ML-For-Beginners/translations/mo/5-Clustering/2-K-Means/solution/R/lesson_15-R.ipynb

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   "source": [
    "## 探索使用 R 和 Tidy 數據原則進行 K-Means 分群\n",
    "\n",
    "### [**課前測驗**](https://gray-sand-07a10f403.1.azurestaticapps.net/quiz/29/)\n",
    "\n",
    "在本課程中，您將學習如何使用 Tidymodels 套件以及 R 生態系統中的其他套件（我們稱它們為朋友 🧑‍🤝‍🧑），以及您之前匯入的尼日利亞音樂數據集來創建分群。我們將介紹 K-Means 分群的基礎知識。請記住，正如您在之前的課程中所學，分群有許多不同的方法，您使用的方法取決於您的數據。我們將嘗試 K-Means，因為它是最常見的分群技術。讓我們開始吧！\n",
    "\n",
    "您將學習的術語：\n",
    "\n",
    "-   Silhouette 評分\n",
    "\n",
    "-   Elbow 方法\n",
    "\n",
    "-   Inertia（慣性）\n",
    "\n",
    "-   Variance（方差）\n",
    "\n",
    "### **簡介**\n",
    "\n",
    "[K-Means 分群](https://wikipedia.org/wiki/K-means_clustering) 是一種源自信號處理領域的方法。它用於根據特徵的相似性將數據分成 `k 個分群`。\n",
    "\n",
    "這些分群可以以 [Voronoi 圖](https://wikipedia.org/wiki/Voronoi_diagram) 的形式進行可視化，其中包括一個點（或“種子”）及其對應的區域。\n",
    "\n",
    "<p >\n",
    "   <img src=\"../../images/voronoi.png\"\n",
    "   width=\"500\"/>\n",
    "   <figcaption>Jen Looper 的信息圖</figcaption>\n",
    "\n",
    "K-Means 分群的步驟如下：\n",
    "\n",
    "1.  數據科學家首先指定希望創建的分群數量。\n",
    "\n",
    "2.  接下來，算法隨機選擇數據集中的 K 個觀測值作為分群的初始中心（即質心）。\n",
    "\n",
    "3.  然後，將其餘的每個觀測值分配到距離最近的質心。\n",
    "\n",
    "4.  接著，計算每個分群的新平均值，並將質心移動到該平均值。\n",
    "\n",
    "5.  現在中心已重新計算，所有觀測值再次被檢查是否可能更接近其他分群。使用更新的分群平均值重新分配所有對象。分群分配和質心更新步驟會反覆進行，直到分群分配不再改變（即達到收斂）。通常，算法在每次新迭代中質心移動微乎其微且分群變得穩定時終止。\n",
    "\n",
    "<div>\n",
    "\n",
    "> 請注意，由於初始 k 個觀測值的隨機化，我們每次應用該程序時可能會得到略有不同的結果。因此，大多數算法使用多次 *隨機起始*，並選擇具有最低 WCSS 的迭代。因此，強烈建議始終使用多個 *nstart* 值運行 K-Means，以避免 *不理想的局部最優解*。\n",
    "\n",
    "</div>\n",
    "\n",
    "以下短動畫使用 Allison Horst 的 [插圖](https://github.com/allisonhorst/stats-illustrations) 解釋了分群過程：\n",
    "\n",
    "<p >\n",
    "   <img src=\"../../images/kmeans.gif\"\n",
    "   width=\"550\"/>\n",
    "   <figcaption>@allison_horst 的插圖</figcaption>\n",
    "\n",
    "分群中出現的一個基本問題是：如何知道應將數據分成多少個分群？使用 K-Means 的一個缺點是您需要確定 `k`，即 `質心` 的數量。幸運的是，`elbow 方法` 有助於估算 `k` 的良好起始值。您稍後將嘗試使用它。\n",
    "\n",
    "### \n",
    "\n",
    "**前置條件**\n",
    "\n",
    "我們將從 [上一課](https://github.com/microsoft/ML-For-Beginners/blob/main/5-Clustering/1-Visualize/solution/R/lesson_14-R.ipynb) 停止的地方繼續，該課程中我們分析了數據集，進行了大量可視化，並篩選了感興趣的觀測值。一定要查看！\n",
    "\n",
    "我們需要一些套件來完成這個模組。您可以通過以下方式安裝它們：`install.packages(c('tidyverse', 'tidymodels', 'cluster', 'summarytools', 'plotly', 'paletteer', 'factoextra', 'patchwork'))`\n",
    "\n",
    "或者，以下腳本會檢查您是否擁有完成此模組所需的套件，並在缺少某些套件時為您安裝它們。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "ah_tBi58LXyi"
   },
   "source": [
    "suppressWarnings(if(!require(\"pacman\")) install.packages(\"pacman\"))\n",
    "\n",
    "pacman::p_load('tidyverse', 'tidymodels', 'cluster', 'summarytools', 'plotly', 'paletteer', 'factoextra', 'patchwork')\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7e--UCUTLXym"
