{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Building a K-Nearest Neighbours Classifier\n",
        "\n",
        "CSI 4106 — Introduction to Artificial Intelligence\n",
        "\n",
        "Marcel Turcotte  \n",
        "2026-09-13\n",
        "\n",
        "# Introduction\n",
        "\n",
        "This notebook develops a small k-nearest neighbours (KNN) classifier\n",
        "from first principles. KNN illustrates an approach to learning that is\n",
        "very different from constructing a decision tree or estimating the\n",
        "coefficients of a linear model. Its central idea can be summarized in\n",
        "three words:\n",
        "\n",
        "> **Store, search, vote.**\n",
        "\n",
        "Learning consists of storing the training examples. When a prediction is\n",
        "requested, the classifier finds nearby examples and lets them vote. The\n",
        "implementation supports multiclass labels and both uniform and\n",
        "distance-weighted voting.\n",
        "\n",
        "# Preparation\n",
        "\n",
        "The installation step runs only if `palmerpenguins` is unavailable,\n",
        "making the notebook suitable for a fresh Google Colab session."
      ],
      "id": "5f98f2cb-f209-4b05-8851-a2ce741b1b4f"
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "import subprocess\n",
        "import sys\n",
        "\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "\n",
        "try:\n",
        "    from palmerpenguins import load_penguins\n",
        "except ImportError:\n",
        "    subprocess.check_call([\n",
        "        sys.executable, \"-m\", \"pip\", \"install\", \"-q\", \"palmerpenguins\"\n",
        "    ])\n",
        "    from palmerpenguins import load_penguins\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.preprocessing import StandardScaler"
      ],
      "id": "imports"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Palmer Penguins\n",
        "\n",
        "We retain bill length and bill depth and classify all three penguin\n",
        "species. These two features produce a useful example: the classes are\n",
        "distinguishable, but not perfectly separable, so changing the\n",
        "neighbourhood changes the decision boundary."
      ],
      "id": "00adc910-1f6f-41d7-a008-01148f745dd4"
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Training examples: 273\n",
            "Test examples: 69\n",
            "Classes: ['Adelie' 'Chinstrap' 'Gentoo']"
          ]
        }
      ],
      "source": [
        "feature_names = [\"bill_length_mm\", \"bill_depth_mm\"]\n",
        "\n",
        "penguins = load_penguins()\n",
        "penguins = penguins[feature_names + [\"species\"]].dropna().copy()\n",
        "\n",
        "X = penguins[feature_names].to_numpy()\n",
        "y = penguins[\"species\"].to_numpy()\n",
        "\n",
        "X_train, X_test, y_train, y_test = train_test_split(\n",
        "    X, y, test_size=0.2, random_state=42, stratify=y\n",
        ")\n",
        "\n",
        "print(f\"Training examples: {len(X_train)}\")\n",
        "print(f\"Test examples: {len(X_test)}\")\n",
        "print(f\"Classes: {np.unique(y_train)}\")"
      ],
      "id": "penguins-data"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Feature Scaling\n",
        "\n",
        "Euclidean distance depends on numerical scale. We therefore standardize\n",
        "each feature using the training-set mean and standard deviation:\n",
        "\n",
        "$$\n",
        "z=\\frac{x-\\mu_{\\mathrm{train}}}{\\sigma_{\\mathrm{train}}}.\n",
        "$$\n",
        "\n",
        "The scaler is fitted only on the training data. The test data must not\n",
        "influence preprocessing choices made during learning."
      ],
      "id": "af7c9031-a660-4ba0-a9bf-814fb42d3725"
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [],
      "source": [
        "scaler = StandardScaler()\n",
        "X_train_scaled = scaler.fit_transform(X_train)\n",
        "X_test_scaled = scaler.transform(X_test)"
      ],
      "id": "scaling"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Searching for Neighbours\n",
        "\n",
        "For a query $x$ and a training example $x_i$, Euclidean distance is\n",
        "\n",
        "$$\n",
        "d(x,x_i)=\\sqrt{\\sum_{j=1}^{D}\\left(x^{(j)}-x_i^{(j)}\\right)^2}.\n",
        "$$\n",
        "\n",
        "The most direct implementation computes every distance, sorts them, and\n",
        "keeps the first $k$ indices."
