File size: 89,798 Bytes
43fa1d2 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 |
{
"cells": [
{
"cell_type": "markdown",
"id": "c73f8bf0-b957-4da5-88ab-4b030586cde5",
"metadata": {},
"source": [
"# DIMENSIONALITY REDUCTION\n",
"\n",
"--------------------------------------------\n",
"PHASE 1: EXPLAIN & BREAKDOWN (LEARNING PHASE)\n",
"--------------------------------------------\n",
"\n",
"## 1. Simple Explanation (100-150 words)\n",
"\n",
"Dimensionality reduction is like taking a 3D object and creating a 2D shadow that preserves the most important information. Imagine you have a dataset with 1000 features (columns) describing each data point, but many features are redundant or noisy. Dimensionality reduction techniques help you compress this data into fewer dimensions (maybe 10-50) while keeping the essential patterns intact.\n",
"\n",
"Think of it like summarizing a 500-page book into a 20-page summary - you lose some details, but the main ideas remain. This is crucial in AI because high-dimensional data is hard to visualize, slow to process, and prone to the \"curse of dimensionality\" (where algorithms perform poorly in high dimensions). Common techniques include PCA (Principal Component Analysis), t-SNE, and autoencoders. It's used everywhere: image compression, data visualization, noise reduction, and preparing data for machine learning models.\n",
"\n",
"## 2. Detailed Roadmap with Concrete Examples\n",
"\n",
"**Step 1: Understanding the Problem**\n",
"- **Curse of Dimensionality**: Example - Finding nearest neighbors in 2D vs 1000D space\n",
"- **Computational Complexity**: Example - Processing 28×28 pixel images (784 features) vs 10 compressed features\n",
"- **Visualization Challenges**: Example - Plotting customer data with 50 attributes\n",
"\n",
"**Step 2: Linear Dimensionality Reduction**\n",
"- **Principal Component Analysis (PCA)**: Example - Reducing face images from 10,000 pixels to 100 principal components\n",
"- **Linear Discriminant Analysis (LDA)**: Example - Separating iris flower species using 2 components instead of 4 features\n",
"- **Factor Analysis**: Example - Finding underlying factors in psychological test scores\n",
"\n",
"**Step 3: Non-Linear Dimensionality Reduction**\n",
"- **t-SNE**: Example - Visualizing high-dimensional word embeddings in 2D scatter plots\n",
"- **UMAP**: Example - Exploring single-cell RNA sequencing data clusters\n",
"- **Isomap**: Example - Unfolding Swiss roll dataset to reveal underlying 2D structure\n",
"\n",
"**Step 4: Neural Network Approaches**\n",
"- **Autoencoders**: Example - Compressing MNIST digit images from 784 to 32 dimensions\n",
"- **Variational Autoencoders (VAE)**: Example - Generating new faces by sampling from learned latent space\n",
"- **Deep Feature Learning**: Example - Using CNN layers as feature extractors\n",
"\n",
"**Step 5: Evaluation and Selection**\n",
"- **Explained Variance**: Example - Choosing number of PCA components to retain 95% variance\n",
"- **Reconstruction Error**: Example - Measuring how well compressed images match originals\n",
"- **Downstream Task Performance**: Example - Classification accuracy after dimensionality reduction\n",
"\n",
"## 3. Formula Memory Aids Section\n",
"\n",
"### PCA Covariance Matrix Formula\n",
"**FORMULA**: C = (1/n) × X^T × X\n",
"\n",
"**REAL-LIFE ANALOGY**: \"How do your friends' personalities relate to each other?\"\n",
"- C = Friendship compatibility matrix\n",
"- X = Each friend's personality traits (rows=friends, columns=traits)\n",
"- X^T = Flipping the friend-trait table\n",
"- 1/n = Averaging across all your friends\n",
"\n",
"**MEMORY TRICK**: \"Covariance = Correlation of Variance - how features dance together!\"\n",
"\n",
"### PCA Eigenvalue Decomposition Formula\n",
"**FORMULA**: C × v = λ × v\n",
"\n",
"**REAL-LIFE ANALOGY**: \"Which direction does your friend group naturally lean?\"\n",
"- C = Group's personality compatibility matrix\n",
"- v = Direction of strongest group tendency (eigenvector)\n",
"- λ = How strong that tendency is (eigenvalue)\n",
"- The equation means: \"Group tendency × Direction = Strength × Same Direction\"\n",
"\n",
"**MEMORY TRICK**: \"Eigen = 'Own' in German - finding data's 'own' natural directions!\"\n",
"\n",
"### Explained Variance Ratio Formula\n",
"**FORMULA**: Explained Variance = λᵢ / Σλⱼ\n",
"\n",
"**REAL-LIFE ANALOGY**: \"What percentage of your friend group's energy goes into sports vs studies?\"\n",
"- λᵢ = Energy spent on sports (one eigenvalue)\n",
"- Σλⱼ = Total energy of the group (sum of all eigenvalues)\n",
"- Ratio = Sports energy / Total energy\n",
"\n",
"**MEMORY TRICK**: \"Explained = Ex-plained on a plane - how much info fits on each dimension!\"\n",
"\n",
"### t-SNE Similarity Formula\n",
"**FORMULA**: pᵢⱼ = exp(-||xᵢ - xⱼ||²/2σᵢ²) / Σₖ≠ᵢ exp(-||xᵢ - xₖ||²/2σᵢ²)\n",
"\n",
"**REAL-LIFE ANALOGY**: \"How similar are two people in a crowded room?\"\n",
"- pᵢⱼ = Similarity between person i and person j\n",
"- ||xᵢ - xⱼ||² = How different their personalities are (squared distance)\n",
"- σᵢ² = How picky person i is about friendships (bandwidth)\n",
"- exp(-distance/pickiness) = Friendship probability decreases with distance/pickiness\n",
"\n",
"**MEMORY TRICK**: \"t-SNE = t-See Neighbors Everywhere - finding similar points!\"\n",
"\n",
"## 4. Step-by-Step Numerical Example (PCA on 2D data)\n",
"\n",
"**Dataset**: 4 points in 2D space\n",
"```\n",
"Point 1: (1, 2)\n",
"Point 2: (3, 4) \n",
"Point 3: (5, 6)\n",
"Point 4: (7, 8)\n",
"```\n",
"\n",
"**Step 1: Center the data (subtract mean)**\n",
"```\n",
"Mean = (4, 5)\n",
"Centered data:\n",
"Point 1: (-3, -3)\n",
"Point 2: (-1, -1)\n",
"Point 3: (1, 1)\n",
"Point 4: (3, 3)\n",
"```\n",
"\n",
"**Step 2: Calculate covariance matrix**\n",
"```\n",
"X = [[-3, -3],\n",
" [-1, -1],\n",
" [1, 1],\n",
" [3, 3]]\n",
"\n",
"C = (1/4) × X^T × X\n",
" = (1/4) × [[20, 20],\n",
" [20, 20]]\n",
" = [[5, 5],\n",
" [5, 5]]\n",
"```\n",
"\n",
"**Step 3: Find eigenvalues and eigenvectors**\n",
"```\n",
"Characteristic equation: det(C - λI) = 0\n",
"(5-λ)² - 25 = 0\n",
"λ² - 10λ = 0\n",
"λ₁ = 10, λ₂ = 0\n",
"\n",
"Eigenvector for λ₁ = 10: v₁ = [1/√2, 1/√2]\n",
"Eigenvector for λ₂ = 0: v₂ = [1/√2, -1/√2]\n",
"```\n",
"\n",
"**Step 4: Project data onto first principal component**\n",
"```\n",
"PC1 = X × v₁ = [[-3, -3], [-1, -1], [1, 1], [3, 3]] × [1/√2, 1/√2]\n",
" = [-6/√2, -2/√2, 2/√2, 6/√2]\n",
" = [-4.24, -1.41, 1.41, 4.24]\n",
"```\n",
"\n",
"**Result**: 2D data reduced to 1D with 100% explained variance!\n",
"\n",
"## 5. Real-World AI Use Case\n",
"\n",
"**Netflix Recommendation System**:\n",
"Netflix has millions of users and thousands of movies, creating a massive user-movie rating matrix. Using matrix factorization (a form of dimensionality reduction), they:\n",
"\n",
"1. **Compress user preferences**: Reduce each user's 10,000+ movie ratings to ~50 latent factors (like \"action lover\", \"comedy fan\", \"indie preference\")\n",
"2. **Compress movie features**: Reduce each movie's characteristics to the same 50 factors\n",
"3. **Make predictions**: Multiply user factors × movie factors to predict ratings\n",
"4. **Handle sparsity**: Most users haven't rated most movies, but the compressed representation can still make predictions\n",
"\n",
"This reduces storage, speeds up computation, and reveals hidden patterns like \"users who like sci-fi also tend to like thrillers.\"\n",
"\n",
"## 6. Tips for Mastering This Topic\n",
"\n",
"**Practice Sources**:\n",
"- Scikit-learn documentation and examples\n",
"- Kaggle datasets (Iris, Wine, Breast Cancer for beginners)\n",
"- Andrew Ng's CS229 Stanford lectures on PCA\n",
"- Sebastian Raschka's \"Python Machine Learning\" book\n",
"\n",
"**Hands-on Projects**:\n",
"1. **Visualize high-dimensional data**: Use t-SNE on MNIST digits\n",
"2. **Image compression**: Apply PCA to face images\n",
"3. **Feature selection**: Compare PCA vs original features for classification\n",
"4. **Clustering**: Use dimensionality reduction before K-means\n",
"\n",
"**Key Resources**:\n",
"- **Theory**: \"Elements of Statistical Learning\" (Hastie, Tibshirani, Friedman)\n",
"- **Implementation**: Scikit-learn user guide on decomposition\n",
"- **Visualization**: Matplotlib and Plotly for 2D/3D scatter plots\n",
"- **Practice**: Coursera ML course assignments\n",
"\n",
"**Common Pitfalls to Avoid**:\n",
"- Don't apply PCA to categorical variables\n",
"- Always scale/normalize data before PCA\n",
"- Remember: PCA removes the mean, so center your data first\n",
"- Choose components based on explained variance, not just arbitrary numbers\n",
"\n",
"Ready to move to implementation? Say \"Understood\" and I'll provide the complete Python code with logging!"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "1af263fd-a090-4126-9af3-cb6afef9efff",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"3925.08s - pydevd: Sending message related to process being replaced timed-out after 5 seconds\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Requirement already satisfied: numpy in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (2.3.1)\n",
"Requirement already satisfied: pandas in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (2.3.1)\n",
