nagoya institute of technology - matsuzoe...
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![Page 1: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/1.jpg)
Nagoya
Institute of
Technology
![Page 2: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/2.jpg)
Nagoya Institute of Technology
発表構成
![Page 3: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/3.jpg)
Nagoya Institute of Technology
クラス分類問題 (例: 文字認識、音声認識)
音声時系列信号
文字
「0」, 「1」, ..., 「9」
単語 (cf. カーナビ)
「大阪市立大学」
画像(画素値)
![Page 4: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/4.jpg)
Nagoya Institute of Technology
クラス分類問題 (例: 遺伝子病理診断)
![Page 5: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/5.jpg)
Nagoya Institute of Technology
(2クラス)分類問題の定式化
![Page 6: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/6.jpg)
Nagoya Institute of Technology
モデルベース分類器/事例ベース分類器
![Page 7: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/7.jpg)
Nagoya Institute of Technology
(例) サポートベクトルマシン (SVM)
![Page 8: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/8.jpg)
Nagoya Institute of Technology
最近傍分類器 (nearest neighbor classifier)
![Page 9: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/9.jpg)
Nagoya Institute of Technology
分類器の特徴選択(変数選択)
![Page 10: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/10.jpg)
Nagoya Institute of Technology
特徴選択アルゴリズムのアプローチ
![Page 11: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/11.jpg)
Nagoya Institute of Technology
Filter Approach
expression level highlow
健常者 癌患者
10000genes
p1p2p3
p10000
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Nagoya Institute of Technology
Wrapper Approach
step 1
gene 1
gene 2
gene 3
gene 6800
gene 6
step 2
gene 6
gene 6
gene 6
gene 6
gene 6
gene 1
gene 2
gene 3
gene 6800
gene 9
step 3
gene 6
gene 6
gene 6
gene 6
gene 6
gene 9
gene 9
gene 9
gene 9
gene 9
gene 1
gene 2
gene 3
gene 6800
gene 321
gene 6 gene 9 gene 321
![Page 13: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/13.jpg)
Nagoya Institute of Technology
正則化(回帰問題)
![Page 14: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/14.jpg)
Nagoya Institute of Technology
正則化パス(回帰問題)
![Page 15: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/15.jpg)
Nagoya Institute of Technology
正則化パス(分類問題)
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Nagoya Institute of Technology
研究目的と発表構成
![Page 17: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/17.jpg)
Nagoya Institute of Technology
最近傍分類器と距離尺度
![Page 18: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/18.jpg)
Nagoya Institute of Technology
k-最近傍分類の損失関数
![Page 19: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/19.jpg)
Nagoya Institute of Technology
k-最近傍分類の損失関数
![Page 20: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/20.jpg)
Nagoya Institute of Technology
k-最近傍分類の損失関数
![Page 21: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/21.jpg)
Nagoya Institute of Technology
k-最近傍分類の損失関数
![Page 22: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/22.jpg)
Nagoya Institute of Technology
k-最近傍分類器特徴選択のための最適化問題
![Page 23: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/23.jpg)
Nagoya Institute of Technology
最適化問題の整理
![Page 24: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/24.jpg)
Nagoya Institute of Technology
標的近傍不変の仮定と凸計画問題
![Page 25: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/25.jpg)
Nagoya Institute of Technology
アクティブ集合
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Nagoya Institute of Technology
最適性条件
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Nagoya Institute of Technology
最適解の区分線形性
![Page 28: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/28.jpg)
Nagoya Institute of Technology
区分線形パスの例(人工データ n = 40, m = 6)
![Page 29: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/29.jpg)
Nagoya Institute of Technology
区分線形パスの例 (拡大図)
![Page 30: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/30.jpg)
Nagoya Institute of Technology
変化点の検出
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Nagoya Institute of Technology
標的近傍の変化
![Page 32: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/32.jpg)
Nagoya Institute of Technology
標的近傍不一致数の推移
![Page 33: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/33.jpg)
Nagoya Institute of Technology
偽の学習誤差 vs. 真の学習誤差
![Page 34: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/34.jpg)
Nagoya Institute of Technology
標的近傍変化の検出
![Page 35: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/35.jpg)
Nagoya Institute of Technology
標的近傍の変化点
![Page 36: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/36.jpg)
Nagoya Institute of Technology
標的近傍の変化点
![Page 37: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/37.jpg)
Nagoya Institute of Technology
標的近傍変化における演算
![Page 38: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/38.jpg)
Nagoya Institute of Technology
Primal Active-Set QP
![Page 39: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/39.jpg)
Nagoya Institute of Technology
アルゴリズムのイメージ
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Nagoya Institute of Technology
アルゴリズムのイメージ
![Page 41: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/41.jpg)
Nagoya Institute of Technology
アルゴリズムのイメージ
![Page 42: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/42.jpg)
Nagoya Institute of Technology
アルゴリズムのイメージ
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Nagoya Institute of Technology
偽の学習誤差 vs. 真の学習誤差
![Page 44: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/44.jpg)
Nagoya Institute of Technology
Discussion (1)
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Nagoya Institute of Technology
Conditional Optimal weights and T.N.
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Nagoya Institute of Technology
Discussion (2)
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Nagoya Institute of Technology
距離学習(Metric Learning)との関連
![Page 48: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/48.jpg)
Nagoya Institute of Technology
従来のアプローチ (1)
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Nagoya Institute of Technology
従来のアプローチ (2)
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Nagoya Institute of Technology
従来のアプローチ (3)
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Nagoya Institute of Technology
マイクロアレイデータへの適用
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Nagoya Institute of Technology
マイクロアレイデータへの適用(学習誤差)
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Nagoya Institute of Technology
マイクロアレイデータへの適用(評価誤差)
![Page 54: Nagoya Institute of Technology - Matsuzoe …matsuzoe.web.nitech.ac.jp/infogeo/OCAMI2010/takeuchi.pdfNagoya Institute of Technology k-最近傍分類器特徴選択のための最適化問題](https://reader030.vdocuments.mx/reader030/viewer/2022040622/5d3425e888c9933c738b9fe1/html5/thumbnails/54.jpg)
Nagoya Institute of Technology
最後に
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Nagoya Institute of Technology
謝辞