      ],
      "id": "0383988c-a5de-43e9-961d-4d1cdd975dad"
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [],
      "source": [
        "def nearest_neighbors(X_train, x, n_neighbors):\n",
        "    \"\"\"Return the nearest training indices and their distances from x.\"\"\"\n",
        "    distances = np.sqrt(np.sum((X_train - x) ** 2, axis=1))\n",
        "    indices = np.argsort(distances, kind=\"stable\")[:n_neighbors]\n",
        "    return indices, distances[indices]"
      ],
      "id": "nearest-neighbors"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The stable sort makes the result deterministic when two training\n",
        "examples are equally distant. Production implementations can avoid a\n",
        "complete sort or use specialized search structures.\n",
        "\n",
        "# Voting\n",
        "\n",
        "With uniform voting, all selected neighbours receive weight 1. With\n",
        "distance weighting, neighbour $i$ receives weight\n",
        "\n",
        "$$\n",
        "w_i=\\frac{1}{d_i}.\n",
        "$$\n",
        "\n",
        "An exact match requires special handling because $1/0$ is undefined. If\n",
        "exact matches exist, our implementation lets only those observations\n",
        "vote."
      ],
      "id": "94112f47-6b8e-41c6-955e-81b8a8936820"
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [],
      "source": [
        "def voting_weights(distances, mode):\n",
        "    \"\"\"Return uniform weights or inverse-distance weights.\"\"\"\n",
        "    if mode == \"uniform\":\n",
        "        return np.ones(len(distances))\n",
        "\n",
        "    exact_matches = distances == 0\n",
        "    if np.any(exact_matches):\n",
        "        return exact_matches.astype(float)\n",
        "\n",
        "    return 1 / distances\n",
        "\n",
        "\n",
        "def vote_probabilities(labels, weights, classes):\n",
        "    \"\"\"Convert the neighbours' weighted votes into probabilities.\"\"\"\n",
        "    scores = np.array([\n",
        "        np.sum(weights[labels == label])\n",
        "        for label in classes\n",
        "    ])\n",
        "    return scores / np.sum(scores)"
      ],
      "id": "voting"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Classifier\n",
        "\n",
        "The `fit` method stores the training set. Most of the work occurs in\n",
        "`_predict_proba_one`: find the neighbours, assign their voting weights,\n",
        "and aggregate votes by class.\n",
        "\n",
        "Validation is included so that unsupported inputs produce clear errors,\n",
        "but it is not part of the central KNN idea."
      ],
      "id": "ec040518-dce1-4891-8bad-36b4eac3da56"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [],
      "source": [
        "class SimpleKNeighborsClassifier:\n",
        "    \"\"\"A didactic classifier with a small scikit-learn-like interface.\"\"\"\n",
        "\n",
        "    def __init__(self, n_neighbors=5, weights=\"uniform\"):\n",
        "        self.n_neighbors = n_neighbors\n",
        "        self.weights = weights\n",
        "\n",
        "    def fit(self, X, y):\n",
        "        X = np.asarray(X, dtype=float)\n",
        "        y = np.asarray(y)\n",
        "        self._validate_training_data(X, y)\n",
        "\n",
        "        self.X_train_ = X.copy()\n",
        "        self.y_train_ = y.copy()\n",
        "        self.classes_ = np.unique(y)\n",
        "        self.n_features_in_ = X.shape[1]\n",
        "        return self\n",
        "\n",
        "    def _predict_proba_one(self, x):\n",
        "        indices, distances = nearest_neighbors(\n",
        "            self.X_train_, x, self.n_neighbors\n",
        "        )\n",
        "        labels = self.y_train_[indices]\n",
        "        weights = voting_weights(distances, self.weights)\n",
        "        return vote_probabilities(labels, weights, self.classes_)\n",
        "\n",
        "    def predict_proba(self, X):\n",
        "        X = self._validate_prediction_data(X)\n",
        "        return np.vstack([self._predict_proba_one(x) for x in X])\n",
        "\n",
        "    def predict(self, X):\n",
        "        probabilities = self.predict_proba(X)\n",
        "        return self.classes_[np.argmax(probabilities, axis=1)]\n",
        "\n",
        "    def score(self, X, y):\n",
        "        return float(np.mean(self.predict(X) == np.asarray(y)))\n",
        "\n",
        "    def _validate_training_data(self, X, y):\n",
        "        if X.ndim != 2 or y.ndim != 1 or len(X) != len(y):\n",
        "            raise ValueError(\n",
        "                \"X must be 2-D and y must be 1-D with matching rows\"\n",
        "            )\n",
        "        if len(y) == 0:\n",
        "            raise ValueError(\"the training set cannot be empty\")\n",
        "        if not np.isfinite(X).all():\n",
        "            raise ValueError(\n",
        "                \"missing and non-finite feature values are unsupported\"\n",
        "            )\n",
        "        if not isinstance(self.n_neighbors, (int, np.integer)):\n",
        "            raise ValueError(\"n_neighbors must be an integer\")\n",
        "        if not 1 <= self.n_neighbors <= len(y):\n",
        "            raise ValueError(\"n_neighbors must be between 1 and len(y)\")\n",
        "        if self.weights not in {\"uniform\", \"distance\"}:\n",
        "            raise ValueError(\"weights must be 'uniform' or 'distance'\")\n",
        "\n",
        "    def _validate_prediction_data(self, X):\n",
        "        if not hasattr(self, \"X_train_\"):\n",
        "            raise ValueError(\"call fit before making predictions\")\n",
        "        X = np.asarray(X, dtype=float)\n",
        "        if X.ndim == 1:\n",
        "            X = X.reshape(1, -1)\n",
        "        if X.ndim != 2 or X.shape[1] != self.n_features_in_:\n",
        "            raise ValueError(\"X has the wrong number of features\")\n",
        "        if not np.isfinite(X).all():\n",
        "            raise ValueError(\n",
        "                \"missing and non-finite feature values are unsupported\"\n",
        "            )\n",
        "        return X"
      ],
      "id": "classifier"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Training and Evaluation\n",
        "\n",
        "The two models below use the same five neighbours. Only their voting\n",
        "rule changes."