"Requirement already satisfied: scikit-learn in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (1.7.0)\n",
"Requirement already satisfied: matplotlib in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (3.10.3)\n",
"Requirement already satisfied: seaborn in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (0.13.2)\n",
"Requirement already satisfied: plotly in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (6.2.0)\n",
"Collecting umap-learn\n",
" Downloading umap_learn-0.5.9.post2-py3-none-any.whl.metadata (25 kB)\n",
"Requirement already satisfied: python-dateutil>=2.8.2 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from pandas) (2.9.0.post0)\n",
"Requirement already satisfied: pytz>=2020.1 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from pandas) (2025.2)\n",
"Requirement already satisfied: tzdata>=2022.7 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from pandas) (2025.2)\n",
"Requirement already satisfied: scipy>=1.8.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from scikit-learn) (1.16.0)\n",
"Requirement already satisfied: joblib>=1.2.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from scikit-learn) (1.5.1)\n",
"Requirement already satisfied: threadpoolctl>=3.1.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from scikit-learn) (3.6.0)\n",
"Requirement already satisfied: contourpy>=1.0.1 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from matplotlib) (1.3.2)\n",
"Requirement already satisfied: cycler>=0.10 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from matplotlib) (0.12.1)\n",
"Requirement already satisfied: fonttools>=4.22.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from matplotlib) (4.58.5)\n",
"Requirement already satisfied: kiwisolver>=1.3.1 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from matplotlib) (1.4.8)\n",
"Requirement already satisfied: packaging>=20.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from matplotlib) (25.0)\n",
"Requirement already satisfied: pillow>=8 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from matplotlib) (11.3.0)\n",
"Requirement already satisfied: pyparsing>=2.3.1 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from matplotlib) (3.2.3)\n",
"Requirement already satisfied: narwhals>=1.15.1 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from plotly) (1.47.0)\n",
"Collecting numba>=0.51.2 (from umap-learn)\n",
" Downloading numba-0.61.2-cp313-cp313-macosx_11_0_arm64.whl.metadata (2.7 kB)\n",
"Collecting pynndescent>=0.5 (from umap-learn)\n",
" Downloading pynndescent-0.5.13-py3-none-any.whl.metadata (6.8 kB)\n",
"Requirement already satisfied: tqdm in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from umap-learn) (4.67.1)\n",
"Collecting llvmlite<0.45,>=0.44.0dev0 (from numba>=0.51.2->umap-learn)\n",
" Downloading llvmlite-0.44.0-cp313-cp313-macosx_11_0_arm64.whl.metadata (4.8 kB)\n",
"Collecting numpy\n",
" Downloading numpy-2.2.6-cp313-cp313-macosx_14_0_arm64.whl.metadata (62 kB)\n",
"Requirement already satisfied: six>=1.5 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from python-dateutil>=2.8.2->pandas) (1.17.0)\n",
"Downloading umap_learn-0.5.9.post2-py3-none-any.whl (90 kB)\n",
"Downloading numba-0.61.2-cp313-cp313-macosx_11_0_arm64.whl (2.8 MB)\n",
"\u001b[2K \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m2.8/2.8 MB\u001b[0m \u001b[31m17.0 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m\n",
"\u001b[?25hDownloading numpy-2.2.6-cp313-cp313-macosx_14_0_arm64.whl (5.1 MB)\n",
"\u001b[2K \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5.1/5.1 MB\u001b[0m \u001b[31m2.5 MB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0m[36m0:00:01\u001b[0m[36m0:00:01\u001b[0m:01\u001b[0m\n",
"\u001b[?25hDownloading llvmlite-0.44.0-cp313-cp313-macosx_11_0_arm64.whl (26.2 MB)\n",
"\u001b[2K \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m26.2/26.2 MB\u001b[0m \u001b[31m541.2 kB/s\u001b[0m eta \u001b[36m0:00:00\u001b[0mm eta \u001b[36m0:00:01\u001b[0m[36m0:00:02\u001b[0m\n",
"\u001b[?25hDownloading pynndescent-0.5.13-py3-none-any.whl (56 kB)\n",
"Installing collected packages: numpy, llvmlite, numba, pynndescent, umap-learn\n",
"\u001b[2K Attempting uninstall: numpy\n",
"\u001b[2K Found existing installation: numpy 2.3.1\n",
"\u001b[2K Uninstalling numpy-2.3.1:\n",
"\u001b[2K Successfully uninstalled numpy-2.3.1\n",
"\u001b[2K \u001b[38;2;114;156;31m━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━\u001b[0m \u001b[32m5/5\u001b[0m [umap-learn]\u001b[0m \u001b[32m2/5\u001b[0m [numba]te]\n",
"\u001b[1A\u001b[2KSuccessfully installed llvmlite-0.44.0 numba-0.61.2 numpy-2.2.6 pynndescent-0.5.13 umap-learn-0.5.9.post2\n"
]
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"3978.36s - pydevd: Sending message related to process being replaced timed-out after 5 seconds\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Requirement already satisfied: torch in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (2.7.1)\n",
"Requirement already satisfied: torchvision in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (0.22.1)\n",
"Requirement already satisfied: filelock in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torch) (3.18.0)\n",
"Requirement already satisfied: typing-extensions>=4.10.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torch) (4.14.1)\n",
"Requirement already satisfied: setuptools in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torch) (80.9.0)\n",
"Requirement already satisfied: sympy>=1.13.3 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torch) (1.14.0)\n",
"Requirement already satisfied: networkx in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torch) (3.5)\n",
"Requirement already satisfied: jinja2 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torch) (3.1.6)\n",
"Requirement already satisfied: fsspec in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torch) (2025.3.0)\n",
"Requirement already satisfied: numpy in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torchvision) (2.2.6)\n",
"Requirement already satisfied: pillow!=8.3.*,>=5.3.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from torchvision) (11.3.0)\n",
"Requirement already satisfied: mpmath<1.4,>=1.1.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from sympy>=1.13.3->torch) (1.3.0)\n",
"Requirement already satisfied: MarkupSafe>=2.0 in /Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages (from jinja2->torch) (3.0.2)\n"
]
}
],
"source": [
"!pip install numpy pandas scikit-learn matplotlib seaborn plotly umap-learn\n",
"!pip install torch torchvision # For autoencoder implementation"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "ba8acc30-65df-4ca8-9852-5a09177e4195",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"2025-07-16 10:36:41,644 - INFO - Starting Dimensionality Reduction Suite\n",
"2025-07-16 10:36:41,645 - INFO - Loading datasets for dimensionality reduction analysis\n",
"2025-07-16 10:36:41,647 - INFO - Iris dataset loaded: (150, 4) features, 3 classes\n",
"2025-07-16 10:36:41,656 - INFO - Digits dataset loaded: (1797, 64) features, 10 classes\n",
"2025-07-16 10:36:41,658 - INFO - Data standardization completed\n",
"2025-07-16 10:36:41,658 - INFO - === APPLYING PCA ===\n",
"2025-07-16 10:36:41,658 - INFO - Applying PCA to iris dataset\n",
"2025-07-16 10:36:41,661 - INFO - PCA completed for iris\n",
"2025-07-16 10:36:41,661 - INFO - Explained variance per component: [0.72962445 0.22850762]\n",
"2025-07-16 10:36:41,661 - INFO - Cumulative explained variance: [0.72962445 0.95813207]\n",
"2025-07-16 10:36:41,662 - INFO - Applying PCA to digits dataset\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/decomposition/_pca.py:604: RuntimeWarning: divide by zero encountered in matmul\n",
" C = X.T @ X\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/decomposition/_pca.py:604: RuntimeWarning: overflow encountered in matmul\n",
" C = X.T @ X\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/decomposition/_pca.py:604: RuntimeWarning: invalid value encountered in matmul\n",
" C = X.T @ X\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/decomposition/_base.py:148: RuntimeWarning: divide by zero encountered in matmul\n",
" X_transformed = X @ self.components_.T\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/decomposition/_base.py:148: RuntimeWarning: overflow encountered in matmul\n",
" X_transformed = X @ self.components_.T\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/decomposition/_base.py:148: RuntimeWarning: invalid value encountered in matmul\n",
" X_transformed = X @ self.components_.T\n",
"2025-07-16 10:36:41,670 - INFO - PCA completed for digits\n",
"2025-07-16 10:36:41,671 - INFO - Explained variance per component: [0.12033916 0.09561054]\n",
"2025-07-16 10:36:41,672 - INFO - Cumulative explained variance: [0.12033916 0.21594971]\n",
"2025-07-16 10:36:41,672 - INFO - === APPLYING t-SNE ===\n",
"2025-07-16 10:36:41,673 - INFO - Applying t-SNE to iris dataset with perplexity=30\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:350: RuntimeWarning: divide by zero encountered in matmul\n",
" Q, _ = normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:350: RuntimeWarning: overflow encountered in matmul\n",