   },
   "source": [
    "讓我們開始吧！\n",
    "\n",
    "## 1. 與數據共舞：縮小至三種最受歡迎的音樂類型\n",
    "\n",
    "這是我們上一課所做內容的回顧。讓我們來切分和分析一些數據吧！\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "Ycamx7GGLXyn"
   },
   "source": [
    "# Load the core tidyverse and make it available in your current R session\n",
    "library(tidyverse)\n",
    "\n",
    "# Import the data into a tibble\n",
    "df <- read_csv(file = \"https://raw.githubusercontent.com/microsoft/ML-For-Beginners/main/5-Clustering/data/nigerian-songs.csv\", show_col_types = FALSE)\n",
    "\n",
    "# Narrow down to top 3 popular genres\n",
    "nigerian_songs <- df %>% \n",
    "  # Concentrate on top 3 genres\n",
    "  filter(artist_top_genre %in% c(\"afro dancehall\", \"afropop\",\"nigerian pop\")) %>% \n",
    "  # Remove unclassified observations\n",
    "  filter(popularity != 0)\n",
    "\n",
    "\n",
    "\n",
    "# Visualize popular genres using bar plots\n",
    "theme_set(theme_light())\n",
    "nigerian_songs %>%\n",
    "  count(artist_top_genre) %>%\n",
    "  ggplot(mapping = aes(x = artist_top_genre, y = n,\n",
    "                       fill = artist_top_genre)) +\n",
    "  geom_col(alpha = 0.8) +\n",
    "  paletteer::scale_fill_paletteer_d(\"ggsci::category10_d3\") +\n",
    "  ggtitle(\"Top genres\") +\n",
    "  theme(plot.title = element_text(hjust = 0.5))\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "b5h5zmkPLXyp"
   },
   "source": [
    "🤩 這進展得很順利！\n",
    "\n",
    "## 2. 更多數據探索\n",
    "\n",
    "這份數據有多乾淨？讓我們使用盒鬚圖檢查是否有異常值。我們將專注於異常值較少的數值型欄位（雖然你也可以清理掉異常值）。盒鬚圖可以顯示數據的範圍，並幫助選擇要使用的欄位。請注意，盒鬚圖並不顯示方差，而方差是良好可聚類數據的一個重要元素。如需進一步了解，請參閱[這篇討論](https://stats.stackexchange.com/questions/91536/deduce-variance-from-boxplot)。\n",
    "\n",
    "[盒鬚圖](https://en.wikipedia.org/wiki/Box_plot) 用於以圖形方式描述「數值型」數據的分佈，因此讓我們從*選擇*所有數值型欄位以及流行音樂類型開始吧。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "HhNreJKLLXyq"
   },
   "source": [
    "# Select top genre column and all other numeric columns\n",
    "df_numeric <- nigerian_songs %>% \n",
    "  select(artist_top_genre, where(is.numeric)) \n",
    "\n",
    "# Display the data\n",
    "df_numeric %>% \n",
    "  slice_head(n = 5)\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uYXrwJRaLXyq"
   },
   "source": [
    "看看選擇輔助工具 `where` 是如何讓這變得簡單的 💁？可以在[這裡](https://tidyselect.r-lib.org/)探索其他類似的函數。\n",
    "\n",
    "由於我們將為每個數值型特徵製作箱型圖，而且我們想避免使用迴圈，因此讓我們將數據重新格式化為*更長*的格式，這樣我們就可以利用 `facets`——每個子圖顯示數據的一個子集。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "gd5bR3f8LXys"
   },
   "source": [
    "# Pivot data from wide to long\n",
    "df_numeric_long <- df_numeric %>% \n",
    "  pivot_longer(!artist_top_genre, names_to = \"feature_names\", values_to = \"values\") \n",
    "\n",
    "# Print out data\n",
    "df_numeric_long %>% \n",
    "  slice_head(n = 15)\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-7tE1swnLXyv"
