\n\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 \uba38\uc2e0\ub7ec\ub2dd \uae30\ubc95 \uc911 \ud558\ub098\uc778 LDA(Linear Discriminant Analysis)\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc54c\uace0\ub9ac\uc998 \ud2b8\ub808\uc774\ub529 \uc804\ub7b5 \uac1c\ubc1c\uc5d0 \ub300\ud55c \uc774\ud574\ub97c \ub192\uc774\uace0, sklearn \ub77c\uc774\ube0c\ub7ec\ub9ac\ub97c \uc774\uc6a9\ud55c \uad6c\ud604 \ubc29\ubc95\uc744 \uc0c1\uc138\ud788 \uc124\uba85\ud569\ub2c8\ub2e4.<\/p>\n<\/header>\n\n1. \uc11c\ub860<\/h2>\n
\uc8fc\uc2dd\uc2dc\uc7a5\uc5d0\uc11c\uc758 \uc790\ub3d9\ub9e4\ub9e4\ub294 \ub9ce\uc740 \ud22c\uc790\uc790\ub4e4\uc5d0\uac8c \ub9e4\ub825\uc801\uc778 \uc635\uc158\uc774 \ub418\uc5c8\uc73c\uba70, \uba38\uc2e0\ub7ec\ub2dd\uacfc \ub525\ub7ec\ub2dd \uae30\uc220\uc740 \uc774\ub7ec\ud55c \ud2b8\ub808\uc774\ub529\uc5d0 \ud601\uc2e0\uc744 \uac00\uc838\uc624\uace0 \uc788\uc2b5\ub2c8\ub2e4. \ubcf8 \uae00\uc5d0\uc11c\ub294 LDA\uc758 \uae30\ubcf8 \uc6d0\ub9ac\uc640 \ud568\uaed8, \uc2e4\uc81c \uae08\uc735 \ub370\uc774\ud130\uc5d0 \uc801\uc6a9\ud558\ub294 \ubc29\ubc95\uc744 \ub2e8\uacc4\uc801\uc73c\ub85c \uc124\uba85\ud569\ub2c8\ub2e4.<\/p>\n<\/section>\n\n2. LDA\ub780 \ubb34\uc5c7\uc778\uac00?<\/h2>\n
LDA\ub294 \uc8fc\ub85c \ubd84\ub958 \ubb38\uc81c\uc5d0\uc11c \uc0ac\uc6a9\ub418\ub294 \uc54c\uace0\ub9ac\uc998\uc73c\ub85c, \ud074\ub798\uc2a4 \uac04\uc758 \ubd84\ub9ac\ub97c \uadf9\ub300\ud654\ud558\uace0 \ud074\ub798\uc2a4 \ub0b4\uc758 \ubd84\uc0b0\uc744 \ucd5c\uc18c\ud654\ud558\ub294 \uae30\ubc95\uc785\ub2c8\ub2e4. \uc8fc\uc2dd \uac70\ub798\uc5d0\uc11c LDA\ub294 \uc8fc\uac00\uac00 \uc0c1\uc2b9\ud560 \uac83\uc778\uc9c0 \ud558\ub77d\ud560 \uac83\uc778\uc9c0\ub97c \uc608\uce21\ud558\ub294 \ub370 \uc720\uc6a9\ud569\ub2c8\ub2e4.<\/p>\n
\uae30\ubcf8 \uc218\ud559\uc801 \uac1c\ub150\uc740 \ub2e4\uc74c\uacfc \uac19\uc2b5\ub2c8\ub2e4:<\/p>\n
\n- \ud074\ub798\uc2a4 \ud3c9\uade0 (Mean of Class)<\/li>\n
- \uc804\uccb4 \ud3c9\uade0 (Overall Mean)<\/li>\n
- \ud074\ub798\uc2a4 \uac04 \uc0b0\ud3ec \ud589\ub82c (Between-Class Scatter Matrix)<\/li>\n
- \ud074\ub798\uc2a4 \ub0b4 \uc0b0\ud3ec \ud589\ub82c (Within-Class Scatter Matrix)<\/li>\n<\/ul>\n
LDA\uc758 \ubaa9\uc801\uc740 \ud074\ub798\uc2a4\ub97c \uad6c\ubd84\ud558\ub294 \ucd5c\uc801\uc758 \ucd95\uc744 \ucc3e\ub294 \uac83\uc785\ub2c8\ub2e4.<\/p>\n<\/section>\n\n3. LDA\uc758 \uc218\ud559\uc801 \uae30\ucd08<\/h2>\n
LDA\ub294 \ud2b9\uc815 \uc218\ud559\uc801 \uacf5\uc2dd\uc744 \uae30\ubc18\uc73c\ub85c \uc791\ub3d9\ud558\uba70, \ubd84\ud3ec\uac00 \uc815\uaddc\ubd84\ud3ec\ub97c \ub530\ub97c \ub54c \ucd5c\ub300 \uc6b0\ub3c4 \ucd94\uc815(MLE)\uc744 \uc218\ud589\ud569\ub2c8\ub2e4. \ub450 \ud074\ub798\uc2a4\uc758 \ud3c9\uade0\uc774 \ub3d9\uc77c\ud558\uace0 \uacf5\ubd84\uc0b0 \ud589\ub82c\uc774 \ub3d9\uc77c\ud558\ub2e4\ub294 \uac00\uc815\uc744 \ub530\ub985\ub2c8\ub2e4.<\/p>\n