" Q, _ = normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:350: RuntimeWarning: invalid value encountered in matmul\n",
" Q, _ = normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:351: RuntimeWarning: divide by zero encountered in matmul\n",
" Q, _ = normalizer(A.T @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:351: RuntimeWarning: overflow encountered in matmul\n",
" Q, _ = normalizer(A.T @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:351: RuntimeWarning: invalid value encountered in matmul\n",
" Q, _ = normalizer(A.T @ Q)\n",
"2025-07-16 10:36:42,159 - INFO - t-SNE completed for iris\n",
"2025-07-16 10:36:42,159 - INFO - Final KL divergence: 0.14698290824890137\n",
"2025-07-16 10:36:42,159 - INFO - Applying t-SNE to digits dataset with perplexity=30\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:350: RuntimeWarning: divide by zero encountered in matmul\n",
" Q, _ = normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:350: RuntimeWarning: overflow encountered in matmul\n",
" Q, _ = normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:350: RuntimeWarning: invalid value encountered in matmul\n",
" Q, _ = normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:351: RuntimeWarning: divide by zero encountered in matmul\n",
" Q, _ = normalizer(A.T @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:351: RuntimeWarning: overflow encountered in matmul\n",
" Q, _ = normalizer(A.T @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:351: RuntimeWarning: invalid value encountered in matmul\n",
" Q, _ = normalizer(A.T @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:355: RuntimeWarning: divide by zero encountered in matmul\n",
" Q, _ = qr_normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:355: RuntimeWarning: overflow encountered in matmul\n",
" Q, _ = qr_normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:355: RuntimeWarning: invalid value encountered in matmul\n",
" Q, _ = qr_normalizer(A @ Q)\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:577: RuntimeWarning: divide by zero encountered in matmul\n",
" B = Q.T @ M\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:577: RuntimeWarning: overflow encountered in matmul\n",
" B = Q.T @ M\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:577: RuntimeWarning: invalid value encountered in matmul\n",
" B = Q.T @ M\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:590: RuntimeWarning: divide by zero encountered in matmul\n",
" U = Q @ Uhat\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:590: RuntimeWarning: overflow encountered in matmul\n",
" U = Q @ Uhat\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/sklearn/utils/extmath.py:590: RuntimeWarning: invalid value encountered in matmul\n",
" U = Q @ Uhat\n",
"2025-07-16 10:36:43,689 - INFO - t-SNE completed for digits\n",
"2025-07-16 10:36:43,690 - INFO - Final KL divergence: 0.8376309275627136\n",
"2025-07-16 10:36:43,690 - INFO - === APPLYING UMAP ===\n",
"2025-07-16 10:36:43,691 - INFO - Applying UMAP to iris dataset with n_neighbors=15\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/umap/umap_.py:1952: UserWarning: n_jobs value 1 overridden to 1 by setting random_state. Use no seed for parallelism.\n",
" warn(\n",
"2025-07-16 10:36:46,402 - INFO - UMAP completed for iris\n",
"2025-07-16 10:36:46,403 - INFO - Applying UMAP to digits dataset with n_neighbors=15\n",
"/Users/karthik/Desktop/importants/venv/lib/python3.13/site-packages/umap/umap_.py:1952: UserWarning: n_jobs value 1 overridden to 1 by setting random_state. Use no seed for parallelism.\n",
" warn(\n",
"2025-07-16 10:36:48,356 - INFO - UMAP completed for digits\n",
"2025-07-16 10:36:48,356 - INFO - === APPLYING AUTOENCODER ===\n",
"2025-07-16 10:36:48,356 - INFO - Training autoencoder for iris dataset\n",
"2025-07-16 10:36:48,357 - INFO - Input dimension: 4, Encoding dimension: 2\n",
"2025-07-16 10:36:49,110 - INFO - Epoch 20/50, Loss: 0.314444\n",
"2025-07-16 10:36:49,122 - INFO - Epoch 40/50, Loss: 0.169524\n",
"2025-07-16 10:36:49,140 - INFO - Autoencoder training completed for iris\n",
"2025-07-16 10:36:49,140 - INFO - Final reconstruction loss: 0.081181\n",
"2025-07-16 10:36:49,143 - INFO - Training autoencoder for digits dataset\n",
"2025-07-16 10:36:49,144 - INFO - Input dimension: 64, Encoding dimension: 10\n",
"2025-07-16 10:36:49,215 - INFO - Epoch 20/100, Loss: 0.856640\n",
"2025-07-16 10:36:49,266 - INFO - Epoch 40/100, Loss: 0.649845\n",
"2025-07-16 10:36:49,316 - INFO - Epoch 60/100, Loss: 0.515600\n",
"2025-07-16 10:36:49,363 - INFO - Epoch 80/100, Loss: 0.427001\n",
"2025-07-16 10:36:49,408 - INFO - Epoch 100/100, Loss: 0.348234\n",
"2025-07-16 10:36:49,409 - INFO - Autoencoder training completed for digits\n",
"2025-07-16 10:36:49,410 - INFO - Final reconstruction loss: 0.348234\n",
"2025-07-16 10:36:49,410 - INFO - === EVALUATING METHODS ===\n",
"2025-07-16 10:36:49,410 - INFO - Evaluating PCA performance on iris dataset\n",
"2025-07-16 10:36:49,511 - INFO - Original data accuracy: 0.8889\n",
"2025-07-16 10:36:49,511 - INFO - Reduced data accuracy: 0.8667\n",
"2025-07-16 10:36:49,512 - INFO - Accuracy retention: 97.50%\n",
"2025-07-16 10:36:49,512 - INFO - Evaluating TSNE performance on iris dataset\n",
"2025-07-16 10:36:49,604 - INFO - Original data accuracy: 0.8889\n",
"2025-07-16 10:36:49,604 - INFO - Reduced data accuracy: 0.9333\n",
"2025-07-16 10:36:49,604 - INFO - Accuracy retention: 105.00%\n",
"2025-07-16 10:36:49,605 - INFO - Evaluating UMAP performance on iris dataset\n",
"2025-07-16 10:36:49,697 - INFO - Original data accuracy: 0.8889\n",
"2025-07-16 10:36:49,698 - INFO - Reduced data accuracy: 0.9111\n",
"2025-07-16 10:36:49,698 - INFO - Accuracy retention: 102.50%\n",
"2025-07-16 10:36:49,698 - INFO - Evaluating PCA performance on digits dataset\n",
"2025-07-16 10:36:49,920 - INFO - Original data accuracy: 0.9685\n",
"2025-07-16 10:36:49,920 - INFO - Reduced data accuracy: 0.5074\n",
"2025-07-16 10:36:49,920 - INFO - Accuracy retention: 52.39%\n",
"2025-07-16 10:36:49,921 - INFO - Evaluating TSNE performance on digits dataset\n",
"2025-07-16 10:36:50,117 - INFO - Original data accuracy: 0.9685\n",
"2025-07-16 10:36:50,117 - INFO - Reduced data accuracy: 0.9722\n",
"2025-07-16 10:36:50,117 - INFO - Accuracy retention: 100.38%\n",
"2025-07-16 10:36:50,118 - INFO - Evaluating UMAP performance on digits dataset\n",
"2025-07-16 10:36:50,325 - INFO - Original data accuracy: 0.9685\n",
"2025-07-16 10:36:50,326 - INFO - Reduced data accuracy: 0.9611\n",
"2025-07-16 10:36:50,326 - INFO - Accuracy retention: 99.24%\n",
"2025-07-16 10:36:50,326 - INFO - Creating comprehensive visualizations\n",
"2025-07-16 10:36:51,350 - INFO - All visualizations saved to visualizations/ directory\n",
"2025-07-16 10:36:51,351 - INFO - Saving trained models\n",
"2025-07-16 10:36:51,360 - INFO - Saving results summary\n",
"2025-07-16 10:36:51,361 - INFO - === FINAL SUMMARY ===\n",
"2025-07-16 10:36:51,362 - INFO - Iris Dataset - PCA Explained Variance: [0.72962445 0.22850762]\n",
"2025-07-16 10:36:51,362 - INFO - Digits Dataset - PCA Explained Variance: [0.12033916 0.09561054]\n",
"2025-07-16 10:36:51,363 - INFO - \n",
"IRIS Dataset Classification Performance:\n",
"2025-07-16 10:36:51,363 - INFO - PCA: 97.50% accuracy retention\n",
"2025-07-16 10:36:51,363 - INFO - TSNE: 105.00% accuracy retention\n",
"2025-07-16 10:36:51,363 - INFO - UMAP: 102.50% accuracy retention\n",
"2025-07-16 10:36:51,363 - INFO - \n",
"DIGITS Dataset Classification Performance:\n",
"2025-07-16 10:36:51,364 - INFO - PCA: 52.39% accuracy retention\n",
"2025-07-16 10:36:51,364 - INFO - TSNE: 100.38% accuracy retention\n",
"2025-07-16 10:36:51,364 - INFO - UMAP: 99.24% accuracy retention\n",
"2025-07-16 10:36:51,365 - INFO - \n",
"All models saved to models/ directory\n",
"2025-07-16 10:36:51,365 - INFO - All results saved to results/ directory\n",
"2025-07-16 10:36:51,365 - INFO - All visualizations saved to visualizations/ directory\n",
"2025-07-16 10:36:51,366 - INFO - Dimensionality Reduction Suite completed successfully!\n"
]
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"import matplotlib.pyplot as plt\n",
"import seaborn as sns\n",
"import plotly.express as px\n",
"import plotly.graph_objects as go\n",
"from sklearn.datasets import load_iris, load_digits\n",
"from sklearn.preprocessing import StandardScaler\n",
"from sklearn.decomposition import PCA\n",
"from sklearn.manifold import TSNE\n",
"from sklearn.model_selection import train_test_split\n",
"from sklearn.ensemble import RandomForestClassifier\n",
"from sklearn.metrics import accuracy_score, classification_report\n",
"import umap\n",
"import torch\n",
"import torch.nn as nn\n",
"import torch.optim as optim\n",
"import pickle\n",
"import json\n",
"import logging\n",
"import os\n",
"from datetime import datetime\n",
"\n",
"# Configure logging\n",
"logging.basicConfig(\n",
" level=logging.INFO,\n",
" format='%(asctime)s - %(levelname)s - %(message)s',\n",
" handlers=[\n",
" logging.FileHandler('dimensionality_reduction.log'),\n",
" logging.StreamHandler()\n",
" ]\n",
")\n",
"\n",
"# Create results directory\n",
"os.makedirs('results', exist_ok=True)\n",
"os.makedirs('models', exist_ok=True)\n",
