{"id":3606,"date":"2023-07-16T14:11:02","date_gmt":"2023-07-16T14:11:02","guid":{"rendered":"https:\/\/statorials.org\/my\/python-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-multidimensional-scaling\/"},"modified":"2023-07-16T14:11:02","modified_gmt":"2023-07-16T14:11:02","slug":"python-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-multidimensional-scaling","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/python-%e1%80%90%e1%80%bd%e1%80%84%e1%80%ba-multidimensional-scaling\/","title":{"rendered":"Python \u1010\u103d\u1004\u103a multidimensional scaling \u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038"},"content":{"rendered":"

<\/p>\n

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\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a\u104a \u1018\u1000\u103a\u1005\u102f\u1036\u1005\u1000\u1031\u1038\u1001\u103b\u1032\u1037\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a<\/strong> \u1005\u102d\u1010\u1039\u1010\u1007 Cartesian space (\u1019\u103b\u102c\u1038\u101e\u1031\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a 2D \u1021\u102c\u1000\u102c\u101e) \u101b\u103e\u102d \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u101b\u103e\u102d \u1005\u1030\u1038\u1005\u1019\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f \u1010\u1030\u100a\u102e\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n

Python \u1010\u103d\u1004\u103a multidimensional scaling \u101c\u102f\u1015\u103a\u101b\u1014\u103a \u1021\u101c\u103d\u101a\u103a\u1000\u1030\u1006\u102f\u1036\u1038\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103e\u102c sklearn.manifold<\/strong> submodule \u104f MDS()<\/strong> function \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u101e\u100a\u103a \u1024\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1021\u101e\u102f\u1036\u1038\u1001\u103b\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n

\u1025\u1015\u1019\u102c- Python \u1010\u103d\u1004\u103a Multidimensional Scaling<\/strong><\/span><\/h2>\n

\u1021\u1019\u103b\u102d\u102f\u1038\u1019\u103b\u102d\u102f\u1038\u101e\u1031\u102c \u1018\u1010\u103a\u1005\u1000\u1010\u103a\u1018\u1031\u102c\u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1015\u1014\u103a\u1012\u102b DataFrame \u101b\u103e\u102d\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n