   },
   "source": [
    "現在來點更長的內容吧！現在是時候使用一些 `ggplots` 了！那麼我們會使用哪種 `geom` 呢？\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "r88bIsyuLXyy"
   },
   "source": [
    "# Make a box plot\n",
    "df_numeric_long %>% \n",
    "  ggplot(mapping = aes(x = feature_names, y = values, fill = feature_names)) +\n",
    "  geom_boxplot() +\n",
    "  facet_wrap(~ feature_names, ncol = 4, scales = \"free\") +\n",
    "  theme(legend.position = \"none\")\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EYVyKIUELXyz"
   },
   "source": [
    "現在我們可以看到這些數據有些雜亂：透過觀察每一列的盒狀圖，可以看到一些異常值。你可以逐一檢查數據集並移除這些異常值，但這樣可能會使數據變得過於簡化。\n",
    "\n",
    "目前，我們來選擇要用於聚類練習的列。讓我們挑選範圍相似的數值型列。我們可以將 `artist_top_genre` 編碼為數值型，但暫時先忽略它。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "-wkpINyZLXy0"
   },
   "source": [
    "# Select variables with similar ranges\n",
    "df_numeric_select <- df_numeric %>% \n",
    "  select(popularity, danceability, acousticness, loudness, energy) \n",
    "\n",
    "# Normalize data\n",
    "# df_numeric_select <- scale(df_numeric_select)\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D7dLzgpqLXy1"
   },
   "source": [
    "## 3. 在 R 中計算 k-means 分群\n",
    "\n",
    "我們可以使用 R 中內建的 `kmeans` 函數來計算 k-means，請參考 `help(\"kmeans()\")`。`kmeans()` 函數的主要參數是一個包含所有數值型欄位的資料框。\n",
    "\n",
    "使用 k-means 分群的第一步是指定最終解決方案中要生成的群組數量 (k)。我們知道從資料集中分出來的歌曲類型有 3 種，因此我們嘗試使用 3：\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "uC4EQ5w7LXy5"
   },
   "source": [
    "set.seed(2056)\n",
    "# Kmeans clustering for 3 clusters\n",
    "kclust <- kmeans(\n",
    "  df_numeric_select,\n",
    "  # Specify the number of clusters\n",
    "  centers = 3,\n",
    "  # How many random initial configurations\n",
    "  nstart = 25\n",
    ")\n",
    "\n",
    "# Display clustering object\n",
    "kclust\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hzfhscWrLXy-"
   },
   "source": [
    "kmeans 物件包含了許多資訊，這些資訊在 `help(\"kmeans()\")` 中有詳細說明。目前，我們先專注於幾個重點。我們可以看到資料被分成了 3 個群組，大小分別為 65、110 和 111。輸出中還包含了這 3 個群組在 5 個變數上的群中心（平均值）。\n",
    "\n",
    "群集向量是每個觀測值的群組分配。我們可以使用 `augment` 函數將群組分配新增到原始資料集中。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "0XwwpFGQLXy_"
   },
   "source": [
    "# Add predicted cluster assignment to data set\n",
    "augment(kclust, df_numeric_select) %>% \n",
    "  relocate(.cluster) %>% \n",
    "  slice_head(n = 10)\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "NXIVXXACLXzA"
   },
   "source": [
    "太好了，我們已經將數據集分成了三個群組。那麼，我們的分群效果如何呢 🤷？讓我們來看看 `Silhouette score`。\n",
    "\n",
    "### **Silhouette score**\n",
    "\n",
    "[Silhouette 分析](https://en.wikipedia.org/wiki/Silhouette_(clustering)) 可以用來研究結果群組之間的分離距離。這個分數範圍從 -1 到 1，如果分數接近 1，表示群組密集且與其他群組分離良好。分數接近 0 則表示群組重疊，樣本非常接近鄰近群組的決策邊界。[來源](https://dzone.com/articles/kmeans-silhouette-score-explained-with-python-exam)。\n",
    "\n",
