## 4 Feature Extraction Techniques
### Principal Component Analysis (PCA)
The operation of PCA can  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(SP\) & Time & \(V_{1}\) & \(V_{2}\) & \(V_{3}\) & \(V_{4}\) & \(V_{5}\) \\ \hline Minimum & \(0\) & \(-56.4075\) & \(-72.7157\) & \(-48.3256\) & \(-5.6832\) & \(-113.7433\) \\ Maximum & \(172792\) & \(2.4549\) & \(22.0577\) & \(9.3826\) & \(16.8753\) & \(34.8017\) \\ Mean & \(94814\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) \\ Median & \(84692\) & \(0.0181\) & \(0.0655\) & \(0.1799\) & \(-0.0199\) & \(-0.5434\) \\ 1 st quartile & \(54202\) & \(-0.9204\) & \(-5.5986\) & \(-0.8904\) & \(-0.8486\) & \(-0.6916\) \\
3 rd quartile & \(139321\) & \(1.3156\) & \(0.8037\) & \(1.0272\) & \(0.7433\) & \(0.6119\) \\ \hline \(SP\) & \(V_{6}\) & \(V_{7}\) & \(V_{8}\) & \(V_{9}\) & \(V_{10}\) & \(V_{11}\) \\ \hline Minimum & \(-26.1605\) & \(-43.5572\) & \(-73.2167\) & \(-13.4341\) & \(-24.5883\) & \(-4.7975\) \\ Maximum & \(73.3016\) & \(120.5895\) & \(20.0072\) & \(15.5950\) & \(23.7451\) & \(12.0189\) \\ Mean & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) \\ Median & \(-0.2742\) & \(0.0401\) & \(0.0224\) & \(-0.0514\) & \(-0.0929\) & \(-0.0328\) \\
1 st quartile & \(-0.7683\) & \(-0.5541\) & \(-0.2086\) & \(-0.6431\) & \(-0.5354\) & \(-0.7625\) \\
3 rd quartile & \(0.3986\) & \(0.5704\) & \(0.32735\) & \(0.5971\) & \(0.45392\) & \(0.7396\) \\ \hline \(SP\) & \(V_{12}\) & \(V_{13}\) & \(V_{14}\) & \(V_{15}\) & \(V_{16}\) & \(V_{17}\) \\ \hline Minimum & \(-12.6837\) & \(-5.7919\) & \(-19.2143\) & \(-4.4989\) & \(-14.1295\) & \(-25.1628\) \\ Maximum & \(7.8484\) & \(7.1268\) & \(10.5268\) & \(8.8777\) & \(17.3151\) & \(9.2535\) \\ Mean & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) \\ Median & \(0.1400\) & \(-0.0136\) & \(0.0506\) & \(0.0481\) & \(0.0664\) & \(-0.6568\) \\
1 st quartile & \(-0.4056\) & \(-0.6485\) & \(-0.4256\) & \(-0.5829\) & \(-0.4680\) & \(-0.4838\) \\
3 rd quartile & \(0.6182\) & \(0.6625\) & \(0.4931\) & \(0.6488\) & \(0.5233\) & \(0.3997\) \\ \hline \(SP\) & \(V_{18}\) & \(V_{19}\) & \(V_{20}\) & \(V_{21}\) & \(V_{22}\) & \(V_{23}\) \\ \hline Minimum & \(-9.4987\) & \(-7.2135\) & \(-54.4977\) & \(-34.8304\) & \(-10.9331\) & \(-44.8077\) \\ Maximum & \(5.0411\) & \(5.5920\) & \(39.4209\) & \(27.2028\) & \(10.5030\) & \(22.5284\) \\ Mean & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) \\ Median & \(-0.0036\) & \(0.0037\) & \(-0.0625\) & \(-0.0295\) & \(0.0068\) & \(-0.0112\) \\
1 st quartile & \(-0.4989\) & \(-0.4563\) & \(-0.2117\) & \(-0.2284\) & \(-0.5424\) & \(-0.1619\) \\
3 rd quartile & \(0.5008\) & \(0.4589\) & \(0.1330\) & \(0.1864\) & \(0.5286\) & \(0.1476\) \\ \hline \(SP\) & \(V_{24}\) & \(V_{25}\) & \(V_{26}\) & \(V_{27}\) & \(V_{28}\) & Amount \\ \hline Minimum & \(-2.8366\) & \(-10.2954\) & \(-2.6046\) & \(-22.5657\) & \(-15.4301\) & \(0.0000\) \\ Maximum & \(4.5846\) & \(7.5196\) & \(3.5173\) & \(31.6122\) & \(33.8478\) & \(25,691.1600\) \\ Mean & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(0.0000\) & \(88.3500\) \\ Median & \(0.0410\) & \(0.0166\) & \(-0.0521\) & \(0.0013\) & \(0.0112\) & \(22.0000\) \\
1 st quartile & \(-0.3546\) & \(-0.3172\) & \(-0.3270\) & \(-0.0708\) & \(-0.0530\) & \(5.6000\) \\
3 rd quartile & \(0.4395\) & \(0.3507\) & \(0.2410\) & \(0.0910\) & \(0.0783\) & \(77.1700\) \\ \hline \(SP\) & Class & & & & & \\ \hline Minimum & \(0.0000\) & & & & & \\ Maximum & \(1.00000\) & & & & & \\ Mean & \(0.0017\) & & & & & \\ Median & \(0.0000\) & & & & & \\be sequentially broken down into three steps: (I) standardisation, (II) computation of covariance matrix, and (III) eigenvector and eigenvalue computation [12].