 import<\/span> pandas as<\/span> pd\n\n#create DataFrane\n<\/span>df = pd. DataFrame<\/span> ({' player<\/span> ': ['A', 'B', 'C', 'D', 'E', 'F', 'G', 'H', 'I', 'J', 'K '],\n                   ' points<\/span> ': [4, 4, 6, 7, 8, 14, 16, 19, 25, 25, 28],\n                   ' assists<\/span> ': [3, 2, 2, 5, 4, 8, 7, 6, 8, 10, 11],\n                   ' blocks<\/span> ': [7, 3, 6, 7, 5, 8, 8, 4, 2, 2, 1],\n                   ' rebounds<\/span> ': [4, 5, 5, 6, 5, 8, 10, 4, 3, 2, 2]})\n\n#set player column as index column\n<\/span>df = df. set_index<\/span> (' player<\/span> ')\n\n#view Dataframe\n<\/span>print<\/span> (df)\n\n        points assists blocks rebounds\nplayer                                   \nA 4 3 7 4\nB 4 2 3 5\nC 6 2 6 5\nD 7 5 7 6\nE 8 4 5 5\nF 14 8 8 8\nG 16 7 8 10\nH 19 6 4 4\nI 25 8 2 3\nD 25 10 2 2\nK 28 11 1 2\n<\/strong><\/pre>\n
 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a sklearn.manifold<\/strong> module \u104f MDS()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1016\u103c\u1004\u1037\u103a \u1018\u1000\u103a\u1005\u102f\u1036\u1005\u1000\u1031\u1038\u1001\u103b\u1032\u1037\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n
 from<\/span> sklearn. manifold<\/span> import<\/span> MDS\n\n#perform multi-dimensional scaling\n<\/span>mds = MDS(random_state= 0<\/span> )\nscaled_df = mds. fit_transform<\/span> (df)\n\n#view results of multi-dimensional scaling\n<\/span>print<\/span> (scaled_df)\n\n[[ 7.43654469 8.10247222]\n [4.13193821 10.27360901]\n [5.20534681 7.46919526]\n [6.22323046 4.45148627]\n [3.74110999 5.25591459]\n [3.69073384 -2.88017811]\n [3.89092087 -5.19100988]\n [ -3.68593169 -3.0821144 ]\n [ -9.13631889 -6.81016012]\n [ -8.97898385 -8.50414387]\n [-12.51859044 -9.08507097]]<\/span><\/span><\/strong><\/pre>\n
 \u1019\u1030\u101b\u1004\u103a\u1038 DataFrame \u104f\u1021\u1010\u1014\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f (x\u104a y) \u101e\u103c\u1012\u102d\u1014\u102d\u1010\u103a\u1010\u1005\u103a\u1001\u102f\u101e\u102d\u102f\u1037 \u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n
 2D space \u1010\u103d\u1004\u103a \u1024\u101e\u103c\u1012\u102d\u1014\u102d\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span> <\/p>\n
 import<\/span> matplotlib.pyplot as<\/span> plt\n\n#create scatterplot\n<\/span>plt. scatter<\/span> (scaled_df[:,0], scaled_df[:,1])\n\n#add axis labels\n<\/span>plt. xlabel<\/span> (' Coordinate 1<\/span> ')\nplt. ylabel<\/span> (' Coordinate 2<\/span> ')\n\n#add lables to each point\n<\/span>for<\/span> i, txt in<\/span> enumerate( df.index<\/span> ):\n    plt. annotate<\/span> (txt, (scaled_df[:,0][i]+.3, scaled_df[:,1][i]))\n\n#display scatterplot\n<\/span>plt. show<\/span> ()\n<\/strong><\/pre>\n
\"Python<\/p>\n
 \u1019\u1030\u101b\u1004\u103a\u1038\u1000\u1031\u102c\u103a\u101c\u1036\u101c\u1031\u1038\u1001\u102f\u1010\u103d\u1004\u103a \u1021\u101c\u102c\u1038\u1010\u1030\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u101b\u103e\u102d\u101e\u100a\u1037\u103a \u1019\u1030\u101b\u1004\u103a\u1038 DataFrame \u101b\u103e\u102d \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038 (points, assists, blocks, and rebounds) \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1007\u102c\u1010\u103a\u1000\u103d\u1000\u103a\u1011\u1032\u1010\u103d\u1004\u103a \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f \u1014\u102e\u1038\u1000\u1015\u103a\u1014\u1031\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n
 \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038 F<\/strong> \u1014\u103e\u1004\u1037\u103a G<\/strong> \u101e\u100a\u103a \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f \u1015\u102d\u1010\u103a\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1024\u101e\u100a\u103a\u1019\u103e\u102c \u1019\u1030\u101b\u1004\u103a\u1038 DataFrame \u1019\u103e \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u104f \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n
 #select rows with index labels 'F' and 'G'\ndf. loc<\/span> [[' F<\/span> ',' G<\/span> ']]\n\n        points assists blocks rebounds\nplayer\t\t\t\t\nF 14 8 8 8\nG 16 7 8 10\n<\/span><\/span><\/strong><\/pre>\n
 \u1021\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u104a \u1021\u1000\u1030\u1021\u100a\u102e\u1019\u103b\u102c\u1038\u104a \u101c\u102f\u1015\u103a\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1015\u103c\u1014\u103a\u101c\u103e\u1014\u103a\u1001\u103c\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a 2D \u1007\u102c\u1010\u103a\u1000\u103d\u1000\u103a\u1010\u103d\u1004\u103a \u1021\u1018\u101a\u103a\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u101c\u103d\u1014\u103a\u1014\u102e\u1038\u1000\u1015\u103a\u1014\u1031\u1000\u103c\u101e\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n