3.1. \uc218\ud559\uc2dd<\/h3>\n
\ud074\ub798\uc2a4\ubcc4 \ud3c9\uade0\uacfc \uc804\uccb4 \ud3c9\uade0\uc744 \uacc4\uc0b0\ud558\uae30 \uc704\ud574 \ub2e4\uc74c \uacf5\uc2dd\uc744 \uc0ac\uc6a9\ud569\ub2c8\ub2e4:<\/p>\n
$$ \\mu = \\frac{1}{N} \\sum_{i=1}^{N} x_i $$<\/p>\n
$$ S_W = \\sum_{i=1}^{k} \\sum_{x \\in C_i}(x – \\mu_i)(x – \\mu_i)^T $$<\/p>\n
$$ S_B = \\sum_{i=1}^{k} N_i(\\mu_i – \\mu)(\\mu_i – \\mu)^T $$<\/p>\n<\/section>\n\n4. sklearn\uc744 \uc774\uc6a9\ud55c LDA \uad6c\ud604<\/h2>\n
\uc774\uc81c LDA\ub97c Python\uc758 sklearn \ub77c\uc774\ube0c\ub7ec\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uad6c\ud604\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \ub2e4\uc74c\uc740 \uc8fc\uc694 \ub2e8\uacc4\uc785\ub2c8\ub2e4:<\/p>\n
\n- \ub370\uc774\ud130 \uc218\uc9d1<\/li>\n
- \ub370\uc774\ud130 \uc804\ucc98\ub9ac<\/li>\n
- \ud2b9\uc131 \uc120\ud0dd \ubc0f LDA \uc801\uc6a9<\/li>\n
- \ubaa8\ub378 \ud3c9\uac00<\/li>\n<\/ol>\n<\/section>\n\n
4.1. \ub370\uc774\ud130 \uc218\uc9d1<\/h3>\n
Python\uc758 pandas \ub77c\uc774\ube0c\ub7ec\ub9ac\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc5ed\uc0ac\uc801\uc778 \uc8fc\uac00 \ub370\uc774\ud130\uc14b\uc744 \uc218\uc9d1\ud569\ub2c8\ub2e4. \ub2e4\uc74c\uc758 \ucf54\ub4dc snippet\uc740 Yahoo Finance\ub85c\ubd80\ud130 \ub370\uc774\ud130\ub97c \ub2e4\uc6b4\ub85c\ub4dc\ud558\ub294 \ubc29\ubc95\uc744 \ubcf4\uc5ec\uc90d\ub2c8\ub2e4:<\/p>\n
\n\nimport pandas as pd\nimport yfinance as yf\n\n# \ub370\uc774\ud130 \ub2e4\uc6b4\ub85c\ub4dc\ndata = yf.download('AAPL', start='2020-01-01', end='2023-01-01')\ndata = data[['Open', 'High', 'Low', 'Close', 'Volume']]\ndata.head()\n<\/code>\n <\/pre>\n\uc774 \ub370\uc774\ud130\ub97c \uae30\ubc18\uc73c\ub85c LDA\ub97c \uc218\ud589\ud558\uae30 \uc704\ud55c \ud2b9\uc815 \ud2b9\uc131\uc744 \uc0dd\uc131\ud574\uc57c \ud569\ub2c8\ub2e4.<\/p>\n<\/section>\n\n4.2. \ub370\uc774\ud130 \uc804\ucc98\ub9ac<\/h3>\n
\ub370\uc774\ud130\ub97c \uc804\ucc98\ub9ac\ud558\uc5ec \ud2b9\uc131\uc744 \ub9cc\ub4e4\uace0, \ud0c0\uac9f \ubcc0\uc218\ub97c \uc0dd\uc131\ud569\ub2c8\ub2e4. \ub2e4\uc74c\uc758 \ucf54\ub4dc\ub294 \uac00\uaca9 \uc0c1\uc2b9\uc744 \ud0c0\uac9f\uc73c\ub85c \uc124\uc815\ud558\ub294 \uc608\uc2dc\uc785\ub2c8\ub2e4:<\/p>\n
\n\n# \ud0c0\uac9f \ubcc0\uc218 \uc0dd\uc131: \ub2e4\uc74c\ub0a0 \uac00\uaca9 \uc0c1\uc2b9 \uc5ec\ubd80\ndata['Target'] = (data['Close'].shift(-1) > data['Close']).astype(int)\n\n# \uacb0\uce21\uac12 \uc81c\uac70\ndata.dropna(inplace=True)\n<\/code>\n <\/pre>\n<\/section>\n\n4.3. \ud2b9\uc131 \uc120\ud0dd \ubc0f LDA \uc801\uc6a9<\/h3>\n