"os.makedirs('visualizations', exist_ok=True)\n",
"\n",
"class DimensionalityReductionSuite:\n",
" def __init__(self):\n",
" self.results = {}\n",
" self.models = {}\n",
" \n",
" def load_and_prepare_data(self):\n",
" logging.info(\"Loading datasets for dimensionality reduction analysis\")\n",
" \n",
" # Load Iris dataset (low-dimensional example)\n",
" iris = load_iris()\n",
" self.iris_data = iris.data\n",
" self.iris_target = iris.target\n",
" self.iris_target_names = iris.target_names\n",
" self.iris_feature_names = iris.feature_names\n",
" \n",
" logging.info(f\"Iris dataset loaded: {self.iris_data.shape} features, {len(np.unique(self.iris_target))} classes\")\n",
" \n",
" # Load Digits dataset (high-dimensional example)\n",
" digits = load_digits()\n",
" self.digits_data = digits.data\n",
" self.digits_target = digits.target\n",
" self.digits_images = digits.images\n",
" \n",
" logging.info(f\"Digits dataset loaded: {self.digits_data.shape} features, {len(np.unique(self.digits_target))} classes\")\n",
" \n",
" # Standardize the data\n",
" self.scaler_iris = StandardScaler()\n",
" self.iris_scaled = self.scaler_iris.fit_transform(self.iris_data)\n",
" \n",
" self.scaler_digits = StandardScaler()\n",
" self.digits_scaled = self.scaler_digits.fit_transform(self.digits_data)\n",
" \n",
" logging.info(\"Data standardization completed\")\n",
" \n",
" def apply_pca(self, data, dataset_name, n_components=2):\n",
" logging.info(f\"Applying PCA to {dataset_name} dataset\")\n",
" \n",
" pca = PCA(n_components=n_components)\n",
" data_pca = pca.fit_transform(data)\n",
" \n",
" # Calculate explained variance\n",
" explained_variance = pca.explained_variance_ratio_\n",
" cumulative_variance = np.cumsum(explained_variance)\n",
" \n",
" logging.info(f\"PCA completed for {dataset_name}\")\n",
" logging.info(f\"Explained variance per component: {explained_variance}\")\n",
" logging.info(f\"Cumulative explained variance: {cumulative_variance}\")\n",
" \n",
" # Store results\n",
" self.results[f'{dataset_name}_pca'] = {\n",
" 'transformed_data': data_pca,\n",
" 'explained_variance': explained_variance,\n",
" 'cumulative_variance': cumulative_variance,\n",
" 'components': pca.components_\n",
" }\n",
" \n",
" self.models[f'{dataset_name}_pca'] = pca\n",
" \n",
" return data_pca, explained_variance\n",
" \n",
" def apply_tsne(self, data, dataset_name, n_components=2, perplexity=30):\n",
" logging.info(f\"Applying t-SNE to {dataset_name} dataset with perplexity={perplexity}\")\n",
" \n",
" tsne = TSNE(n_components=n_components, perplexity=perplexity, random_state=42)\n",
" data_tsne = tsne.fit_transform(data)\n",
" \n",
" logging.info(f\"t-SNE completed for {dataset_name}\")\n",
" logging.info(f\"Final KL divergence: {tsne.kl_divergence_}\")\n",
" \n",
" # Store results\n",
" self.results[f'{dataset_name}_tsne'] = {\n",
" 'transformed_data': data_tsne,\n",
" 'kl_divergence': tsne.kl_divergence_\n",
" }\n",
" \n",
" return data_tsne\n",
" \n",
" def apply_umap(self, data, dataset_name, n_components=2, n_neighbors=15):\n",
" logging.info(f\"Applying UMAP to {dataset_name} dataset with n_neighbors={n_neighbors}\")\n",
" \n",
" umap_reducer = umap.UMAP(n_components=n_components, n_neighbors=n_neighbors, random_state=42)\n",
" data_umap = umap_reducer.fit_transform(data)\n",
" \n",
" logging.info(f\"UMAP completed for {dataset_name}\")\n",
" \n",
" # Store results\n",
" self.results[f'{dataset_name}_umap'] = {\n",
" 'transformed_data': data_umap\n",
" }\n",
" \n",
" self.models[f'{dataset_name}_umap'] = umap_reducer\n",
" \n",
" return data_umap\n",
"\n",
"class SimpleAutoencoder(nn.Module):\n",
" def __init__(self, input_dim, encoding_dim):\n",
" super(SimpleAutoencoder, self).__init__()\n",
" self.encoder = nn.Sequential(\n",
" nn.Linear(input_dim, 128),\n",
" nn.ReLU(),\n",
" nn.Linear(128, 64),\n",
" nn.ReLU(),\n",
" nn.Linear(64, encoding_dim)\n",
" )\n",
" \n",
" self.decoder = nn.Sequential(\n",
" nn.Linear(encoding_dim, 64),\n",
" nn.ReLU(),\n",
" nn.Linear(64, 128),\n",
" nn.ReLU(),\n",
" nn.Linear(128, input_dim)\n",
" )\n",
" \n",
" def forward(self, x):\n",
" encoded = self.encoder(x)\n",
" decoded = self.decoder(encoded)\n",
" return decoded, encoded\n",
"\n",
"def train_autoencoder(data, dataset_name, encoding_dim=10, epochs=100, lr=0.001):\n",
" logging.info(f\"Training autoencoder for {dataset_name} dataset\")\n",
" logging.info(f\"Input dimension: {data.shape[1]}, Encoding dimension: {encoding_dim}\")\n",
" \n",
" # Convert to PyTorch tensors\n",
" data_tensor = torch.FloatTensor(data)\n",
" \n",
" # Initialize model\n",
" model = SimpleAutoencoder(data.shape[1], encoding_dim)\n",
" criterion = nn.MSELoss()\n",
" optimizer = optim.Adam(model.parameters(), lr=lr)\n",
" \n",
" # Training loop\n",
" losses = []\n",
" for epoch in range(epochs):\n",
" optimizer.zero_grad()\n",
" reconstructed, encoded = model(data_tensor)\n",
" loss = criterion(reconstructed, data_tensor)\n",
" loss.backward()\n",
" optimizer.step()\n",
" \n",
" losses.append(loss.item())\n",
" \n",
" if (epoch + 1) % 20 == 0:\n",
" logging.info(f\"Epoch {epoch+1}/{epochs}, Loss: {loss.item():.6f}\")\n",
" \n",
" # Get final encodings\n",
" with torch.no_grad():\n",
" _, final_encoded = model(data_tensor)\n",
" final_encoded = final_encoded.numpy()\n",
" \n",
" logging.info(f\"Autoencoder training completed for {dataset_name}\")\n",
" logging.info(f\"Final reconstruction loss: {losses[-1]:.6f}\")\n",
" \n",
" return final_encoded, model, losses\n",
"\n",
"def evaluate_dimensionality_reduction(original_data, reduced_data, target, dataset_name, method_name):\n",
" logging.info(f\"Evaluating {method_name} performance on {dataset_name} dataset\")\n",
" \n",
" # Split data for classification test\n",
" X_train_orig, X_test_orig, y_train, y_test = train_test_split(\n",
" original_data, target, test_size=0.3, random_state=42, stratify=target\n",
" )\n",
" \n",
" X_train_red, X_test_red, _, _ = train_test_split(\n",
" reduced_data, target, test_size=0.3, random_state=42, stratify=target\n",
" )\n",
" \n",
" # Train classifiers\n",
" rf_orig = RandomForestClassifier(random_state=42)\n",
" rf_red = RandomForestClassifier(random_state=42)\n",
" \n",
" rf_orig.fit(X_train_orig, y_train)\n",
" rf_red.fit(X_train_red, y_train)\n",
" \n",
" # Evaluate\n",
" acc_orig = accuracy_score(y_test, rf_orig.predict(X_test_orig))\n",
" acc_red = accuracy_score(y_test, rf_red.predict(X_test_red))\n",
" \n",
" logging.info(f\"Original data accuracy: {acc_orig:.4f}\")\n",
" logging.info(f\"Reduced data accuracy: {acc_red:.4f}\")\n",
" logging.info(f\"Accuracy retention: {(acc_red/acc_orig)*100:.2f}%\")\n",
" \n",
" return {\n",
" 'original_accuracy': acc_orig,\n",
" 'reduced_accuracy': acc_red,\n",
" 'accuracy_retention': (acc_red/acc_orig)*100\n",
" }\n",
"\n",
"def create_visualizations(dr_suite):\n",
" logging.info(\"Creating comprehensive visualizations\")\n",
" \n",
" # 1. PCA Explained Variance Plot\n",
" plt.figure(figsize=(12, 5))\n",
" \n",
" plt.subplot(1, 2, 1)\n",
" iris_pca_var = dr_suite.results['iris_pca']['explained_variance']\n",
" plt.bar(range(1, len(iris_pca_var)+1), iris_pca_var)\n",
" plt.title('Iris Dataset - PCA Explained Variance')\n",
" plt.xlabel('Principal Component')\n",
" plt.ylabel('Explained Variance Ratio')\n",
" \n",
" plt.subplot(1, 2, 2)\n",
" digits_pca_var = dr_suite.results['digits_pca']['explained_variance']\n",
" plt.bar(range(1, len(digits_pca_var)+1), digits_pca_var)\n",
" plt.title('Digits Dataset - PCA Explained Variance')\n",
" plt.xlabel('Principal Component')\n",
" plt.ylabel('Explained Variance Ratio')\n",
" \n",
" plt.tight_layout()\n",
" plt.savefig('visualizations/pca_explained_variance.png', dpi=300, bbox_inches='tight')\n",
" plt.close()\n",
" \n",
" # 2. Comparison of methods on Iris dataset\n",
" fig, axes = plt.subplots(2, 2, figsize=(15, 12))\n",
" \n",
" # Original data (first 2 features)\n",
" axes[0, 0].scatter(dr_suite.iris_data[:, 0], dr_suite.iris_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[0, 0].set_title('Original Data (First 2 Features)')\n",
" axes[0, 0].set_xlabel('Sepal Length')\n",
" axes[0, 0].set_ylabel('Sepal Width')\n",
" \n",
" # PCA\n",
" pca_data = dr_suite.results['iris_pca']['transformed_data']\n",
" axes[0, 1].scatter(pca_data[:, 0], pca_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[0, 1].set_title('PCA Reduction')\n",
" axes[0, 1].set_xlabel('PC1')\n",
" axes[0, 1].set_ylabel('PC2')\n",
" \n",
" # t-SNE\n",
" tsne_data = dr_suite.results['iris_tsne']['transformed_data']\n",
" axes[1, 0].scatter(tsne_data[:, 0], tsne_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[1, 0].set_title('t-SNE Reduction')\n",
" axes[1, 0].set_xlabel('t-SNE 1')\n",
" axes[1, 0].set_ylabel('t-SNE 2')\n",
" \n",
" # UMAP\n",
" umap_data = dr_suite.results['iris_umap']['transformed_data']\n",
" axes[1, 1].scatter(umap_data[:, 0], umap_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[1, 1].set_title('UMAP Reduction')\n",
" axes[1, 1].set_xlabel('UMAP 1')\n",
" axes[1, 1].set_ylabel('UMAP 2')\n",
" \n",
" plt.tight_layout()\n",
" plt.savefig('visualizations/iris_comparison.png', dpi=300, bbox_inches='tight')\n",
" plt.close()\n",
" \n",