      ],
      "id": "730f14d9-1670-4073-8868-9459826483f3"
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "k=5, weights='uniform': accuracy=0.957\n",
            "k=5, weights='distance': accuracy=0.957"
          ]
        }
      ],
      "source": [
        "for mode in (\"uniform\", \"distance\"):\n",
        "    knn = SimpleKNeighborsClassifier(n_neighbors=5, weights=mode)\n",
        "    knn.fit(X_train_scaled, y_train)\n",
        "    accuracy = knn.score(X_test_scaled, y_test)\n",
        "    print(f\"k=5, weights='{mode}': accuracy={accuracy:.3f}\")"
      ],
      "id": "evaluation"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Inspecting one prediction\n",
        "\n",
        "Because KNN bases a prediction directly on stored examples, we can\n",
        "inspect the neighbourhood responsible for an individual result."
      ],
      "id": "d5cddf56-6c1a-4142-ac29-ce5e17777f7c"
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "True class: Adelie\n",
            "Predicted class: Adelie\n",
            "\n",
            "Neighbours:\n",
            "1: Adelie    distance=0.018\n",
            "2: Adelie    distance=0.053\n",
            "3: Adelie    distance=0.088\n",
            "4: Adelie    distance=0.100\n",
            "5: Adelie    distance=0.128"
          ]
        }
      ],
      "source": [
        "query = X_test_scaled[0]\n",
        "indices, distances = nearest_neighbors(X_train_scaled, query, n_neighbors=5)\n",
        "\n",
        "print(f\"True class: {y_test[0]}\")\n",
        "print(f\"Predicted class: {knn.predict(query)[0]}\")\n",
        "print(\"\\nNeighbours:\")\n",
        "for rank, (index, distance) in enumerate(zip(indices, distances), start=1):\n",
        "    print(f\"{rank}: {y_train[index]:9s} distance={distance:.3f}\")"
      ],
      "id": "inspect-prediction"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Decision Boundaries\n",
        "\n",
        "The custom classifier is sufficient for prediction, but plotting four\n",
        "dense grids would distract from its essential logic. The following\n",
        "visualization therefore uses scikit-learn’s optimized\n",
        "`KNeighborsClassifier` and `DecisionBoundaryDisplay`.\n",
        "\n",
        "A pipeline standardizes the features internally, allowing the axes to\n",
        "remain in their original units."
