{
  "nbformat": 4,
  "nbformat_minor": 5,
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "name": "python",
      "version": "3.11"
    },
    "colab": {
      "name": "week-06-exercise.ipynb"
    },
    "course_exercise": {
      "id": "W06",
      "week": "06",
      "hour": null,
      "date": "2026-10-12",
      "title": "PCA, clusters, and what geometry can establish",
      "minutes": 35,
      "optional": false,
      "worksheet": "notes/exercises/week-06-exercise.html",
      "notebook": "notebooks/exercises/week-06-exercise.ipynb",
      "colab": "https://colab.research.google.com/github/CHjonnyYu/MLES-Fall-2026/blob/main/notebooks/exercises/week-06-exercise.ipynb",
      "guided_notebook": "notebooks/week-06-practice.ipynb",
      "execution_status": "New exercise extension not executed in this authoring run"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "# W06 Exercise: PCA, clusters, and what geometry can establish\n\nMachine Learning in Engineering Science | NCKU / LAiMM | Fall 2026\n\n**Date:** 2026-10-12. **Exercise time:** 35 minutes within the class/practice allocation, not extra time after class.\n\n**Classroom formative practice. No new weekly graded submission is created.**\n\n## How to work independently\n1. In Colab, save a copy to your Drive and use a CPU runtime. In Jupyter, open this notebook and select a Python kernel.\n2. Run the complete worked walkthrough below from top to bottom. Read every Markdown checkpoint; the walkthrough is included so no previous notebook state is needed.\n3. At the Independent Exercise section, write each prediction in the response cell before running its experiment.\n4. Run the starter experiment, make the requested controlled change, and record the actual result. Edit only the declared factor; preserve split rules and preprocessing.\n5. Explain one mechanism and one limitation. Export the evidence JSON and discuss it with a partner.\n\nThe core exercises need no paid API, private dataset, or GPU. The agent units use clearly labeled offline simulators, not real LLM calls.\n\n**Reproducibility boundary:** the original guided notebooks were previously executed; the new extension cells have not yet been execution-tested in this revision. Report unexpected behavior rather than claiming a check passed.\n"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "# Week 06: Unsupervised learning and representation\n\nMachine Learning in Engineering Science | NCKU + LAiMM | Fall 2026\n\n**Purpose:** a fully worked, self-paced in-class practice with an optional extension. Weeks 11 and 18 are optional examination-readiness materials. These notebooks do not create weekly graded assignments.\n\n**Before running:** choose a Python 3 kernel in Jupyter or a CPU runtime in Colab. Run every cell from top to bottom with Shift+Enter. Setup installs missing free packages. No API key or external dataset download is required.\n\n**Learning target:** complete the calculation, inspect intermediate values, and explain why the protocol supports a limited claim.\n\n**Time:** about 25-45 minutes including reading, prediction, execution, and explain-back.\n",
      "id": "cell-000"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "## 1. Set up and record the environment\n\nKeep the seed fixed for the first run. Record actual outputs and package versions rather than copying a claimed performance number.\n",
      "id": "cell-001"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "metadata": {},
      "source": "import sys, subprocess, importlib.util, platform, json, random, hashlib\nfrom pathlib import Path\nrequired = {\"numpy\": \"numpy\", \"matplotlib\": \"matplotlib\", \"sklearn\": \"scikit-learn\"}\nmissing = [package for module, package in required.items() if importlib.util.find_spec(module) is None]\nif missing:\n    subprocess.check_call([sys.executable, \"-m\", \"pip\", \"install\", *missing])\nimport numpy as np\nimport matplotlib.pyplot as plt\nSEED = 2026\nrandom.seed(SEED)\nnp.random.seed(SEED)\nrng = np.random.default_rng(SEED)\nARTIFACTS = Path(\"artifacts\")\nARTIFACTS.mkdir(exist_ok=True)\nprint(\"Python:\", platform.python_version(), \"NumPy:\", np.__version__, \"Seed:\", SEED)\n",
      "id": "cell-002"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "**Checkpoint.** The environment cell must finish before any analysis cell. Restart and run all if a variable is missing.\n",
      "id": "cell-003"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "## 2. Generate unlabeled structure\n\nThe model receives only X. Generating labels are retained solely for optional teaching comparisons and never passed into fitting.\n",
      "id": "cell-004"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "metadata": {},