" # 3. Digits dataset visualization\n",
" fig, axes = plt.subplots(2, 2, figsize=(15, 12))\n",
" \n",
" # Original digits (sample)\n",
" for i in range(4):\n",
" axes[0, 0].imshow(dr_suite.digits_images[i], cmap='gray')\n",
" break\n",
" axes[0, 0].set_title('Original Digit Images (8x8 pixels)')\n",
" \n",
" # PCA\n",
" pca_data = dr_suite.results['digits_pca']['transformed_data']\n",
" scatter = axes[0, 1].scatter(pca_data[:, 0], pca_data[:, 1], \n",
" c=dr_suite.digits_target, cmap='tab10', alpha=0.7)\n",
" axes[0, 1].set_title('PCA - Digits Dataset')\n",
" axes[0, 1].set_xlabel('PC1')\n",
" axes[0, 1].set_ylabel('PC2')\n",
" \n",
" # t-SNE\n",
" tsne_data = dr_suite.results['digits_tsne']['transformed_data']\n",
" axes[1, 0].scatter(tsne_data[:, 0], tsne_data[:, 1], \n",
" c=dr_suite.digits_target, cmap='tab10', alpha=0.7)\n",
" axes[1, 0].set_title('t-SNE - Digits Dataset')\n",
" axes[1, 0].set_xlabel('t-SNE 1')\n",
" axes[1, 0].set_ylabel('t-SNE 2')\n",
" \n",
" # UMAP\n",
" umap_data = dr_suite.results['digits_umap']['transformed_data']\n",
" axes[1, 1].scatter(umap_data[:, 0], umap_data[:, 1], \n",
" c=dr_suite.digits_target, cmap='tab10', alpha=0.7)\n",
" axes[1, 1].set_title('UMAP - Digits Dataset')\n",
" axes[1, 1].set_xlabel('UMAP 1')\n",
" axes[1, 1].set_ylabel('UMAP 2')\n",
" \n",
" plt.tight_layout()\n",
" plt.savefig('visualizations/digits_comparison.png', dpi=300, bbox_inches='tight')\n",
" plt.close()\n",
" \n",
" logging.info(\"All visualizations saved to visualizations/ directory\")\n",
"\n",
"def main():\n",
" logging.info(\"Starting Dimensionality Reduction Suite\")\n",
" \n",
" # Initialize the suite\n",
" dr_suite = DimensionalityReductionSuite()\n",
" \n",
" # Load and prepare data\n",
" dr_suite.load_and_prepare_data()\n",
" \n",
" # Apply PCA\n",
" logging.info(\"=== APPLYING PCA ===\")\n",
" dr_suite.apply_pca(dr_suite.iris_scaled, 'iris', n_components=2)\n",
" dr_suite.apply_pca(dr_suite.digits_scaled, 'digits', n_components=2)\n",
" \n",
" # Apply t-SNE\n",
" logging.info(\"=== APPLYING t-SNE ===\")\n",
" dr_suite.apply_tsne(dr_suite.iris_scaled, 'iris', perplexity=30)\n",
" dr_suite.apply_tsne(dr_suite.digits_scaled, 'digits', perplexity=30)\n",
" \n",
" # Apply UMAP\n",
" logging.info(\"=== APPLYING UMAP ===\")\n",
" dr_suite.apply_umap(dr_suite.iris_scaled, 'iris', n_neighbors=15)\n",
" dr_suite.apply_umap(dr_suite.digits_scaled, 'digits', n_neighbors=15)\n",
" \n",
" # Apply Autoencoder\n",
" logging.info(\"=== APPLYING AUTOENCODER ===\")\n",
" iris_encoded, iris_autoencoder, iris_losses = train_autoencoder(\n",
" dr_suite.iris_scaled, 'iris', encoding_dim=2, epochs=50, lr=0.001\n",
" )\n",
" \n",
" digits_encoded, digits_autoencoder, digits_losses = train_autoencoder(\n",
" dr_suite.digits_scaled, 'digits', encoding_dim=10, epochs=100, lr=0.001\n",
" )\n",
" \n",
" # Store autoencoder results\n",
" dr_suite.results['iris_autoencoder'] = {\n",
" 'transformed_data': iris_encoded,\n",
" 'training_losses': iris_losses\n",
" }\n",
" \n",
" dr_suite.results['digits_autoencoder'] = {\n",
" 'transformed_data': digits_encoded,\n",
" 'training_losses': digits_losses\n",
" }\n",
" \n",
" # Evaluate all methods\n",
" logging.info(\"=== EVALUATING METHODS ===\")\n",
" evaluation_results = {}\n",
" \n",
" # Evaluate on Iris dataset\n",
" methods = ['pca', 'tsne', 'umap']\n",
" for method in methods:\n",
" eval_result = evaluate_dimensionality_reduction(\n",
" dr_suite.iris_scaled, \n",
" dr_suite.results[f'iris_{method}']['transformed_data'],\n",
" dr_suite.iris_target,\n",
" 'iris',\n",
" method.upper()\n",
" )\n",
" evaluation_results[f'iris_{method}'] = eval_result\n",
" \n",
" # Evaluate on Digits dataset\n",
" for method in methods:\n",
" eval_result = evaluate_dimensionality_reduction(\n",
" dr_suite.digits_scaled,\n",
" dr_suite.results[f'digits_{method}']['transformed_data'],\n",
" dr_suite.digits_target,\n",
" 'digits',\n",
" method.upper()\n",
" )\n",
" evaluation_results[f'digits_{method}'] = eval_result\n",
" \n",
" # Create visualizations\n",
" create_visualizations(dr_suite)\n",
" \n",
" # Save models\n",
" logging.info(\"Saving trained models\")\n",
" with open('models/pca_iris.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['iris_pca'], f)\n",
" \n",
" with open('models/pca_digits.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['digits_pca'], f)\n",
" \n",
" with open('models/umap_iris.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['iris_umap'], f)\n",
" \n",
" with open('models/umap_digits.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['digits_umap'], f)\n",
" \n",
" torch.save(iris_autoencoder.state_dict(), 'models/autoencoder_iris.pth')\n",
" torch.save(digits_autoencoder.state_dict(), 'models/autoencoder_digits.pth')\n",
" \n",
" # Save results summary\n",
" logging.info(\"Saving results summary\")\n",
" results_summary = {\n",
" 'timestamp': datetime.now().isoformat(),\n",
" 'datasets': {\n",
" 'iris': {\n",
" 'original_features': dr_suite.iris_data.shape[1],\n",
" 'samples': dr_suite.iris_data.shape[0],\n",
" 'classes': len(np.unique(dr_suite.iris_target))\n",
" },\n",
" 'digits': {\n",
" 'original_features': dr_suite.digits_data.shape[1],\n",
" 'samples': dr_suite.digits_data.shape[0],\n",
" 'classes': len(np.unique(dr_suite.digits_target))\n",
" }\n",
" },\n",
" 'pca_explained_variance': {\n",
" 'iris': dr_suite.results['iris_pca']['explained_variance'].tolist(),\n",
" 'digits': dr_suite.results['digits_pca']['explained_variance'].tolist()\n",
" },\n",
" 'evaluation_results': evaluation_results,\n",
" 'autoencoder_final_losses': {\n",
" 'iris': iris_losses[-1],\n",
" 'digits': digits_losses[-1]\n",
" }\n",
" }\n",
" \n",
" with open('results/dimensionality_reduction_summary.json', 'w') as f:\n",
" json.dump(results_summary, f, indent=2)\n",
" \n",
" # Print final summary\n",
" logging.info(\"=== FINAL SUMMARY ===\")\n",
" logging.info(f\"Iris Dataset - PCA Explained Variance: {dr_suite.results['iris_pca']['explained_variance']}\")\n",
" logging.info(f\"Digits Dataset - PCA Explained Variance: {dr_suite.results['digits_pca']['explained_variance']}\")\n",
" \n",
" for dataset in ['iris', 'digits']:\n",
" logging.info(f\"\\n{dataset.upper()} Dataset Classification Performance:\")\n",
" for method in ['pca', 'tsne', 'umap']:\n",
" result = evaluation_results[f'{dataset}_{method}']\n",
" logging.info(f\" {method.upper()}: {result['accuracy_retention']:.2f}% accuracy retention\")\n",
" \n",
" logging.info(\"\\nAll models saved to models/ directory\")\n",
" logging.info(\"All results saved to results/ directory\")\n",
" logging.info(\"All visualizations saved to visualizations/ directory\")\n",
" logging.info(\"Dimensionality Reduction Suite completed successfully!\")\n",
"\n",
"if __name__ == \"__main__\":\n",
" main()\n",
" "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ea6dd258-7eed-4e21-b9a0-388dfd1fd622",
"metadata": {},
"outputs": [],
"source": [
"# Import all necessary libraries for dimensionality reduction analysis\n",
"import numpy as np # Numerical computing foundation\n",
"import pandas as pd # Data manipulation (though we use sklearn datasets directly)\n",
"import matplotlib.pyplot as plt # Plotting library for static visualizations\n",
"import seaborn as sns # Statistical plotting enhancements\n",
"import plotly.express as px # Interactive plotting (not used but available)\n",
"import plotly.graph_objects as go # More complex interactive plots\n",
"from sklearn.datasets import load_iris, load_digits # Standard ML datasets\n",
"from sklearn.preprocessing import StandardScaler # Feature scaling (critical for DR)\n",
"from sklearn.decomposition import PCA # Principal Component Analysis\n",
"from sklearn.manifold import TSNE # t-Distributed Stochastic Neighbor Embedding\n",
"from sklearn.model_selection import train_test_split # Data splitting for evaluation\n",
"from sklearn.ensemble import RandomForestClassifier # Robust classifier for evaluation\n",
"from sklearn.metrics import accuracy_score, classification_report # Performance metrics\n",
"import umap # Uniform Manifold Approximation and Projection\n",
"import torch # PyTorch for neural network autoencoder\n",
"import torch.nn as nn # Neural network modules\n",
"import torch.optim as optim # Optimization algorithms\n",
"import pickle # Model serialization for sklearn models\n",
"import json # Results storage in human-readable format\n",
"import logging # Comprehensive logging instead of print statements\n",
"import os # Directory and file operations\n",
"from datetime import datetime # Timestamps for results\n",
"\n",
"# Configure logging to both file and console\n",
"# This replaces print statements and provides timestamps and log levels\n",
"logging.basicConfig(\n",
" level=logging.INFO, # Show INFO level and above\n",
" format='%(asctime)s - %(levelname)s - %(message)s', # Include timestamp\n",
" handlers=[\n",
" logging.FileHandler('dimensionality_reduction.log'), # Save to file\n",
" logging.StreamHandler() # Also display in console\n",
" ]\n",
")\n",
"\n",
"# Create directories for organized output storage\n",
"# exist_ok=True prevents errors if directories already exist\n",
"os.makedirs('results', exist_ok=True) # Numerical results and summaries\n",
