+       "  1146.36,532.511 1143.65,529.887 1133.68,519.384 1123.34,508.828 1120.77,506.258 1107,493.131 1103.03,489.348 1093.05,480.005 1082.71,469.03 1080.65,466.878 \n",
+       "  1070.13,453.752 1062.4,442.101 1061.33,440.625 1052.05,427.499 1042.08,415.305 1041.03,414.373 1021.77,401.373 1021.35,401.246 1001.46,396.471 981.142,397.823 \n",
+       "  971.778,401.246 960.828,406.423 950.731,414.373 940.514,424.389 937.717,427.499 926.116,440.625 920.2,446.571 911.663,453.752 899.886,462.397 891.778,466.878 \n",
+       "  879.572,474.13 867.906,480.005 859.258,486.712 851.729,493.131 847.975,506.258 856.032,519.384 859.258,521.856 878.419,532.511 879.572,533.048 899.886,541.548 \n",
+       "  909.489,545.637 920.2,550.903 934.706,558.764 940.514,563.43 949.567,571.89 955.717,585.016 955.59,598.143 953.818,611.269 955.497,624.396 960.828,633.374 \n",
+       "  962.71,637.522 974.303,650.649 981.142,656.045 989.362,663.775 1001.46,673.014 1006.06,676.902 1021.77,689.406 1022.51,690.028 1037.33,703.155 1042.08,707.858 \n",
+       "  1050.18,716.281 1061.71,729.408 1062.4,730.156 1074.21,742.534 1082.71,750.559 1088.72,755.66 1103.03,766.946 1105.67,768.787 1123.01,781.913 1123.34,782.222 \n",
+       "  1137.08,795.04 1143.65,805.719 1145.2,808.166 1148.02,821.293 1145.36,834.419 1143.65,837.156 1136.92,847.546 1123.34,858.935 1121,860.672 1103.03,870.508 \n",
+       "  1096.32,873.799 1082.71,879.678 1066.08,886.925 1062.4,888.554 1042.08,899.044 1040.45,900.051 1022.66,913.178 1021.77,914.028 1010.83,926.304 1002.18,939.431 \n",
+       "  1001.46,940.872 995.97,952.557 990.629,965.684 984.976,978.81 981.142,986.404 978.225,991.937 970.221,1005.06 961.3,1018.19 960.828,1018.95 951.79,1031.32 \n",
+       "  944.982,1044.44 941.988,1057.57 942.2,1070.7 943.946,1083.82 945.441,1096.95 945.585,1110.07 944.357,1123.2 942.571,1136.33 941.135,1149.45 \n",
        "  \"/>\n",
        "</svg>\n"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -16943,9 +20871,9 @@
    "source": [
     "## Final remarks\n",
     "\n",
-    "For more details on how we set the gamma and C parameter in our one-class active learning article [6], see the [code on github here](https://github.com/kit-dbis/ocal-evaluation).\n",
+    "For more details on how we set the gamma and C parameter in our one-class active learning article [8], see the [code on github here](https://github.com/kit-dbis/ocal-evaluation).\n",
     "\n",
-    "[6] Holger Trittenbach, Adrian Englhardt, Klemens Böhm, \"An Overview and a Benchmark of Active Learning for One-Class Classification\" arXiv:1808.04759, 14 Aug 2018."
+    "[8] Holger Trittenbach, Adrian Englhardt, Klemens Böhm, \"An Overview and a Benchmark of Active Learning for One-Class Classification\" arXiv:1808.04759, 14 Aug 2018."
    ]
   }
  ],
diff --git a/src/SVDD.jl b/src/SVDD.jl
index f0741ca..0dafe59 100644
--- a/src/SVDD.jl
+++ b/src/SVDD.jl
@@ -56,6 +56,8 @@ export
     BoundedTaxErrorEstimate,
     RuleOfThumbSilverman,
     RuleOfThumbScott,
+    MeanCriterion,
+    ModifiedMeanCriterion,
     WangGammaStrategy,
     WangCombinedInitializationStrategy,
     SimpleSubspaceStrategy,
diff --git a/src/init_strategies/strategies_gamma.jl b/src/init_strategies/strategies_gamma.jl
index 1fb6a81..4ffb75b 100644
--- a/src/init_strategies/strategies_gamma.jl
+++ b/src/init_strategies/strategies_gamma.jl
@@ -43,6 +43,47 @@ function calculate_gamma(model::SubSVDD, strategy::RuleOfThumbScott, subspace_id
     return rule_of_scott(model.data[model.subspaces[subspace_idx], :])
 end
 
+"""
+Original publication:
+Chaudhuri, A., Kakde, D., Sadek, C., Gonzalez, L. and Kong, S., 2017, November.
+The mean and median criteria for kernel bandwidth selection for support vector data description.
+In 2017 IEEE International Conference on Data Mining Workshops (ICDMW) (pp. 842-849). IEEE.
+"""
+DEFAULT_MEAN_CRIT_DELTA = sqrt(2)*10^-6
+
+struct MeanCriterion <: InitializationStrategyGamma
+    δ::Real
+    function MeanCriterion(δ::Real=DEFAULT_MEAN_CRIT_DELTA)
+        return new(δ)
+    end
+end
+
+function mean_criterion(data::Array{T,2}, δ::Real=DEFAULT_MEAN_CRIT_DELTA) where T <: Real
+    N = size(data, 2)
+    # Note that the (N-1) factor in the denominator original formula is already
+    # included in the var calculation
+    s = 2  * N * sum(var(data, dims=2)) / log((N - 1) / δ^2)
+    return 1 / (2 * s^2)
+end
+
+calculate_gamma(model, strategy::MeanCriterion) = mean_criterion(model.data, strategy.δ)
+
+"""
+Liao, Y., Kakde, D., Chaudhuri, A., Jiang, H., Sadek, C. and Kong, S., 2018, May.
+A new bandwidth selection criterion for using SVDD to analyze hyperspectral data.
+In Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XXIV (Vol. 10644, p. 106441M). International Society for Optics and Photonics.
+"""
+struct ModifiedMeanCriterion <: InitializationStrategyGamma end
+
+function modified_mean_criterion(data::Array{T,2}, δ::Real=DEFAULT_MEAN_CRIT_DELTA) where T <: Real
+    N = size(data, 2)
+    ϕ = 1 / log(N - 1)
+    δ = -0.14818008 * ϕ^4 + 0.284623624 * ϕ^3 - 0.252853808 * ϕ^2 + 0.159059498 * ϕ - 0.001381145
+    return mean_criterion(data, δ)
+end
+
+calculate_gamma(model, strategy::ModifiedMeanCriterion) = modified_mean_criterion(model.data)
+
 """
 Generate binary data to tune a one class classifier according to the following paper:
 Wang, S. et al. 2018. Hyperparameter selection of one-class support vector machine by self-adaptive data
diff --git a/test/init_strategies/init_strategies_test.jl b/test/init_strategies/init_strategies_test.jl
index 5a256d6..2aadfa9 100644
--- a/test/init_strategies/init_strategies_test.jl
+++ b/test/init_strategies/init_strategies_test.jl
@@ -6,7 +6,8 @@
     pools = fill(:U, size(dummy_data, 2))
     model = SVDD.VanillaSVDD(dummy_data)
 
-    for s in [:RuleOfThumbSilverman, :RuleOfThumbScott]
+    for s in [:RuleOfThumbSilverman, :RuleOfThumbScott,
+              :MeanCriterion, :ModifiedMeanCriterion]
         @testset "$s" begin
             @test SVDD.calculate_gamma(model, SVDD.eval(s)()) > 0
         end