    "平均 Silhouette 方法計算不同 *k* 值下觀測值的平均 Silhouette 分數。高平均 Silhouette 分數表示分群效果良好。\n",
    "\n",
    "使用 cluster 套件中的 `silhouette` 函數來計算平均 Silhouette 寬度。\n",
    "\n",
    "> Silhouette 可以使用任何[距離](https://en.wikipedia.org/wiki/Distance \"Distance\")度量來計算，例如我們在[上一課](https://github.com/microsoft/ML-For-Beginners/blob/main/5-Clustering/1-Visualize/solution/R/lesson_14-R.ipynb)中討論過的[歐幾里得距離](https://en.wikipedia.org/wiki/Euclidean_distance \"Euclidean distance\")或[曼哈頓距離](https://en.wikipedia.org/wiki/Manhattan_distance \"Manhattan distance\")。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "Jn0McL28LXzB"
   },
   "source": [
    "# Load cluster package\n",
    "library(cluster)\n",
    "\n",
    "# Compute average silhouette score\n",
    "ss <- silhouette(kclust$cluster,\n",
    "                 # Compute euclidean distance\n",
    "                 dist = dist(df_numeric_select))\n",
    "mean(ss[, 3])\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QyQRn97nLXzC"
   },
   "source": [
    "我們的分數是 **.549**，正好位於中間位置。這表明我們的數據並不特別適合這種類型的聚類。讓我們看看是否可以通過視覺化來驗證這個猜測。[factoextra 套件](https://rpkgs.datanovia.com/factoextra/index.html) 提供了用於視覺化聚類的函數（`fviz_cluster()`）。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "7a6Km1_FLXzD"
   },
   "source": [
    "library(factoextra)\n",
    "\n",
    "# Visualize clustering results\n",
    "fviz_cluster(kclust, df_numeric_select)\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IBwCWt-0LXzD"
   },
   "source": [
    "群集之間的重疊表明，我們的數據並不特別適合這種類型的群集，但我們還是繼續進行。\n",
    "\n",
    "## 4. 確定最佳群集數量\n",
    "\n",
    "在 K-Means 群集分析中，經常出現的一個基本問題是——在沒有已知類別標籤的情況下，如何知道應將數據分成多少個群集？\n",
    "\n",
    "我們可以嘗試的一種方法是使用數據樣本來`創建一系列群集模型`，並逐步增加群集的數量（例如從 1 到 10），然後評估群集指標，例如 **Silhouette 分數**。\n",
    "\n",
    "讓我們通過計算不同 *k* 值的群集算法來確定最佳群集數量，並評估 **群集內平方和**（WCSS）。群集內平方和（WCSS）衡量群集的緊密性，我們希望它越小越好，較低的值意味著數據點更接近。\n",
    "\n",
    "讓我們探索不同的 `k` 值（從 1 到 10）對此群集的影響。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "hSeIiylDLXzE"
   },
   "source": [
    "# Create a series of clustering models\n",
    "kclusts <- tibble(k = 1:10) %>% \n",
    "  # Perform kmeans clustering for 1,2,3 ... ,10 clusters\n",
    "  mutate(model = map(k, ~ kmeans(df_numeric_select, centers = .x, nstart = 25)),\n",
    "  # Farm out clustering metrics eg WCSS\n",
    "         glanced = map(model, ~ glance(.x))) %>% \n",
    "  unnest(cols = glanced)\n",
    "  \n",
    "\n",
    "# View clustering rsulsts\n",
    "kclusts\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "m7rS2U1eLXzE"
   },
   "source": [
    "現在我們已經獲得每個聚類算法在中心 *k* 下的總體內部平方和 (tot.withinss)，接下來我們使用[肘部法](https://en.wikipedia.org/wiki/Elbow_method_(clustering))來尋找最佳的聚類數量。此方法的步驟是將 WCSS 繪製成聚類數量的函數圖，並選擇[曲線的肘部](https://en.wikipedia.org/wiki/Elbow_of_the_curve \"Elbow of the curve\")作為要使用的聚類數量。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "o_DjHGItLXzF"
   },
   "source": [
    "set.seed(2056)\n",