      "source": "from sklearn.datasets import make_blobs\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.preprocessing import StandardScaler\nfrom sklearn.decomposition import PCA\nfrom sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score\nX,hidden_labels=make_blobs(n_samples=360,n_features=5,centers=3,cluster_std=1.4,random_state=SEED)\nXtr,Xte=train_test_split(X,test_size=.25,random_state=SEED)\nscaler=StandardScaler().fit(Xtr)\nZtr,Zte=scaler.transform(Xtr),scaler.transform(Xte)\n",
      "id": "cell-005"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "**Checkpoint.** No target is available to the clustering algorithm. Preprocessing still learns statistics and must fit training only.\n",
      "id": "cell-006"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "## 3. Fit PCA and inspect retained variation\n\nPCA chooses orthogonal directions of maximum training variance. Two components simplify plotting but may discard useful information.\n",
      "id": "cell-007"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "metadata": {},
      "source": "pca=PCA(n_components=2).fit(Ztr)\nP=pca.transform(Zte)\nprint(\"Explained variance ratios:\",pca.explained_variance_ratio_)\nplt.scatter(P[:,0],P[:,1]); plt.xlabel(\"PC1\"); plt.ylabel(\"PC2\"); plt.show()\n",
      "id": "cell-008"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "**Checkpoint.** Explained variance is not prediction accuracy or a guarantee of physically meaningful factors.\n",
      "id": "cell-009"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "## 4. Cluster in the original standardized space\n\nK-means finds geometric groups under a chosen distance and k. Labels are arbitrary IDs; cluster 0 is not an engineering diagnosis.\n",
      "id": "cell-010"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "metadata": {},
      "source": "kmeans=KMeans(n_clusters=3,n_init=10,random_state=SEED).fit(Ztr)\ngroups=kmeans.predict(Zte)\nplt.scatter(P[:,0],P[:,1],c=groups,cmap=\"viridis\"); plt.xlabel(\"PC1\"); plt.ylabel(\"PC2\"); plt.show()\nsummary={\"test_silhouette\":float(silhouette_score(Zte,groups)),\n         \"retained_training_variance\":float(pca.explained_variance_ratio_.sum())}\nprint(summary)\n",
      "id": "cell-011"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "**Checkpoint.** A high silhouette supports separation in this representation, not a causal or semantic interpretation of clusters.\n",
      "id": "cell-012"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "## 6. Preserve your evidence\n\nExport a JSON record with a seed, package version, and measured result. Download the artifacts directory before leaving Colab; runtime storage is temporary.\n",
      "id": "cell-013"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "outputs": [],
      "metadata": {},
      "source": "record={\"week\":6,\"seed\":SEED,\"numpy\":np.__version__,\"python\":platform.python_version(),\"result\":summary}\n(ARTIFACTS/\"week-06-evidence.json\").write_text(json.dumps(record,indent=2))\nprint(json.dumps(record,indent=2))\n",
      "id": "cell-014"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "**Checkpoint.** The evidence file must match the result you actually obtained. A saved screenshot alone does not permit rerunning the calculation.\n",
      "id": "cell-015"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "## 7. Try one change and explain it\n1. Predict the effect of one change before editing code. Change one parameter, input, or boundary condition only.\n2. Rerun all cells in a fresh kernel. Keep the original evidence record and compare the observed difference.\n3. Explain the result using the mechanism, not just the final number.\n4. Name one assumption that limits the claim, and a new test that could challenge it.\n\n**Troubleshooting:** if installation fails, restore network access; if a variable is undefined, run earlier cells; if your output differs, compare package versions, seed, and data construction. Do not repeatedly edit code until a preferred score appears.\n\n**Completion criterion:** one executed notebook, one evidence JSON, and a brief claim/evidence/limitation statement.\n\n### Reference documentation\n- [NumPy user guide](https://numpy.org/doc/stable/user/)\n- [scikit-learn user guide](https://scikit-learn.org/stable/user_guide.html)\n- [Course repository](https://github.com/CHjonnyYu/MLES-Fall-2026)\n",
      "id": "cell-016"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "## Independent Exercise: W06\n\nComplete the three tasks below after the walkthrough. The starter cells produce observations, not your written interpretation. Fill the response fields in the next cell. Save separate records for the original run and any controlled change."
