exercise-classfication: sort eigenvectors and eigenvalues and select …

…the largest ones (#83)

Co-authored-by: Lucas Weber <[email protected]>

exercise/2-Data-Analysis-Preprocessing/Data-Reduction-Transformation-and-Discretization.ipynb

@@ -1048,7 +1048,7 @@
     "\n",
     "**Task 13:**\n",
     "    \n",
-    "Calculate the associated eigenvalues and eigenvectors. (Help: [NumPy documentation](https://numpy.org/doc/stable/reference/generated/numpy.linalg.eig.html)) \n",
+    "Calculate the associated eigenvalues, eigenvectors and sort them. (Help: [NumPy documentation](https://numpy.org/doc/stable/reference/generated/numpy.linalg.eig.html)) \n",
     "</div>"
    ]
   },
@@ -1062,7 +1062,8 @@
    },
    "outputs": [],
    "source": [
-    "# Calculate the associated eigenvalues and eigenvectors"
+    "# Calculate the associated eigenvalues and eigenvectors\n",
+    "# then sort both in increasing order of the eigenvalues"
    ]
   },
   {
@@ -1078,6 +1079,11 @@
     "# Calculate the associated eigenvalues and eigenvectors\n",
     "eigenvalues, eigenvectors = np.linalg.eig(covariance_matrix)\n",
     "\n",
+    "# sort the eigenvalues and eigenvectors (so they are in increasing order)\n",
+    "idx = np.argsort(eigenvalues)\n",
+    "eigenvalues = eigenvalues[idx]\n",
+    "eigenvectors = eigenvectors[:, idx]\n",
+    "\n",
     "# Display the eigenvalues and eigenvectors\n",
     "print(\"Eigenvalues:\")\n",
     "print(eigenvalues)\n",
@@ -1185,8 +1191,8 @@
    "outputs": [],
    "source": [
     "# Select the feature matrix\n",
-    "# The first eigenvector contains nearly all information => select only that one\n",
-    "feature_matrix = eigenvectors[:, 0]\n",
+    "# The largest eigenvector contains nearly all information => select only that one\n",
+    "feature_matrix = eigenvectors[:, 1]\n",
     "\n",
     "# Print the feature_matrix\n",
     "feature_matrix"