"os.makedirs('models', exist_ok=True) # Trained models for reuse\n",
"os.makedirs('visualizations', exist_ok=True) # Generated plots\n",
"\n",
"class DimensionalityReductionSuite:\n",
" \"\"\"\n",
" Main class to organize all dimensionality reduction experiments\n",
" \n",
" Design Choice: Using a class to maintain state and organize methods\n",
" - Keeps related data and methods together\n",
" - Allows easy access to results across different methods\n",
" - Facilitates comparison and evaluation\n",
" \"\"\"\n",
" \n",
" def __init__(self):\n",
" \"\"\"Initialize storage for results and trained models\"\"\"\n",
" self.results = {} # Store transformed data and metrics\n",
" self.models = {} # Store trained models for reuse\n",
" \n",
" def load_and_prepare_data(self):\n",
" \"\"\"\n",
" Load standard datasets and prepare them for dimensionality reduction\n",
" \n",
" Dataset Choice Rationale:\n",
" - Iris: Low-dimensional (4 features), well-separated classes, good for understanding\n",
" - Digits: High-dimensional (64 features), more challenging, realistic scenario\n",
" \"\"\"\n",
" logging.info(\"Loading datasets for dimensionality reduction analysis\")\n",
" \n",
" # Load Iris dataset - classic 4D dataset with 3 flower species\n",
" iris = load_iris()\n",
" self.iris_data = iris.data # 150 samples × 4 features\n",
" self.iris_target = iris.target # Class labels (0, 1, 2)\n",
" self.iris_target_names = iris.target_names # ['setosa', 'versicolor', 'virginica']\n",
" self.iris_feature_names = iris.feature_names # Sepal/petal length/width\n",
" \n",
" logging.info(f\"Iris dataset loaded: {self.iris_data.shape} features, {len(np.unique(self.iris_target))} classes\")\n",
" \n",
" # Load Digits dataset - 8×8 pixel images of handwritten digits (0-9)\n",
" digits = load_digits()\n",
" self.digits_data = digits.data # 1797 samples × 64 features (flattened 8×8 images)\n",
" self.digits_target = digits.target # Digit labels (0-9)\n",
" self.digits_images = digits.images # Original 8×8 image format for visualization\n",
" \n",
" logging.info(f\"Digits dataset loaded: {self.digits_data.shape} features, {len(np.unique(self.digits_target))} classes\")\n",
" \n",
" # CRITICAL: Standardize the data before applying dimensionality reduction\n",
" # Why standardization is essential:\n",
" # 1. Features have different scales (e.g., sepal length vs width)\n",
" # 2. PCA is sensitive to feature scales - larger values dominate\n",
" # 3. Distance-based methods (t-SNE, UMAP) need comparable scales\n",
" # 4. Neural networks train better with normalized inputs\n",
" \n",
" self.scaler_iris = StandardScaler() # Create scaler for iris data\n",
" # fit_transform: (1) calculates mean and std, (2) applies transformation\n",
" self.iris_scaled = self.scaler_iris.fit_transform(self.iris_data)\n",
" \n",
" self.scaler_digits = StandardScaler() # Separate scaler for digits\n",
" self.digits_scaled = self.scaler_digits.fit_transform(self.digits_data)\n",
" \n",
" logging.info(\"Data standardization completed\")\n",
" \n",
" def apply_pca(self, data, dataset_name, n_components=2):\n",
" \"\"\"\n",
" Apply Principal Component Analysis\n",
" \n",
" PCA finds linear combinations of original features that explain maximum variance\n",
" \n",
" Parameters:\n",
" - data: Standardized input data\n",
" - dataset_name: For organizing results\n",
" - n_components: Number of dimensions to reduce to (2 for visualization)\n",
" \n",
" Design Choice: Using 2 components for easy visualization and comparison\n",
" \"\"\"\n",
" logging.info(f\"Applying PCA to {dataset_name} dataset\")\n",
" \n",
" # Create PCA object with specified number of components\n",
" pca = PCA(n_components=n_components)\n",
" \n",
" # fit_transform: (1) finds principal components, (2) projects data\n",
" data_pca = pca.fit_transform(data)\n",
" \n",
" # Extract variance information - crucial for understanding quality\n",
" explained_variance = pca.explained_variance_ratio_ # Proportion of variance per component\n",
" cumulative_variance = np.cumsum(explained_variance) # Running total of explained variance\n",
" \n",
" logging.info(f\"PCA completed for {dataset_name}\")\n",
" logging.info(f\"Explained variance per component: {explained_variance}\")\n",
" logging.info(f\"Cumulative explained variance: {cumulative_variance}\")\n",
" \n",
" # Store comprehensive results for later analysis\n",
" self.results[f'{dataset_name}_pca'] = {\n",
" 'transformed_data': data_pca, # Projected data points\n",
" 'explained_variance': explained_variance, # How much variance each PC explains\n",
" 'cumulative_variance': cumulative_variance, # Total variance captured\n",
" 'components': pca.components_ # The actual principal components (directions)\n",
" }\n",
" \n",
" # Store trained model for potential reuse (e.g., transforming new data)\n",
" self.models[f'{dataset_name}_pca'] = pca\n",
" \n",
" return data_pca, explained_variance\n",
" \n",
" def apply_tsne(self, data, dataset_name, n_components=2, perplexity=30):\n",
" \"\"\"\n",
" Apply t-Distributed Stochastic Neighbor Embedding\n",
" \n",
" t-SNE preserves local neighborhood structure, excellent for visualization\n",
" \n",
" Key Parameters:\n",
" - perplexity: Balance between local and global structure (typically 5-50)\n",
" - n_components: Output dimensions (2 or 3 for visualization)\n",
" \n",
" Important: t-SNE is non-linear and non-deterministic\n",
" \"\"\"\n",
" logging.info(f\"Applying t-SNE to {dataset_name} dataset with perplexity={perplexity}\")\n",
" \n",
" # Create t-SNE object with careful parameter selection\n",
" # random_state=42: Ensures reproducible results\n",
" # perplexity=30: Good default for most datasets (roughly sqrt(n_samples))\n",
" tsne = TSNE(n_components=n_components, perplexity=perplexity, random_state=42)\n",
" \n",
" # fit_transform: t-SNE doesn't have separate fit/transform like PCA\n",
" # It optimizes embedding directly from the data\n",
" data_tsne = tsne.fit_transform(data)\n",
" \n",
" logging.info(f\"t-SNE completed for {dataset_name}\")\n",
" # KL divergence: Lower values indicate better optimization\n",
" logging.info(f\"Final KL divergence: {tsne.kl_divergence_}\")\n",
" \n",
" # Store results (note: no reusable model for t-SNE)\n",
" self.results[f'{dataset_name}_tsne'] = {\n",
" 'transformed_data': data_tsne,\n",
" 'kl_divergence': tsne.kl_divergence_ # Quality metric\n",
" }\n",
" \n",
" return data_tsne\n",
" \n",
" def apply_umap(self, data, dataset_name, n_components=2, n_neighbors=15):\n",
" \"\"\"\n",
" Apply Uniform Manifold Approximation and Projection\n",
" \n",
" UMAP preserves both local and global structure better than t-SNE\n",
" \n",
" Key Parameters:\n",
" - n_neighbors: Size of local neighborhood (typically 5-50)\n",
" - n_components: Output dimensions\n",
" \n",
" Advantage: UMAP can transform new data (unlike t-SNE)\n",
" \"\"\"\n",
" logging.info(f\"Applying UMAP to {dataset_name} dataset with n_neighbors={n_neighbors}\")\n",
" \n",
" # Create UMAP reducer with balanced parameters\n",
" # n_neighbors=15: Good balance between local and global structure\n",
" # random_state=42: Reproducible results\n",
" umap_reducer = umap.UMAP(n_components=n_components, n_neighbors=n_neighbors, random_state=42)\n",
" \n",
" # fit_transform: UMAP learns mapping and applies it\n",
" data_umap = umap_reducer.fit_transform(data)\n",
" \n",
" logging.info(f\"UMAP completed for {dataset_name}\")\n",
" \n",
" # Store results and model (UMAP can transform new data)\n",
" self.results[f'{dataset_name}_umap'] = {\n",
" 'transformed_data': data_umap\n",
" }\n",
" \n",
" # Save model for potential reuse\n",
" self.models[f'{dataset_name}_umap'] = umap_reducer\n",
" \n",
" return data_umap\n",
"\n",
"class SimpleAutoencoder(nn.Module):\n",
" \"\"\"\n",
" Neural network autoencoder for dimensionality reduction\n",
" \n",
" Architecture Design Rationale:\n",
" - Encoder: Progressively reduces dimensions (input → 128 → 64 → encoding_dim)\n",
" - Decoder: Mirrors encoder in reverse (encoding_dim → 64 → 128 → input)\n",
" - ReLU activations: Introduce non-linearity while avoiding vanishing gradients\n",
" - No activation on final layer: Allows reconstruction of any real values\n",
" \n",
" Design Choice: Simple but effective architecture\n",
" - Avoids overly complex models that might not converge\n",
" - Sufficient capacity for the datasets used\n",
" - Easy to understand and modify\n",
" \"\"\"\n",
" \n",
" def __init__(self, input_dim, encoding_dim):\n",
" \"\"\"\n",
" Initialize autoencoder layers\n",
" \n",
" Parameters:\n",
" - input_dim: Original feature count (4 for iris, 64 for digits)\n",
" - encoding_dim: Compressed representation size\n",
" \"\"\"\n",
" super(SimpleAutoencoder, self).__init__()\n",
" \n",
" # Encoder: Compress input to lower dimensional representation\n",
" self.encoder = nn.Sequential(\n",
" nn.Linear(input_dim, 128), # First compression layer\n",
" nn.ReLU(), # Non-linear activation\n",
" nn.Linear(128, 64), # Second compression layer\n",
" nn.ReLU(), # Non-linear activation\n",
" nn.Linear(64, encoding_dim) # Final encoding layer (no activation)\n",
" )\n",
" \n",
" # Decoder: Reconstruct original input from encoding\n",
" self.decoder = nn.Sequential(\n",