    "# Use elbow method to determine optimum number of clusters\n",
    "kclusts %>% \n",
    "  ggplot(mapping = aes(x = k, y = tot.withinss)) +\n",
    "  geom_line(size = 1.2, alpha = 0.8, color = \"#FF7F0EFF\") +\n",
    "  geom_point(size = 2, color = \"#FF7F0EFF\")\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pLYyt5XSLXzG"
   },
   "source": [
    "該圖顯示，當群集數量從一個增加到兩個時，WCSS（因此*緊密性*）大幅減少，從兩個增加到三個群集時也有明顯的減少。之後，減少的幅度變得不那麼明顯，導致圖表在大約三個群集處出現一個「肘部」💪。這是一個很好的指標，表明數據點大致可以分為兩到三個相對獨立的群集。\n",
    "\n",
    "現在我們可以繼續提取 `k = 3` 的群集模型：\n",
    "\n",
    "> `pull()`: 用於提取單一列\n",
    ">\n",
    "> `pluck()`: 用於索引像列表這樣的數據結構\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "JP_JPKBILXzG"
   },
   "source": [
    "# Extract k = 3 clustering\n",
    "final_kmeans <- kclusts %>% \n",
    "  filter(k == 3) %>% \n",
    "  pull(model) %>% \n",
    "  pluck(1)\n",
    "\n",
    "\n",
    "final_kmeans\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l_PDTu8tLXzI"
   },
   "source": [
    "太好了！讓我們來看看獲得的群集。想用 `plotly` 增加一些互動性嗎？\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "dNcleFe-LXzJ"
   },
   "source": [
    "# Add predicted cluster assignment to data set\n",
    "results <-  augment(final_kmeans, df_numeric_select) %>% \n",
    "  bind_cols(df_numeric %>% select(artist_top_genre)) \n",
    "\n",
    "# Plot cluster assignments\n",
    "clust_plt <- results %>% \n",
    "  ggplot(mapping = aes(x = popularity, y = danceability, color = .cluster, shape = artist_top_genre)) +\n",
    "  geom_point(size = 2, alpha = 0.8) +\n",
    "  paletteer::scale_color_paletteer_d(\"ggthemes::Tableau_10\")\n",
    "\n",
    "ggplotly(clust_plt)\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "6JUM_51VLXzK"
   },
   "source": [
    "或許我們原本預期，每個群集（以不同顏色表示）會有明顯不同的類型（以不同形狀表示）。\n",
    "\n",
    "讓我們來看看模型的準確性。\n"
   ]
  },
  {
   "cell_type": "code",
   "metadata": {
    "id": "HdIMUGq7LXzL"
   },
   "source": [
    "# Assign genres to predefined integers\n",
    "label_count <- results %>% \n",
    "  group_by(artist_top_genre) %>% \n",
    "  mutate(id = cur_group_id()) %>% \n",
    "  ungroup() %>% \n",
    "  summarise(correct_labels = sum(.cluster == id))\n",
    "\n",
    "\n",
    "# Print results  \n",
    "cat(\"Result:\", label_count$correct_labels, \"out of\", nrow(results), \"samples were correctly labeled.\")\n",
    "\n",
    "cat(\"\\nAccuracy score:\", label_count$correct_labels/nrow(results))\n"
   ],
   "execution_count": null,
   "outputs": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "C50wvaAOLXzM"
   },
   "source": [
    "這個模型的準確性不算差，但也不算好。可能是因為這些數據不太適合使用 K-Means 分群。這些數據過於不平衡，相關性太低，而且欄位值之間的差異太大，導致分群效果不佳。事實上，形成的群集可能受到我們之前定義的三個類型分類的影響或偏斜。\n",
    "\n",
    "儘管如此，這仍然是一個相當有趣的學習過程！\n",
    "\n",
    "在 Scikit-learn 的文件中，你可以看到像這樣的模型，群集劃分不太清晰，存在「變異」問題：\n",
    "\n",
    "<p >\n",
    "   <img src=\"../../images/problems.png\"\n",
    "   width=\"500\"/>\n",