      ],
      "id": "218e5160-d8c9-42f6-ab2c-188fa8f16867"
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {
        "fig-height": 7,
        "fig-width": 11
      },
      "outputs": [
        {
          "output_type": "display_data",
          "metadata": {},
          "data": {
            "image/png": 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hJHwges3RuLBkyZKACgPiIh8X9ohOQyFI5L5DS3Ex79xOcc2aNapgpDfDgtYV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dpc4pgaN2pYYB6smlNLCCGhJFrWB1bVfiN0H5p75vTxAq9B+xs0qK8u9M2g+/5qP3Wf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\nR9FTESZ36RW+eEMA8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kch79Sx5SchhBCiF9Ah1CeCRiLfHwZ/FBmG0d/xPUiN8PWxq31o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wgNoK+PH1PNpNEusJZI3HAgKeilb9u6jntTBFeAMqN6vneh5A0OHt8FXQyV8oY7D6CC17d1DP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\no/3UfeKOfSp/EWJz4tm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7t8mn703WVdDQn+fl0KHD8vTTIw2/332svgowGRkrIYQQP4Ua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\nourANddco6IU33//fc6pn+hu7Vroa70ZbDsR2bJli4q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          }
        }
      ],
      "source": [
        "from sklearn.inspection import DecisionBoundaryDisplay\n",
        "from sklearn.neighbors import KNeighborsClassifier\n",
        "from sklearn.pipeline import make_pipeline\n",
        "\n",
        "configurations = [\n",
        "    (1, \"uniform\"),\n",
        "    (5, \"uniform\"),\n",
        "    (25, \"uniform\"),\n",
        "    (5, \"distance\"),\n",
        "]\n",
        "classes, y_encoded = np.unique(y_train, return_inverse=True)\n",
        "\n",
        "fig, axes = plt.subplots(2, 2, figsize=(11, 7), sharex=True, sharey=True)\n",
        "for ax, (n_neighbors, weights) in zip(axes.ravel(), configurations):\n",
        "    sklearn_knn = make_pipeline(\n",
        "        StandardScaler(),\n",
        "        KNeighborsClassifier(n_neighbors=n_neighbors, weights=weights),\n",
        "    )\n",
        "    sklearn_knn.fit(X_train, y_encoded)\n",
        "    DecisionBoundaryDisplay.from_estimator(\n",
        "        sklearn_knn,\n",
        "        X_train,\n",
        "        response_method=\"predict\",\n",
        "        multiclass_colors=\"Set2\",\n",
        "        alpha=0.25,\n",
        "        ax=ax,\n",
        "    )\n",
        "\n",
        "    for label, name in enumerate(classes):\n",
        "        selected = y_encoded == label\n",
        "        ax.scatter(\n",
        "            X_train[selected, 0],\n",
        "            X_train[selected, 1],\n",
        "            color=plt.get_cmap(\"Set2\")(label),\n",
        "            edgecolor=\"black\",\n",
        "            s=20,\n",
        "            label=name,\n",
        "        )\n",
        "\n",
        "    ax.set_title(f\"k={n_neighbors}, weights='{weights}'\")\n",
        "    ax.set_xlabel(\"Bill length (mm)\")\n",
        "    ax.set_ylabel(\"Bill depth (mm)\")\n",
        "\n",
        "handles, labels = axes[0, 0].get_legend_handles_labels()\n",
        "fig.legend(handles, labels, loc=\"upper center\", ncols=len(classes))\n",
        "fig.tight_layout(rect=(0, 0, 1, 0.93))\n",
        "plt.show()"
      ],
      "id": "cell-decision-boundaries"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "With $k=1$, individual training observations control small regions,\n",
        "producing a highly irregular boundary. Increasing $k$ smooths the\n",
        "boundary because a larger neighbourhood must agree. Distance weighting\n",
        "allows nearby observations to retain greater local influence.\n",
        "\n",
        "# Regression\n",
        "\n",
        "The neighbour search does not change for regression. We replace the\n",
        "class vote with a weighted average of numerical targets:"
      ],
      "id": "21e95d9a-8095-47d0-825c-71700bd08c11"
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "metadata": {},
      "outputs": [],
      "source": [
        "def regression_prediction(targets, distances, mode=\"uniform\"):\n",
        "    weights = voting_weights(distances, mode)\n",
        "    return float(np.average(targets, weights=weights))"
      ],
      "id": "regression-aggregation"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Since the result is an average of observed neighbour targets, ordinary\n",
        "KNN regression does not extrapolate beyond their range.\n",
        "\n",
        "# Complexity and Limitations\n",
        "\n",
        "For each query, this straightforward implementation computes distances\n",
        "in $\\mathcal{O}(ND)$ and performs a complete $\\mathcal{O}(N\\log N)$\n",
        "sort. It also retains the $\\mathcal{O}(ND)$ training set in memory.\n",
        "\n",
        "Other important limitations include:\n",
        "\n",
        "- distances are sensitive to feature scaling and the selected metric;\n",
        "- neighbourhoods become less informative in high-dimensional spaces;\n",
        "- small $k$ can be sensitive to noise, whereas large $k$ can hide local\n",
        "  structure; and\n",
        "- class imbalance can dominate a neighbourhood’s vote.\n",
        "\n",
        "# Suggested Experiments\n",
        "\n",
        "1.  Compare test accuracy for several values of `n_neighbors`.\n",
        "2.  Change the four configurations in the decision-boundary figure.\n",
        "3.  Remove standardization and observe how the results change.\n",
        "4.  Replace Euclidean distance with Manhattan distance.\n",
        "5.  Create a query equal to a training example and inspect distance\n",
        "    weighting.\n",
        "6.  Compare this implementation with scikit-learn’s\n",
        "    `KNeighborsClassifier`."
      ],
      "id": "5e0841a9-45fd-44d8-a00e-4556b878a8b6"
    }
  ],
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3 (ipykernel)",
      "language": "python",
      "path": "/Users/turcotte/.virtualenvs/csi4106/share/jupyter/kernels/python3"
    }
  }
}