\uc8fc\uc131\ubd84 \ubd84\uc11d(Principal Component Analysis, PCA)\uc740 \ub370\uc774\ud130\uc758 \ucc28\uc6d0\uc744 \ucd95\uc18c\ud558\ub294 \ub300\ud45c\uc801\uc778 \uae30\ubc95\uc73c\ub85c,
\n \uc8fc\ub85c \uace0\ucc28\uc6d0 \ub370\uc774\ud130 \ubd84\uc11d, \ub370\uc774\ud130 \uc2dc\uac01\ud654, \uc7a1\uc74c \uc81c\uac70, \ud2b9\uc9d5 \ucd94\ucd9c \ub4f1\uc758 \ubaa9\uc801\uc73c\ub85c \uc0ac\uc6a9\ub429\ub2c8\ub2e4.
\n \ub525\ub7ec\ub2dd \ubc0f \uba38\uc2e0\ub7ec\ub2dd \ubd84\uc57c\uc5d0\uc11c\ub3c4 PCA\ub294 \ub370\uc774\ud130 \uc804\ucc98\ub9ac \ubc0f \ubd84\uc11d \ub2e8\uacc4\uc5d0\uc11c \ub9e4\uc6b0 \uc911\uc694\ud55c \uc5ed\ud560\uc744 \ud569\ub2c8\ub2e4.<\/p>\n
PCA\ub294 \ub300\uaddc\ubaa8 \ub370\uc774\ud130 \uc138\ud2b8\ub97c \ucc98\ub9ac\ud560 \ub54c \uc720\uc6a9\ud55c \ub3c4\uad6c\ub85c, \ub2e4\uc74c\uacfc \uac19\uc740 \ubaa9\uc801\uc744 \uac00\uc9c0\uace0 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n
PCA\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \uacfc\uc815\uc73c\ub85c \uc9c4\ud589\ub429\ub2c8\ub2e4:<\/p>\n
\uc774\uc81c PCA\ub97c \ud30c\uc774\ud1a0\uce58(Pytorch)\ub97c \uc774\uc6a9\ud558\uc5ec \uad6c\ud604\ud574\ubcf4\uaca0\uc2b5\ub2c8\ub2e4. \uc544\ub798\uc758 \ucf54\ub4dc\ub294 PCA \uc54c\uace0\ub9ac\uc998\uc744 \uc218\ub3d9\uc73c\ub85c \uad6c\ud604\ud558\uace0,
\n \uc774\ub97c \uc774\uc6a9\ud574 \ub370\uc774\ud130\ub97c \ubcc0\ud658\ud558\ub294 \ubc29\ubc95\uc744 \ubcf4\uc5ec\uc90d\ub2c8\ub2e4.<\/p>\n
import numpy as np\nimport matplotlib.pyplot as plt\n\n# \ub79c\ub364 \ub370\uc774\ud130 \uc0dd\uc131\nnp.random.seed(0)\nmean = [0, 0]\ncov = [[1, 0.8], [0.8, 1]] # \uacf5\ubd84\uc0b0 \ud589\ub82c\ndata = np.random.multivariate_normal(mean, cov, 100)\n\n# \ub370\uc774\ud130 \uc2dc\uac01\ud654\nplt.scatter(data[:, 0], data[:, 1])\nplt.title('\uc6d0\ubcf8 \ub370\uc774\ud130')\nplt.xlabel('X1')\nplt.ylabel('X2')\nplt.axis('equal')\nplt.grid()\nplt.show()<\/code><\/pre>\n3.2. PCA \uad6c\ud604<\/h3>\nimport torch\n\ndef pca_manual(data, num_components=1):\n # 1. \ub370\uc774\ud130 \uc815\uaddc\ud654\n data_mean = data.mean(dim=0)\n normalized_data = data - data_mean\n\n # 2. \uacf5\ubd84\uc0b0 \ud589\ub82c \uacc4\uc0b0\n covariance_matrix = torch.mm(normalized_data.t(), normalized_data) \/ (normalized_data.size(0) - 1)\n\n # 3. \uace0\uc720\uac12 \ubd84\ud574\n eigenvalues, eigenvectors = torch.eig(covariance_matrix, eigenvectors=True)\n\n # 4. \uace0\uc720\uac12\uc744 \uae30\uc900\uc73c\ub85c \uc815\ub82c\n sorted_indices = torch.argsort(eigenvalues[:, 0], descending=True)\n selected_indices = sorted_indices[:num_components]\n\n # 5. \uc8fc\uc131\ubd84 \uc120\ud0dd\n principal_components = eigenvectors[:, selected_indices]\n\n # 6. \ub370\uc774\ud130 \ubcc0\ud658\n transformed_data = torch.mm(normalized_data, principal_components)\n \n return transformed_data\n\n# \ub370\uc774\ud130 \ud150\uc11c\ub85c \ubcc0\ud658\ndata_tensor = torch.tensor(data, dtype=torch.float32)\n\n# PCA \uc801\uc6a9\ntransformed_data = pca_manual(data_tensor, num_components=1)\n\n# \ubcc0\ud658\ub41c \ub370\uc774\ud130 \uc2dc\uac01\ud654\nplt.scatter(transformed_data.numpy(), np.zeros_like(transformed_data.numpy()), alpha=0.5)\nplt.title('PCA \ubcc0\ud658\ub41c \ub370\uc774\ud130')\nplt.xlabel('\uc8fc\uc131\ubd84 1')\nplt.axis('equal')\nplt.grid()\nplt.show()<\/code><\/pre>\n4. PCA\uc758 \ud65c\uc6a9 \uc0ac\ub840<\/h2>\n
PCA\ub294 \ub2e4\uc591\ud55c \ubd84\uc57c\uc5d0\uc11c \ud65c\uc6a9\ub418\uace0 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
\n- \uc774\ubbf8\uc9c0 \uc555\ucd95:<\/strong> \uace0\ud574\uc0c1\ub3c4 \uc774\ubbf8\uc9c0\uc758 \ud53d\uc140 \ub370\uc774\ud130\ub97c \uc904\uc774\uae30 \uc704\ud574 PCA\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc774\ubbf8\uc9c0 \ud488\uc9c8 \uc190\uc2e4\uc744 \ucd5c\uc18c\ud654\ud558\uba74\uc11c \uacf5\uac04\uc744 \uc808\uc57d\ud569\ub2c8\ub2e4.<\/li>\n
- \uc720\uc804\uc790 \ub370\uc774\ud130 \ubd84\uc11d:<\/strong> \uc0dd\ubb3c\ud559\uc801 \ub370\uc774\ud130\uc758 \ucc28\uc6d0\uc744 \ucd95\uc18c\ud558\uc5ec \ub370\uc774\ud130 \ubd84\uc11d \ubc0f \uc2dc\uac01\ud654\ub97c \uc6a9\uc774\ud558\uac8c \ub9cc\ub4ed\ub2c8\ub2e4.<\/li>\n
- \uc790\uc5f0\uc5b4 \ucc98\ub9ac:<\/strong> \ub2e8\uc5b4 \uc784\ubca0\ub529\uc744 \ucc28\uc6d0 \ucd95\uc18c\ud558\uc5ec \ucef4\ud4e8\ud130\uac00 \ub2e8\uc5b4 \uac04\uc758 \uc720\uc0ac\uc131\uc744 \uc774\ud574\ud558\ub294 \ub370 \ub3c4\uc6c0\uc744 \uc90d\ub2c8\ub2e4.<\/li>\n<\/ul>\n
5. PCA\ub97c \uc0ac\uc6a9\ud55c \ub525\ub7ec\ub2dd \uc804\ucc98\ub9ac<\/h2>\n
\ub525\ub7ec\ub2dd\uc5d0\uc11c PCA\ub294 \uc885\uc885 \ub370\uc774\ud130 \uc804\ucc98\ub9ac \ub2e8\uacc4\uc5d0\uc11c \uc0ac\uc6a9\ub429\ub2c8\ub2e4. \ub370\uc774\ud130\uc758 \ucc28\uc6d0\uc744 \uc904\uc784\uc73c\ub85c\uc368
\n \ubaa8\ub378 \ud559\uc2b5\uc758 \ud6a8\uc728\uc131\uc744 \ub192\uc774\uace0, \uc624\ubc84\ud53c\ud305\uc744 \ubc29\uc9c0\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc608\ub97c \ub4e4\uc5b4,
\n \uc774\ubbf8\uc9c0 \ub370\uc774\ud130\ub97c \ucc98\ub9ac\ud560 \ub54c PCA\ub97c \uc0ac\uc6a9\ud558\uc5ec \uc785\ub825 \uc774\ubbf8\uc9c0\uc758 \ucc28\uc6d0\uc744 \uc904\uc774\uace0,
\n \uc8fc\uc694 \ud2b9\uc9d5\ub9cc \ubaa8\ub378\uc5d0 \uc81c\uacf5\ud560 \uc218 \uc788\uc2b5\ub2c8\ub2e4. \uc774\ub97c \ud1b5\ud574 \uacc4\uc0b0 \ube44\uc6a9\uc744 \uc904\uc774\uace0, \ubaa8\ub378\uc758 \ud559\uc2b5 \uc18d\ub3c4\ub97c \ud5a5\uc0c1\uc2dc\ud0ac \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/p>\n