    "   <figcaption>來自 Scikit-learn 的資訊圖表</figcaption>\n",
    "\n",
    "\n",
    "\n",
    "## **變異**\n",
    "\n",
    "變異被定義為「與平均值的平方差的平均值」[來源](https://www.mathsisfun.com/data/standard-deviation.html)。在這個分群問題的背景下，它指的是數據集中數值偏離平均值的程度。\n",
    "\n",
    "✅ 這是一個很好的時機來思考如何解決這個問題。稍微調整數據？使用不同的欄位？使用不同的演算法？提示：試試[縮放你的數據](https://www.mygreatlearning.com/blog/learning-data-science-with-k-means-clustering/)以進行正規化，並測試其他欄位。\n",
    "\n",
    "> 試試這個「[變異計算器](https://www.calculatorsoup.com/calculators/statistics/variance-calculator.php)」來更深入了解這個概念。\n",
    "\n",
    "------------------------------------------------------------------------\n",
    "\n",
    "## **🚀挑戰**\n",
    "\n",
    "花些時間使用這個筆記本，調整參數。你能否通過更清理數據（例如移除異常值）來提高模型的準確性？你可以使用權重來給某些數據樣本更高的權重。還有什麼方法可以用來創建更好的群集？\n",
    "\n",
    "提示：試著縮放你的數據。筆記本中有註解的程式碼，添加了標準縮放以使數據欄位在範圍上更接近。你會發現，雖然輪廓分數下降了，但肘部圖中的「折點」變得更平滑。這是因為未縮放的數據允許變異較小的數據佔據更大的權重。可以在[這裡](https://stats.stackexchange.com/questions/21222/are-mean-normalization-and-feature-scaling-needed-for-k-means-clustering/21226#21226)閱讀更多相關問題。\n",
    "\n",
    "## [**課後測驗**](https://gray-sand-07a10f403.1.azurestaticapps.net/quiz/30/)\n",
    "\n",
    "## **回顧與自學**\n",
    "\n",
    "-   看看一個 K-Means 模擬器[例如這個](https://user.ceng.metu.edu.tr/~akifakkus/courses/ceng574/k-means/)。你可以使用這個工具來視覺化樣本數據點並確定其中心點。你可以編輯數據的隨機性、群集數量和中心點數量。這是否幫助你更好地理解數據如何分組？\n",
    "\n",
    "-   另外，看看[這份來自 Stanford 的 K-Means 手冊](https://stanford.edu/~cpiech/cs221/handouts/kmeans.html)。\n",
    "\n",
    "想要嘗試使用你新學到的分群技能來處理適合 K-Means 分群的數據集嗎？請參考：\n",
    "\n",
    "-   [訓練和評估分群模型](https://rpubs.com/eR_ic/clustering)，使用 Tidymodels 和相關工具\n",
    "\n",
    "-   [K-Means 分群分析](https://uc-r.github.io/kmeans_clustering)，UC 商業分析 R 編程指南\n",
    "\n",
    "-   [使用整潔數據原則進行 K-Means 分群](https://www.tidymodels.org/learn/statistics/k-means/)\n",
    "\n",
    "## **作業**\n",
    "\n",
    "[嘗試不同的分群方法](https://github.com/microsoft/ML-For-Beginners/blob/main/5-Clustering/2-K-Means/assignment.md)\n",
    "\n",
    "## 特別感謝：\n",
    "\n",
    "[Jen Looper](https://www.twitter.com/jenlooper) 創建了這個模組的原始 Python 版本 ♥️\n",
    "\n",
    "[`Allison Horst`](https://twitter.com/allison_horst/) 創作了令人驚嘆的插圖，使 R 更加友好和吸引人。可以在她的[畫廊](https://www.google.com/url?q=https://github.com/allisonhorst/stats-illustrations&sa=D&source=editors&ust=1626380772530000&usg=AOvVaw3zcfyCizFQZpkSLzxiiQEM)找到更多插圖。\n",
    "\n",
    "祝學習愉快，\n",
    "\n",
    "[Eric](https://twitter.com/ericntay)，Gold Microsoft Learn 學生大使。\n",
    "\n",
    "<p >\n",
    "   <img src=\"../../images/r_learners_sm.jpeg\"\n",
    "   width=\"500\"/>\n",
    "   <figcaption>@allison_horst 的作品</figcaption>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n---\n\n**免責聲明**：  \n本文件已使用 AI 翻譯服務 [Co-op Translator](https://github.com/Azure/co-op-translator) 進行翻譯。儘管我們努力確保翻譯的準確性，但請注意，自動翻譯可能包含錯誤或不準確之處。原始文件的母語版本應被視為權威來源。對於關鍵信息，建議使用專業人工翻譯。我們對因使用此翻譯而引起的任何誤解或錯誤解釋不承擔責任。\n"
   ]
  }
 ]
}