{
  "schema_version": "1.0",
  "document_id": "functional-pca-lecture-terracotta",
  "title": "Functional PCA 講義ノート",
  "language": "ja",
  "theme": "terracotta",
  "generated_at": "2026-09-02",
  "source": {
    "conversation_title": "functional PCA講義",
    "attached_pdf": "source/OAGmax遷延.pdf"
  },
  "blocks": [
    {
      "id": "opening",
      "type": "html",
      "heading_level": 2,
      "title": "この講義の地図",
      "content": "<p>Functional PCA（FPCA）は、時間に沿って変化する波形を、少数の共通パターンと個人ごとのスコアに分けて読む方法です。</p>"
    },
    {
      "id": "pca-fpca-bridge",
      "type": "diagram",
      "heading_level": 3,
      "title": "PCAからFPCAへ",
      "diagram_source": "flowchart LR\\n  A[PCA: vector data] --> B[PC direction]\\n  B --> C[score]\\n  D[FPCA: waveform data] --> E[PC function]\\n  E --> F[score]",
      "image": {
        "source_path": "assets/pca-fpca-bridge.png",
        "alt": "通常のPCAとFPCAを、点の雲と波形の図で対比した概念図",
        "caption": "PCAの主成分ベクトルを、波形上の主成分関数へ読み替える。"
      }
    },
    {
      "id": "bspline-assembly",
      "type": "diagram",
      "heading_level": 3,
      "title": "B-splineを視覚で理解する",
      "diagram_source": "flowchart LR\\n  A[B-spline basis] --> B[coefficients]\\n  B --> C[weighted sum]\\n  C --> D[one smooth curve]",
      "image": {
        "source_path": "assets/bspline-assembly.png",
        "prompt": "A scientific educational infographic showing overlapping local smooth B-spline basis hills, knot markers, coefficients, a weighted sum, one smooth curve, and the contrast between Gaussian infinite tails and B-spline zero outside its span.",
        "alt": "B-splineの局所的な滑らかな基底関数、ノット、係数、重み付き和、Gaussianとの違いを示す概念図",
        "caption": "B-splineは波形を作る局所的な部品。係数を掛けて足すと、滑らかな1本の曲線になる。"
      }
    },
    {
      "id": "fpca-results",
      "type": "diagram",
      "heading_level": 3,
      "title": "FPCAの結果を読む",
      "diagram_source": "flowchart LR\\n  A[Explained variance] --> B[mean / +PC / -PC]\\n  B --> C[Scores]",
      "image": {
        "source_path": "assets/fpca-results-reading.png",
        "alt": "説明分散、平均波形とプラスマイナスの主成分、スコアを並べた概念図",
        "caption": "説明分散だけでなく、波形の差と対象者のスコアを一緒に見る。"
      }
    },
    {
      "id": "fpca-reading-order",
      "type": "diagram",
      "heading_level": 3,
      "title": "結果グラフを読む順番",
      "diagram_source": "flowchart LR\\n  A[1 Raw waveforms] --> B[2 Mean waveform]\\n  B --> C[3 Explained variance]\\n  C --> D[4 PC1 function]\\n  D --> E[5 Mean ± PC]\\n  E --> F[6 Scores]\\n  F --> G[7 Reconstruction]",
      "image": {
        "source_path": "assets/fpca-results-walkthrough.png",
        "prompt": "A scientific educational infographic showing seven connected FPCA result-reading panels in order: raw waveforms, mean waveform, explained variance, PC1 function, mean plus/minus PC, score scatter plot, and reconstruction.",
        "alt": "FPCAの結果を、元波形、平均波形、説明分散、PC1関数、平均プラスマイナスPC、score散布図、再構成の7段階で読む順番を示した概念図",
        "caption": "元波形と平均を土台に、説明分散、PC関数、平均±PC、score、再構成へ順番に進む。"
      }
    },
    {
      "id": "validation",
      "type": "diagram",
      "heading_level": 3,
      "title": "妥当性評価のループ",
      "diagram_source": "flowchart LR\\n  A[FPCA fit] --> B[Leave-one-out]\\n  A --> C[Bootstrap]\\n  A --> D[Sensitivity]\\n  A --> E[Compare]\\n  B --> E\\n  C --> E\\n  D --> E\\n  E --> F{Stable pattern?}",
      "image": {
        "source_path": "assets/fpca-validation-loop.png",
        "alt": "FPCAの適合後にleave-one-out、bootstrap、sensitivityを比較し、安定性を判断するフロー図",
        "caption": "FPCAは一度計算して終わりではなく、パターンの安定性を確かめて解釈する。"
      }
    },
    {
      "id": "chat-qa",
      "type": "html",
      "heading_level": 2,
      "title": "チャットで立ち止まったところ",
      "content": "<p>元講義で実際に出てきた質問と返答を、PCAとFPCAの関係、無限次元、B-spline、固有関数の符号、score、before／after、妥当性、クラスタリングの順に再構成して収録する。</p>"
    },
    {
      "id": "quiz",
      "type": "html",
      "heading_level": 2,
      "title": "4択で、理解を確かめる",
      "content": "<p>チャットで実際に出た疑問10問と、共分散・固有値・符号反転・score・PC数・前後比較・Gram行列・再構成・研究解釈を問う深掘り10問を、回答後の理由つき4択クイズとして収録する。</p>"
    },
    {
      "id": "paper-example",
      "type": "callout",
      "variant": "info",
      "title": "添付論文の位置づけ",
      "content": "添付論文はstride×101点の歩行EMGにPCAを適用した近縁例です。論文のXᵀXの定義と中心化の記載を踏まえると、本文のFPCAの理論結果と同一視せず、波形PCAの応用例として読むのが安全です。"
    }
  ]
}