\uc774\uc81c \ud2b9\uc131 \uc120\ud0dd\uc744 \uc704\ud574 LDA\ub97c \uc801\uc6a9\ud560 \uc900\ube44\uac00 \ub418\uc5c8\uc2b5\ub2c8\ub2e4. LDA \ubaa8\ub378\uc744 \ud559\uc2b5\uc2dc\ud0a4\uae30 \uc704\ud574 X\uc640 y\ub97c \uc900\ube44\ud569\ub2c8\ub2e4:<\/p>\n
\n\nfrom sklearn.discriminant_analysis import LinearDiscriminantAnalysis\n\n# \ud2b9\uc131(X)\uacfc \ud0c0\uac9f(y) \ubd84\ub9ac\nX = data[['Open', 'High', 'Low', 'Close', 'Volume']]\ny = data['Target']\n\n# LDA \ubaa8\ub378 \ucd08\uae30\ud654 \ubc0f \ud559\uc2b5\nlda = LinearDiscriminantAnalysis()\nlda.fit(X, y)\n<\/code>\n <\/pre>\n<\/section>\n\n4.4. \ubaa8\ub378 \ud3c9\uac00<\/h3>\n
\ubaa8\ub378\uc774 \ud559\uc2b5\ub418\uc5c8\uc73c\ubbc0\ub85c, \uc774\uc81c \ud14c\uc2a4\ud2b8 \ub370\uc774\ud130\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc131\ub2a5\uc744 \ud3c9\uac00\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n
\n\nfrom sklearn.model_selection import train_test_split\nfrom sklearn.metrics import accuracy_score\n\n# Train\/Test split\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n\n# \ubaa8\ub378 \ud559\uc2b5\nlda.fit(X_train, y_train)\n\n# \uc608\uce21\ny_pred = lda.predict(X_test)\n\n# \uc815\ud655\ub3c4 \ud3c9\uac00\naccuracy = accuracy_score(y_test, y_pred)\nprint(f'\uc815\ud655\ub3c4: {accuracy:.2f}')\n<\/code>\n <\/pre>\n<\/section>\n\n5. \uacb0\uacfc \ud574\uc11d <\/p>\n\n
LDA \ubaa8\ub378\uc5d0\uc11c \uc0dd\uc131\ub41c \ud074\ub798\uc2a4 \uad6c\ubd84\uc744 \ubd84\uc11d\ud558\uace0, \uacb0\uacfc\ub97c \ud574\uc11d\ud558\ub294 \ubc29\ubc95\uc5d0 \ub300\ud574 \uc790\uc138\ud788 \uc124\uba85\ud569\ub2c8\ub2e4. \uc815\ud655\ub3c4 \uc678\uc5d0\ub3c4 \ud63c\ub3d9 \ud589\ub82c, ROC \ucee4\ube0c \ub4f1\uc744 \uc0ac\uc6a9\ud558\uc5ec \ubaa8\ub378 \uc131\ub2a5\uc744 \ud3c9\uac00\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n<\/h2>\n<\/h2>\n<\/section>\n\n6. \uacb0\ub860<\/h2>\n
\ubcf8 \uac15\uc88c\uc5d0\uc11c\ub294 LDA\ub97c \uc0ac\uc6a9\ud55c \uc54c\uace0\ub9ac\uc998 \ud2b8\ub808\uc774\ub529\uc758 \uae30\ubcf8 \uc6d0\ub9ac\uc640 sklearn\uc744 \ud1b5\ud55c \uad6c\uccb4\uc801\uc778 \uad6c\ud604 \ubc29\ubc95\uc744 \uc54c\uc544\ubcf4\uc558\uc2b5\ub2c8\ub2e4. \uc8fc\uac00 \uc608\uce21\uc5d0 \ud65c\uc6a9 \uac00\ub2a5\ud55c \ub2e4\ub978 \uba38\uc2e0\ub7ec\ub2dd \uae30\ubc95\ub3c4 \ub2e4\uc591\ud55c \ubc29\ubc95\uc73c\ub85c \ud65c\uc6a9\ud560 \uc218 \uc788\uc73c\ub2c8 \uc774\uc5b4\uc9c0\ub294 \ud559\uc2b5\ub3c4 \ucd94\ucc9c\ud569\ub2c8\ub2e4.<\/p>\n<\/section>\n