" nn.Linear(encoding_dim, 64), # Start expanding\n",
" nn.ReLU(), # Non-linear activation\n",
" nn.Linear(64, 128), # Continue expanding\n",
" nn.ReLU(), # Non-linear activation\n",
" nn.Linear(128, input_dim) # Final reconstruction (no activation)\n",
" )\n",
" \n",
" def forward(self, x):\n",
" \"\"\"\n",
" Forward pass through autoencoder\n",
" \n",
" Returns both decoded output and encoded representation\n",
" This allows us to use the encoded representation for dimensionality reduction\n",
" \"\"\"\n",
" encoded = self.encoder(x) # Compress input\n",
" decoded = self.decoder(encoded) # Reconstruct from compression\n",
" return decoded, encoded\n",
"\n",
"def train_autoencoder(data, dataset_name, encoding_dim=10, epochs=100, lr=0.001):\n",
" \"\"\"\n",
" Train autoencoder for dimensionality reduction\n",
" \n",
" Training Process:\n",
" 1. Convert data to PyTorch tensors\n",
" 2. Initialize model, loss function, and optimizer\n",
" 3. Training loop: forward pass → loss calculation → backpropagation\n",
" 4. Extract final encoded representations\n",
" \n",
" Hyperparameter Choices:\n",
" - epochs=100: Sufficient for convergence on small datasets\n",
" - lr=0.001: Conservative learning rate to avoid instability\n",
" - Adam optimizer: Adaptive learning rate, good default choice\n",
" - MSE loss: Appropriate for reconstruction tasks\n",
" \"\"\"\n",
" logging.info(f\"Training autoencoder for {dataset_name} dataset\")\n",
" logging.info(f\"Input dimension: {data.shape[1]}, Encoding dimension: {encoding_dim}\")\n",
" \n",
" # Convert numpy array to PyTorch tensor\n",
" # FloatTensor: Standard data type for neural networks\n",
" data_tensor = torch.FloatTensor(data)\n",
" \n",
" # Initialize model with appropriate dimensions\n",
" model = SimpleAutoencoder(data.shape[1], encoding_dim)\n",
" \n",
" # Loss function: Mean Squared Error for reconstruction\n",
" # Measures average squared difference between input and reconstruction\n",
" criterion = nn.MSELoss()\n",
" \n",
" # Optimizer: Adam with learning rate\n",
" # Adam adapts learning rate per parameter, generally robust\n",
" optimizer = optim.Adam(model.parameters(), lr=lr)\n",
" \n",
" # Track training progress\n",
" losses = []\n",
" \n",
" # Training loop\n",
" for epoch in range(epochs):\n",
" # Reset gradients (PyTorch accumulates gradients by default)\n",
" optimizer.zero_grad()\n",
" \n",
" # Forward pass: get reconstruction and encoding\n",
" reconstructed, encoded = model(data_tensor)\n",
" \n",
" # Calculate reconstruction loss\n",
" # Goal: minimize difference between input and reconstruction\n",
" loss = criterion(reconstructed, data_tensor)\n",
" \n",
" # Backward pass: calculate gradients\n",
" loss.backward()\n",
" \n",
" # Update model parameters\n",
" optimizer.step()\n",
" \n",
" # Store loss for monitoring\n",
" losses.append(loss.item())\n",
" \n",
" # Periodic logging to monitor training progress\n",
" if (epoch + 1) % 20 == 0:\n",
" logging.info(f\"Epoch {epoch+1}/{epochs}, Loss: {loss.item():.6f}\")\n",
" \n",
" # Extract final encoded representations for dimensionality reduction\n",
" with torch.no_grad(): # Disable gradient computation for inference\n",
" _, final_encoded = model(data_tensor)\n",
" final_encoded = final_encoded.numpy() # Convert back to numpy\n",
" \n",
" logging.info(f\"Autoencoder training completed for {dataset_name}\")\n",
" logging.info(f\"Final reconstruction loss: {losses[-1]:.6f}\")\n",
" \n",
" return final_encoded, model, losses\n",
"\n",
"def evaluate_dimensionality_reduction(original_data, reduced_data, target, dataset_name, method_name):\n",
" \"\"\"\n",
" Evaluate quality of dimensionality reduction using downstream classification\n",
" \n",
" Evaluation Strategy:\n",
" 1. Train classifier on original high-dimensional data\n",
" 2. Train classifier on reduced low-dimensional data\n",
" 3. Compare classification accuracies\n",
" 4. High accuracy retention indicates good dimensionality reduction\n",
" \n",
" Why This Evaluation Makes Sense:\n",
" - Tests whether important information is preserved\n",
" - Uses realistic downstream task (classification)\n",
" - Provides interpretable metric (accuracy retention percentage)\n",
" \"\"\"\n",
" logging.info(f\"Evaluating {method_name} performance on {dataset_name} dataset\")\n",
" \n",
" # Split data consistently for fair comparison\n",
" # stratify=target: Ensures balanced class distribution in train/test sets\n",
" # random_state=42: Reproducible splits\n",
" X_train_orig, X_test_orig, y_train, y_test = train_test_split(\n",
" original_data, target, test_size=0.3, random_state=42, stratify=target\n",
" )\n",
" \n",
" # Split reduced data with identical split (same random_state)\n",
" X_train_red, X_test_red, _, _ = train_test_split(\n",
" reduced_data, target, test_size=0.3, random_state=42, stratify=target\n",
" )\n",
" \n",
" # Train Random Forest classifiers\n",
" # Random Forest Choice: Robust, handles different feature types well, good baseline\n",
" rf_orig = RandomForestClassifier(random_state=42) # For original data\n",
" rf_red = RandomForestClassifier(random_state=42) # For reduced data\n",
" \n",
" # Train both classifiers\n",
" rf_orig.fit(X_train_orig, y_train)\n",
" rf_red.fit(X_train_red, y_train)\n",
" \n",
" # Evaluate performance\n",
" acc_orig = accuracy_score(y_test, rf_orig.predict(X_test_orig))\n",
" acc_red = accuracy_score(y_test, rf_red.predict(X_test_red))\n",
" \n",
" # Log results with clear interpretation\n",
" logging.info(f\"Original data accuracy: {acc_orig:.4f}\")\n",
" logging.info(f\"Reduced data accuracy: {acc_red:.4f}\")\n",
" logging.info(f\"Accuracy retention: {(acc_red/acc_orig)*100:.2f}%\")\n",
" \n",
" # Return structured results\n",
" return {\n",
" 'original_accuracy': acc_orig,\n",
" 'reduced_accuracy': acc_red,\n",
" 'accuracy_retention': (acc_red/acc_orig)*100 # Key metric for comparison\n",
" }\n",
"\n",
"def create_visualizations(dr_suite):\n",
" \"\"\"\n",
" Generate comprehensive visualizations comparing all methods\n",
" \n",
" Visualization Strategy:\n",
" 1. PCA explained variance plots - understand information retention\n",
" 2. Side-by-side method comparisons - visual quality assessment\n",
" 3. Dataset-specific plots - accommodate different characteristics\n",
" \n",
" Design Choices:\n",
" - High DPI (300) for publication quality\n",
" - Consistent color schemes for easy comparison\n",
" - Clear titles and labels for interpretation\n",
" \"\"\"\n",
" logging.info(\"Creating comprehensive visualizations\")\n",
" \n",
" # 1. PCA Explained Variance Analysis\n",
" # Shows how much information each principal component captures\n",
" plt.figure(figsize=(12, 5))\n",
" \n",
" # Iris dataset explained variance\n",
" plt.subplot(1, 2, 1)\n",
" iris_pca_var = dr_suite.results['iris_pca']['explained_variance']\n",
" plt.bar(range(1, len(iris_pca_var)+1), iris_pca_var)\n",
" plt.title('Iris Dataset - PCA Explained Variance')\n",
" plt.xlabel('Principal Component')\n",
" plt.ylabel('Explained Variance Ratio')\n",
" # Add percentage labels on bars for clarity\n",
" for i, v in enumerate(iris_pca_var):\n",
" plt.text(i+1, v + 0.01, f'{v:.1%}', ha='center')\n",
" \n",
" # Digits dataset explained variance\n",
" plt.subplot(1, 2, 2)\n",
" digits_pca_var = dr_suite.results['digits_pca']['explained_variance']\n",
" plt.bar(range(1, len(digits_pca_var)+1), digits_pca_var)\n",
" plt.title('Digits Dataset - PCA Explained Variance')\n",
" plt.xlabel('Principal Component')\n",
" plt.ylabel('Explained Variance Ratio')\n",
" # Add percentage labels on bars\n",
" for i, v in enumerate(digits_pca_var):\n",
" plt.text(i+1, v + 0.002, f'{v:.1%}', ha='center')\n",
" \n",
" plt.tight_layout()\n",
" plt.savefig('visualizations/pca_explained_variance.png', dpi=300, bbox_inches='tight')\n",
" plt.close() # Close figure to free memory\n",
" \n",
" # 2. Iris Dataset Method Comparison\n",
" # 2×2 grid showing different dimensionality reduction results\n",
" fig, axes = plt.subplots(2, 2, figsize=(15, 12))\n",
" \n",
" # Original data visualization (using first 2 features)\n",
" axes[0, 0].scatter(dr_suite.iris_data[:, 0], dr_suite.iris_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[0, 0].set_title('Original Data (First 2 Features)')\n",
" axes[0, 0].set_xlabel('Sepal Length')\n",
" axes[0, 0].set_ylabel('Sepal Width')\n",
" # Add colorbar to show class mapping\n",
" \n",
" # PCA results\n",
" pca_data = dr_suite.results['iris_pca']['transformed_data']\n",
" scatter1 = axes[0, 1].scatter(pca_data[:, 0], pca_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[0, 1].set_title('PCA Reduction')\n",
" axes[0, 1].set_xlabel('PC1')\n",
" axes[0, 1].set_ylabel('PC2')\n",
" \n",
" # t-SNE results\n",
" tsne_data = dr_suite.results['iris_tsne']['transformed_data']\n",
" axes[1, 0].scatter(tsne_data[:, 0], tsne_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[1, 0].set_title('t-SNE Reduction')\n",
" axes[1, 0].set_xlabel('t-SNE 1')\n",
" axes[1, 0].set_ylabel('t-SNE 2')\n",
" \n",
" # UMAP results\n",
" umap_data = dr_suite.results['iris_umap']['transformed_data']\n",
" axes[1, 1].scatter(umap_data[:, 0], umap_data[:, 1], \n",
" c=dr_suite.iris_target, cmap='viridis', alpha=0.7)\n",
" axes[1, 1].set_title('UMAP Reduction')\n",
