avoid ties in sorting eigenvalues in PCA sec

Author: rasbt

code/ch05/ch05.ipynb

@@ -747,7 +747,13 @@
     "               for i in range(len(eigen_vals))]\n",
     "\n",
     "# Sort the (eigenvalue, eigenvector) tuples from high to low\n",
-    "eigen_pairs.sort(reverse=True)"
+    "eigen_pairs.sort(key=lambda k: k[0], reverse=True)\n",
+    "\n",
+    "# Note: I added the `key=lambda k: k[0]` in the sort call above\n",
+    "# just like I used it further below in the LDA section.\n",
+    "# This is to avoid problems if there are ties in the eigenvalue\n",
+    "# arrays (i.e., the sorting algorithm will only regard the\n",
+    "# first element of the tuples, now)."
    ]
   },
   {
@@ -2318,21 +2324,21 @@
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