Merge pull request #52 from pykale/refine

Refine exercises
pykale · Mar 18, 2023 · 9fd3120 · 9fd3120
2 parents 481e184 + bba351a
commit 9fd3120
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diff --git a/content/09-pca-clustering/clustering.ipynb b/content/09-pca-clustering/clustering.ipynb
@@ -894,7 +894,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**(b)** Using **hierarchical clustering** with **complete linkage** and **Euclidean distance**, cluster the **states**."
+    "**(b)** Using **agglomerative hierarchical clustering** with **complete linkage** and **Euclidean distance**, cluster the **states**."
    ]
   },
   {
@@ -977,14 +977,16 @@
     "plt.axhline(y=150, c=\"k\", ls=\"dashed\")\n",
     "plt.show()\n",
     "\n",
-    "print(res1)"
+    "print(res1)\n",
+    "\n",
+    "# Cutting the dendrogram at height 150 results in three distinct clusters."
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**(d)** **Hierarchically cluster** the states using **complete linkage** and **Euclidean distance**, after **scaling** the variables to have a **standard deviation** of one, and then **cut the dendrogram** at a height that results in three distinct clusters. Now, which states belong to which clusters?"
+    "**(d)** Perform **agglomerative hierarchical clustering** of the states using **complete linkage** and **Euclidean distance** after scaling the variables to have a standard deviation of one. Then, **cut the dendrogram** at a height that results in **six distinct clusters**. Which states belong to which clusters?"
    ]
   },
   {
@@ -1014,7 +1016,7 @@
    "outputs": [],
    "source": [
     "hc_complete2 = linkage(scaled_x, \"complete\")\n",
-    "res2 = pd.DataFrame(cut_tree(hc_complete2, n_clusters=3), index=state_name)\n",
+    "res2 = pd.DataFrame(cut_tree(hc_complete2, n_clusters=6), index=state_name)\n",
     "res2.index.name = \"states\"\n",
     "res2.rename(columns={0: \"ID\"}, inplace=True)\n",
     "\n",
@@ -1023,10 +1025,11 @@
     "plt.xlabel(\"states\")\n",
     "plt.ylabel(\"Ecludian distance\")\n",
     "dendrogram(hc_complete2, labels=res2.index, leaf_rotation=90, leaf_font_size=8)\n",
-    "plt.axhline(y=4.45, c=\"k\", ls=\"dashed\")\n",
+    "plt.axhline(y=2.8, c=\"k\", ls=\"dashed\")\n",
     "plt.show()\n",
     "\n",
-    "print(res2)"
+    "print(res2)\n",
+    "# Cutting the dendrogram at height 2.8 results in six distinct clusters."
    ]
   }
  ],

diff --git a/content/09-pca-clustering/pca.ipynb b/content/09-pca-clustering/pca.ipynb
@@ -608,7 +608,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**3.** Now, run **PCA** from **sklearn** explaining at least $95\\%$ variance on the **standardised mouse protein dataset** and display the **top ten eigenvalues**. "
+    "**3.** Now, run **PCA** from **sklearn** explaining at least $95\\%$ variance on the **standardised mouse protein dataset** and display the **top ten eigenvalues**. **Hint:** Eigenvalue equals the explained variance specific to PCA."
    ]
   },
   {
@@ -637,19 +637,21 @@
    },
    "outputs": [],
    "source": [
+    "from sklearn.decomposition import PCA\n",
+    "\n",
     "pca = PCA(n_components=0.95)\n",
     "pca.fit(X)\n",
-    "cov_matrix = np.dot(X.T, X) / len(X)\n",
     "\n",
-    "for eigenvector in pca.components_[:10]:\n",
-    "    print(np.dot(eigenvector.T, np.dot(cov_matrix, eigenvector)))"
+    "print(\n",
+    "    \"The first 10 explained variance/eigenvalues are: \\n\", pca.explained_variance_[:10]\n",
+    ")"
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**4.** Using the fitted PCA model in **Exercise 3**, find out the **proportion of explained variance (PVE)** and its **ratio** for the top 10 principal components. "
+    "**4.** Using the fitted PCA model in **Exercise 3**, find out the **explained variance ratio** for the top 10 principal components. "
    ]
   },
   {
@@ -678,7 +680,6 @@
    },
    "outputs": [],
    "source": [
-    "print(\"The first 10 explained variance are: \\n\", pca.explained_variance_[:10])\n",
     "print(\n",
     "    \"The first 10 explained variance ratio are: \\n\", pca.explained_variance_ratio_[:10]\n",
     ")"
@@ -688,7 +689,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "**5.** After observing the **PVE** from **Exercise 4** carefuly, find out how many **principal components** should we take to preserve $70\\%$ of variance of the data?"
+    "**5.** After observing the **explained varience ratio** from **Exercise 4** carefuly, find out how many **principal components** should we take to preserve $70\\%$ of variance of the data?"
    ]
   },
   {