" axes[1, 1].set_xlabel('UMAP 1')\n",
" axes[1, 1].set_ylabel('UMAP 2')\n",
" \n",
" plt.tight_layout()\n",
" plt.savefig('visualizations/iris_comparison.png', dpi=300, bbox_inches='tight')\n",
" plt.close()\n",
" \n",
" # 3. Digits Dataset Visualization\n",
" # More challenging due to higher dimensionality and more classes\n",
" fig, axes = plt.subplots(2, 2, figsize=(15, 12))\n",
" \n",
" # Show sample original digit\n",
" axes[0, 0].imshow(dr_suite.digits_images[0], cmap='gray')\n",
" axes[0, 0].set_title('Original Digit Images (8×8 pixels)')\n",
" axes[0, 0].axis('off') # Remove axes for cleaner image display\n",
" \n",
" # PCA results for digits\n",
" pca_data = dr_suite.results['digits_pca']['transformed_data']\n",
" scatter2 = axes[0, 1].scatter(pca_data[:, 0], pca_data[:, 1], \n",
" c=dr_suite.digits_target, cmap='tab10', alpha=0.7)\n",
" axes[0, 1].set_title('PCA - Digits Dataset')\n",
" axes[0, 1].set_xlabel('PC1')\n",
" axes[0, 1].set_ylabel('PC2')\n",
" \n",
" # t-SNE results for digits\n",
" tsne_data = dr_suite.results['digits_tsne']['transformed_data']\n",
" axes[1, 0].scatter(tsne_data[:, 0], tsne_data[:, 1], \n",
" c=dr_suite.digits_target, cmap='tab10', alpha=0.7)\n",
" axes[1, 0].set_title('t-SNE - Digits Dataset')\n",
" axes[1, 0].set_xlabel('t-SNE 1')\n",
" axes[1, 0].set_ylabel('t-SNE 2')\n",
" \n",
" # UMAP results for digits\n",
" umap_data = dr_suite.results['digits_umap']['transformed_data']\n",
" axes[1, 1].scatter(umap_data[:, 0], umap_data[:, 1], \n",
" c=dr_suite.digits_target, cmap='tab10', alpha=0.7)\n",
" axes[1, 1].set_title('UMAP - Digits Dataset')\n",
" axes[1, 1].set_xlabel('UMAP 1')\n",
" axes[1, 1].set_ylabel('UMAP 2')\n",
" \n",
" plt.tight_layout()\n",
" plt.savefig('visualizations/digits_comparison.png', dpi=300, bbox_inches='tight')\n",
" plt.close()\n",
" \n",
" logging.info(\"All visualizations saved to visualizations/ directory\")\n",
"\n",
"def main():\n",
" \"\"\"\n",
" Main execution function that orchestrates the entire analysis\n",
" \n",
" Execution Flow:\n",
" 1. Initialize suite and load data\n",
" 2. Apply all dimensionality reduction methods\n",
" 3. Evaluate performance using classification\n",
" 4. Generate visualizations\n",
" 5. Save models and results\n",
" 6. Provide comprehensive summary\n",
" \n",
" Design Choice: Structured workflow ensures reproducibility and completeness\n",
" \"\"\"\n",
" logging.info(\"Starting Dimensionality Reduction Suite\")\n",
" \n",
" # Initialize the comprehensive suite\n",
" dr_suite = DimensionalityReductionSuite()\n",
" \n",
" # Step 1: Data preparation\n",
" dr_suite.load_and_prepare_data()\n",
" \n",
" # Step 2: Apply linear method (PCA)\n",
" logging.info(\"=== APPLYING PCA ===\")\n",
" # Apply to both datasets with 2 components for comparison\n",
" dr_suite.apply_pca(dr_suite.iris_scaled, 'iris', n_components=2)\n",
" dr_suite.apply_pca(dr_suite.digits_scaled, 'digits', n_components=2)\n",
" \n",
" # Step 3: Apply non-linear manifold learning (t-SNE)\n",
" logging.info(\"=== APPLYING t-SNE ===\")\n",
" # Use consistent parameters across datasets\n",
" dr_suite.apply_tsne(dr_suite.iris_scaled, 'iris', perplexity=30)\n",
" dr_suite.apply_tsne(dr_suite.digits_scaled, 'digits', perplexity=30)\n",
" \n",
" # Step 4: Apply modern manifold learning (UMAP)\n",
" logging.info(\"=== APPLYING UMAP ===\")\n",
" # UMAP often provides good balance of local and global structure\n",
" dr_suite.apply_umap(dr_suite.iris_scaled, 'iris', n_neighbors=15)\n",
" dr_suite.apply_umap(dr_suite.digits_scaled, 'digits', n_neighbors=15)\n",
" \n",
" # Step 5: Apply neural network approach (Autoencoder)\n",
" logging.info(\"=== APPLYING AUTOENCODER ===\")\n",
" # Different encoding dimensions based on dataset complexity\n",
" iris_encoded, iris_autoencoder, iris_losses = train_autoencoder(\n",
" dr_suite.iris_scaled, 'iris', encoding_dim=2, epochs=50, lr=0.001\n",
" )\n",
" \n",
" digits_encoded, digits_autoencoder, digits_losses = train_autoencoder(\n",
" dr_suite.digits_scaled, 'digits', encoding_dim=10, epochs=100, lr=0.001\n",
" )\n",
" \n",
" # Store autoencoder results in consistent format\n",
" dr_suite.results['iris_autoencoder'] = {\n",
" 'transformed_data': iris_encoded,\n",
" 'training_losses': iris_losses\n",
" }\n",
" \n",
" dr_suite.results['digits_autoencoder'] = {\n",
" 'transformed_data': digits_encoded,\n",
" 'training_losses': digits_losses\n",
" }\n",
" \n",
" # Step 6: Comprehensive evaluation\n",
" logging.info(\"=== EVALUATING METHODS ===\")\n",
" evaluation_results = {}\n",
" \n",
" # Evaluate traditional methods on both datasets\n",
" methods = ['pca', 'tsne', 'umap'] # Methods that work with 2D output\n",
" \n",
" # Iris dataset evaluation\n",
" for method in methods:\n",
" eval_result = evaluate_dimensionality_reduction(\n",
" dr_suite.iris_scaled, # Original standardized data\n",
" dr_suite.results[f'iris_{method}']['transformed_data'], # Reduced data\n",
" dr_suite.iris_target, # Class labels for classification\n",
" 'iris', # Dataset name\n",
" method.upper() # Method name for logging\n",
" )\n",
" evaluation_results[f'iris_{method}'] = eval_result\n",
" \n",
" # Digits dataset evaluation\n",
" for method in methods:\n",
" eval_result = evaluate_dimensionality_reduction(\n",
" dr_suite.digits_scaled,\n",
" dr_suite.results[f'digits_{method}']['transformed_data'],\n",
" dr_suite.digits_target,\n",
" 'digits',\n",
" method.upper()\n",
" )\n",
" evaluation_results[f'digits_{method}'] = eval_result\n",
" \n",
" # Step 7: Generate comprehensive visualizations\n",
" create_visualizations(dr_suite)\n",
" \n",
" # Step 8: Save all trained models for future use\n",
" logging.info(\"Saving trained models\")\n",
" \n",
" # Save sklearn models using pickle (standard approach)\n",
" with open('models/pca_iris.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['iris_pca'], f)\n",
" \n",
" with open('models/pca_digits.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['digits_pca'], f)\n",
" \n",
" with open('models/umap_iris.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['iris_umap'], f)\n",
" \n",
" with open('models/umap_digits.pkl', 'wb') as f:\n",
" pickle.dump(dr_suite.models['digits_umap'], f)\n",
" \n",
" # Save PyTorch models using torch.save (state dictionaries)\n",
" torch.save(iris_autoencoder.state_dict(), 'models/autoencoder_iris.pth')\n",
" torch.save(digits_autoencoder.state_dict(), 'models/autoencoder_digits.pth')\n",
" \n",
" # Step 9: Create comprehensive results summary\n",
" logging.info(\"Saving results summary\")\n",
" results_summary = {\n",
" 'timestamp': datetime.now().isoformat(), # When analysis was run\n",
" 'datasets': {\n",
" 'iris': {\n",
" 'original_features': dr_suite.iris_data.shape[1],\n",
" 'samples': dr_suite.iris_data.shape[0],\n",
" 'classes': len(np.unique(dr_suite.iris_target))\n",
" },\n",
" 'digits': {\n",
" 'original_features': dr_suite.digits_data.shape[1],\n",
" 'samples': dr_suite.digits_data.shape[0],\n",
" 'classes': len(np.unique(dr_suite.digits_target))\n",
" }\n",
" },\n",
" # PCA explained variance is crucial for understanding information retention\n",
" 'pca_explained_variance': {\n",
" 'iris': dr_suite.results['iris_pca']['explained_variance'].tolist(),\n",
" 'digits': dr_suite.results['digits_pca']['explained_variance'].tolist()\n",
" },\n",
" # Classification performance comparison across all methods\n",
" 'evaluation_results': evaluation_results,\n",
" # Autoencoder training convergence metrics\n",
" 'autoencoder_final_losses': {\n",
" 'iris': iris_losses[-1], # Final reconstruction loss for iris\n",
" 'digits': digits_losses[-1] # Final reconstruction loss for digits\n",
" }\n",
" }\n",
" \n",
" # Save as JSON for easy reading and further analysis\n",
" with open('results/dimensionality_reduction_summary.json', 'w') as f:\n",
" json.dump(results_summary, f, indent=2) # indent=2 for readability\n",
" \n",
" # Step 10: Print comprehensive summary to console and log\n",
" logging.info(\"=== FINAL SUMMARY ===\")\n",
" \n",
" # PCA explained variance summary\n",
" logging.info(f\"Iris Dataset - PCA Explained Variance: {dr_suite.results['iris_pca']['explained_variance']}\")\n",
" logging.info(f\"Digits Dataset - PCA Explained Variance: {dr_suite.results['digits_pca']['explained_variance']}\")\n",
" \n",
" # Classification performance summary for easy comparison\n",
" for dataset in ['iris', 'digits']:\n",
" logging.info(f\"\\n{dataset.upper()} Dataset Classification Performance:\")\n",
" for method in ['pca', 'tsne', 'umap']:\n",
" result = evaluation_results[f'{dataset}_{method}']\n",
" logging.info(f\" {method.upper()}: {result['accuracy_retention']:.2f}% accuracy retention\")\n",
" \n",
" # Final status messages\n",
" logging.info(\"\\nAll models saved to models/ directory\")\n",
" logging.info(\"All results saved to results/ directory\") \n",
" logging.info(\"All visualizations saved to visualizations/ directory\")\n",
" logging.info(\"Dimensionality Reduction Suite completed successfully!\")\n",
"\n",
"# Execute the main function when script is run directly\n",
"if __name__ == \"__main__\":\n",
" main()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.5"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
|