 \u1006\u1014\u1037\u103a\u1000\u103b\u1004\u103a\u1018\u1000\u103a\u1021\u1014\u1031\u1014\u103e\u1004\u1037\u103a\u104a \u1007\u102c\u1010\u103a\u1000\u103d\u1000\u103a\u1011\u1032\u1010\u103d\u1004\u103a \u101d\u1031\u1038\u1000\u103d\u102c\u1014\u1031\u101e\u1031\u102c \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038 B<\/strong> \u1014\u103e\u1004\u1037\u103a K<\/strong> \u1000\u102d\u102f \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1005\u1009\u103a\u1038\u1005\u102c\u1038\u1015\u102b\u104b<\/span><\/p>\n
 \u1019\u1030\u101b\u1004\u103a\u1038 DataFrame \u1010\u103d\u1004\u103a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u104f\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u1015\u102b\u1000\u104a \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n
 #select rows with index labels 'B' and 'K'\ndf. loc<\/span> [[' B<\/span> ',' K<\/span> ']]<\/span><\/span>\n\n        points assists blocks rebounds\nplayer\t\t\t\t\nB 4 2 3 5\nK 28 11 1 2<\/strong><\/pre>\n
 \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a 2D \u1007\u102c\u1010\u103a\u1000\u103d\u1000\u103a\u101e\u100a\u103a DataFframe \u101b\u103e\u102d \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u1010\u103d\u1004\u103a \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1010\u1005\u103a\u1026\u1038\u1005\u102e\u1014\u103e\u1004\u1037\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1006\u1004\u103a\u1010\u1030\u101e\u100a\u103a\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u101e\u1031\u102c\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n
 \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u101b\u103e\u102d\u101e\u100a\u1037\u103a \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1007\u102c\u1010\u103a\u1000\u103d\u1000\u103a\u1011\u1032\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u101b\u103e\u102d\u101e\u100a\u1037\u103a \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1005\u103a\u1026\u1038\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1026\u1038 \u101d\u1031\u1038\u1000\u103d\u102c\u1014\u1031\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u1010\u1030\u1010\u1000\u103d \u1021\u102f\u1015\u103a\u1005\u102f\u1016\u103d\u1032\u1037\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n
 \u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n
 \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a Python \u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1021\u101e\u102f\u1036\u1038\u1019\u103b\u102c\u1038\u101e\u1031\u102c \u1021\u101c\u102f\u1015\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a-<\/span><\/p>\n
 Python \u1010\u103d\u1004\u103a\u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1005\u103a\u1021\u1031\u102c\u1004\u103a\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038<\/a>
 Python \u101b\u103e\u102d Outliers \u1000\u102d\u102f\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1016\u101a\u103a\u101b\u103e\u102c\u1038\u1014\u100a\u103a\u1038<\/a>
 Python \u1010\u103d\u1004\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1021\u1010\u103d\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u100a\u103a\u1038<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a\u104a \u1018\u1000\u103a\u1005\u102f\u1036\u1005\u1000\u1031\u1038\u1001\u103b\u1032\u1037\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1005\u102d\u1010\u1039\u1010\u1007 Cartesian space (\u1019\u103b\u102c\u1038\u101e\u1031\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a 2D \u1021\u102c\u1000\u102c\u101e) \u101b\u103e\u102d \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u101b\u103e\u102d \u1005\u1030\u1038\u1005\u1019\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f \u1010\u1030\u100a\u102e\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b Python \u1010\u103d\u1004\u103a multidimensional scaling \u101c\u102f\u1015\u103a\u101b\u1014\u103a \u1021\u101c\u103d\u101a\u103a\u1000\u1030\u1006\u102f\u1036\u1038\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103e\u102c sklearn.manifold submodule \u104f MDS() function \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u101e\u100a\u103a \u1024\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1021\u101e\u102f\u1036\u1038\u1001\u103b\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c- Python \u1010\u103d\u1004\u103a Multidimensional Scaling \u1021\u1019\u103b\u102d\u102f\u1038\u1019\u103b\u102d\u102f\u1038\u101e\u1031\u102c \u1018\u1010\u103a\u1005\u1000\u1010\u103a\u1018\u1031\u102c\u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1015\u1014\u103a\u1012\u102b DataFrame \u101b\u103e\u102d\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b import pandas as pd #create DataFrane df = pd. 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