    },
    {
      "cell_type": "code",
      "metadata": {},
      "execution_count": null,
      "outputs": [],
      "source": "exercise_id=\"W06\"\nobservations={}\nresponses={\n    'task1_prediction':'', 'task1_explanation':'',\n    'task2_prediction':'', 'task2_explanation':'',\n    'task3_prediction':'', 'task3_explanation':'',\n    'controlled_change':'', 'limitation':'', 'ai_use_and_checks':''\n}\n# Fill these strings before and after each experiment. Use 'none' if no AI assistance was used.\nprint('Exercise record initialized:', exercise_id)"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "### Task 1: Read retained variance correctly\n\nRun the PCA part of the worked notebook. Explain why two explained-variance ratios are not classification accuracies.\n\n**Steps**\n1. Write your prediction in `responses['task1_prediction']` before running.\n2. Run the starter cell; read every printed quantity and retain the observation.\n3. Make the controlled comparison requested above. Record its configuration in `responses['controlled_change']`.\n4. Write a mechanism-based explanation in `responses['task1_explanation']`; do not merely repeat a score.\n\n**Checkpoint:** The ratios describe variation retained by this fitted representation. They do not supply semantic or causal labels."
    },
    {
      "cell_type": "code",
      "metadata": {},
      "execution_count": null,
      "outputs": [],
      "source": "observations['task1']={'explained_variance_ratio':pca.explained_variance_ratio_.tolist(),'retained_fraction':float(pca.explained_variance_ratio_.sum())}\nprint(observations['task1'])"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "### Task 2: Vary the cluster count\n\nFit k=2,3,4 using training features only, and inspect test-space silhouette scores. Treat this as exploratory representation analysis, not supervised class recovery.\n\n**Steps**\n1. Write your prediction in `responses['task2_prediction']` before running.\n2. Run the starter cell; read every printed quantity and retain the observation.\n3. Make the controlled comparison requested above. Record its configuration in `responses['controlled_change']`.\n4. Write a mechanism-based explanation in `responses['task2_explanation']`; do not merely repeat a score.\n\n**Checkpoint:** Report actual scores. A larger silhouette is evidence about separation in this representation, not proof of meaningful physical categories."
    },
    {
      "cell_type": "code",
      "metadata": {},
      "execution_count": null,
      "outputs": [],
      "source": "from sklearn.cluster import KMeans\nfrom sklearn.metrics import silhouette_score\nobservations['task2']=[]\nfor k_demo in [2,3,4]:\n    fitted=KMeans(n_clusters=k_demo,n_init=10,random_state=2026).fit(Ztr)\n    assigned=fitted.predict(Zte)\n    observations['task2'].append({'k':k_demo,'silhouette':float(silhouette_score(Zte,assigned))})\nprint(observations['task2'])"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "### Task 3: Rename clusters without changing membership\n\nPermute the cluster IDs below. Compare pairwise co-membership before and after the renaming.\n\n**Steps**\n1. Write your prediction in `responses['task3_prediction']` before running.\n2. Run the starter cell; read every printed quantity and retain the observation.\n3. Make the controlled comparison requested above. Record its configuration in `responses['controlled_change']`.\n4. Write a mechanism-based explanation in `responses['task3_explanation']`; do not merely repeat a score.\n\n**Checkpoint:** Co-membership is unchanged. Cluster numbers are identifiers rather than ordered physical quantities."
    },
    {
      "cell_type": "code",
      "metadata": {},
      "execution_count": null,
      "outputs": [],
      "source": "before=np.array([0,0,1,2,1,2]); after=np.array([2,2,0,1,0,1])\nobservations['task3']={'same_membership':bool(np.array_equal(before[:,None]==before[None,:],after[:,None]==after[None,:]))}\nprint(observations['task3'])"
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": "### Finish: preserve and explain\n\nFill all response strings, then run the export cell. A draft file is intentionally labeled incomplete; a complete response record is not automatically a scientifically correct result. Download the JSON before the Colab session ends. Share it with a partner for explain-back, not as an additional weekly submission.\n\n**Exit questions:** What changed? Which observation supports your explanation? What does this experiment not establish?"
    },
    {
      "cell_type": "code",
      "metadata": {},
      "execution_count": null,
      "outputs": [],
      "source": "missing_responses=[key for key,value in responses.items() if not str(value).strip()]\nexercise_record={'exercise':exercise_id,'status':'draft' if missing_responses else 'ready for peer discussion','responses':responses,'observations':observations,'missing_responses':missing_responses,'environment':{'python':platform.python_version(),'numpy':np.__version__},'data_scope':'course-provided or synthetic teaching data'}\nexercise_folder=Path('artifacts')/'exercises'; exercise_folder.mkdir(parents=True,exist_ok=True)\nexercise_path=exercise_folder/(exercise_id+'-evidence.json')\nexercise_path.write_text(json.dumps(exercise_record,indent=2,default=lambda value:value.tolist() if hasattr(value,'tolist') else str(value)))\nprint('Saved:',exercise_path)\nprint('Status:',exercise_record['status'])\nprint('Fields still to complete:',missing_responses)"
    }
  ]
}