6. PCA\uc758 \ud55c\uacc4<\/h2>\n
PCA\ub294 \uac15\ub825\ud55c \uae30\ubc95\uc774\uc9c0\ub9cc \uba87 \uac00\uc9c0 \ud55c\uacc4\uac00 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n
\n- \uc120\ud615\uc131 \uac00\uc815:<\/strong> PCA\ub294 \ub370\uc774\ud130\uac00 \uc120\ud615\uc801\uc73c\ub85c \ubd84\ud3ec\ub418\uc5b4 \uc788\uc744 \ub54c \uac00\uc7a5 \ud6a8\uacfc\uc801\uc785\ub2c8\ub2e4. \ube44\uc120\ud615 \ub370\uc774\ud130\uc5d0 \ub300\ud574\uc11c\ub294 \ucda9\ubd84\ud788 \ud6a8\uacfc\uc801\uc774\uc9c0 \uc54a\uc744 \uc218 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n
- \uacf5\uac04\uc758 \ud574\uc11d:<\/strong> PCA\ub85c \ucd95\uc18c\ud55c \ucc28\uc6d0\uc744 \ud574\uc11d\ud558\ub294 \uac83\uc774 \uc5b4\ub824\uc6b8 \uc218 \uc788\uc73c\uba70, \uc8fc\uc131\ubd84\uc774 \uc2e4\uc81c \ubb38\uc81c\uc640 \uad00\ub828\uc774 \uc5c6\uc744 \uc218\ub3c4 \uc788\uc2b5\ub2c8\ub2e4.<\/li>\n<\/ul>\n
7. \ub300\uccb4 \uae30\ubc95<\/h2>\n
PCA\uc758 \ub300\uc548\uc73c\ub85c \ub2e4\uc74c\uacfc \uac19\uc740 \ube44\uc120\ud615 \ucc28\uc6d0 \ucd95\uc18c \uae30\uc220\ub4e4\uc774 \uc788\uc2b5\ub2c8\ub2e4:<\/p>\n
\n- \ucee4\ub110 PCA:<\/strong> \ube44\uc120\ud615 \ub370\uc774\ud130\ub97c \ucc98\ub9ac\ud558\uae30 \uc704\ud574 \ucee4\ub110 \uae30\ubc95\uc744 \uc0ac\uc6a9\ud558\ub294 PCA \ubc84\uc804\uc785\ub2c8\ub2e4.<\/li>\n
- t-SNE:<\/strong> \ub370\uc774\ud130 \uc2dc\uac01\ud654\uc5d0 \uc720\uc6a9\ud558\uba70, \ube44\uc2b7\ud55c \ub370\uc774\ud130\ub97c \uac00\uae5d\uac8c \ubc30\uce58\ud569\ub2c8\ub2e4.<\/li>\n
- UMAP:<\/strong> t-SNE\ubcf4\ub2e4 \ub354 \ube60\ub974\uace0 \ud6a8\uc728\uc801\uc778 \ub370\uc774\ud130 \uc2dc\uac01\ud654 \uae30\ubc95\uc785\ub2c8\ub2e4.<\/li>\n<\/ul>\n
8. \uacb0\ub860<\/h2>\n
\uc8fc\uc131\ubd84 \ubd84\uc11d(PCA)\uc740 \ub525\ub7ec\ub2dd \ubc0f \uba38\uc2e0\ub7ec\ub2dd\uc5d0\uc11c \ud575\uc2ec\uc801\uc778 \uae30\ubc95 \uc911 \ud558\ub098\ub85c,
\n \ub370\uc774\ud130 \ucc28\uc6d0 \ucd95\uc18c, \uc2dc\uac01\ud654, \ud2b9\uc9d5 \ucd94\ucd9c \ub4f1 \ub2e4\uc591\ud55c \ubaa9\uc801\uc5d0 \uc0ac\uc6a9\ub429\ub2c8\ub2e4.
\n \ubcf8 \uac15\uc88c\ub97c \ud1b5\ud574 PCA\uc758 \uc6d0\ub9ac \ubc0f \ud30c\uc774\ud1a0\uce58\ub97c \uc774\uc6a9\ud55c \uad6c\ud604 \ubc29\ubc95\uc744 \ubc30\uc6b0\uc168\uae30\ub97c \ubc14\ub78d\ub2c8\ub2e4.
\n \ud5a5\ud6c4 \ub370\uc774\ud130 \ubd84\uc11d \ubc0f \ubaa8\ub378\ub9c1 \uacfc\uc815\uc5d0\uc11c PCA\ub97c \ud65c\uc6a9\ud558\uc5ec \ub354 \ub098\uc740 \uc131\uacfc\ub97c \uac70\ub450\uae38 \uae30\ub300\ud569\ub2c8\ub2e4.
\n \ub2e4\uc74c \uac15\uc88c\uc5d0\uc11c\ub294 \ub354\uc6b1 \uae4a\uc774 \uc788\ub294 \ub525\ub7ec\ub2dd \uc8fc\uc81c\ub97c \ub2e4\ub8f0 \uc608\uc815\uc785\ub2c8\ub2e4.<\/p>\n
<\/body><\/p>\n","protected":false},"excerpt":{"rendered":"