{"id":22039517,"url":"https://github.com/mpolinowski/isometric-mapping","last_synced_at":"2026-05-06T22:02:48.866Z","repository":{"id":234831422,"uuid":"627278064","full_name":"mpolinowski/isometric-mapping","owner":"mpolinowski","description":"Non-linear dimensionality reduction through Isometric Mapping","archived":false,"fork":false,"pushed_at":"2023-04-13T06:26:22.000Z","size":437,"stargazers_count":1,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-01-28T19:17:43.755Z","etag":null,"topics":["isomap","matplotlib-pyplot","python","scikit-learn"],"latest_commit_sha":null,"homepage":"https://mpolinowski.github.io/docs/IoT-and-Machine-Learning/ML/2023-04-13-isometric-mapping/2023-04-13","language":"Jupyter 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Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"---\njupyter:\n  jupytext:\n    formats: ipynb,md\n    text_representation:\n      extension: .md\n      format_name: markdown\n      format_version: '1.3'\n      jupytext_version: 1.14.4\n  kernelspec:\n    display_name: Python 3 (ipykernel)\n    language: python\n    name: python3\n---\n\n# Isometric Mapping (ISOMAP)\n\nNon-linear dimensionality reduction through Isometric Mapping\n\n```python\nimport matplotlib.pyplot as plt\nfrom mpl_toolkits.mplot3d import Axes3D\nimport pandas as pd\nimport seaborn as sns\nfrom sklearn.preprocessing import MinMaxScaler\nfrom sklearn.manifold import Isomap\n```\n\n```python\nraw_data = pd.read_csv('data/A_multivariate_study_of_variation_in_two_species_of_rock_crab_of_genus_Leptograpsus.csv')\n\ndata = raw_data.rename(columns={\n    'sp': 'Species',\n    'sex': 'Sex',\n    'index': 'Index',\n    'FL': 'Frontal Lobe',\n    'RW': 'Rear Width',\n    'CL': 'Carapace Midline',\n    'CW': 'Maximum Width',\n    'BD': 'Body Depth'})\n\ndata['Species'] = data['Species'].map({'B':'Blue', 'O':'Orange'})\ndata['Sex'] = data['Sex'].map({'M':'Male', 'F':'Female'})\ndata['Class'] = data.Species + data.Sex\n\ndata_columns = ['Frontal Lobe',\n                'Rear Width',\n                'Carapace Midline',\n                'Maximum Width',\n                'Body Depth']\n\ndata.head()\n```\n\n```python\n# generate a class variable for all 4 classes\ndata['Class'] = data.Species + data.Sex\n\nprint(data['Class'].value_counts())\ndata.head(5)\n```\n\n|    | Species | Sex | Index | Frontal Lobe | Rear Width | Carapace Midline | Maximum Width | Body Depth | Class |\n| -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |\n| 0 | Blue | Male | 1 | 8.1 | 6.7 | 16.1 | 19.0 | 7.0 | BlueMale |\n| 1 | Blue | Male | 2 | 8.8 | 7.7 | 18.1 | 20.8 | 7.4 | BlueMale |\n| 2 | Blue | Male | 3 | 9.2 | 7.8 | 19.0 | 22.4 | 7.7 | BlueMale |\n| 3 | Blue | Male | 4 | 9.6 | 7.9 | 20.1 | 23.1 | 8.2 | BlueMale |\n| 4 | Blue | Male | 5 | 9.8 | 8.0 | 20.3 | 23.0 | 8.2 | BlueMale |\n\n```python\n# normalize data columns\ndata_norm = data.copy()\ndata_norm[data_columns] = MinMaxScaler().fit_transform(data[data_columns])\n\ndata_norm.describe()\n```\n\n|  | Index | Frontal Lobe | Rear Width | Carapace Midline | Maximum Width | Body Depth |\n| -- | -- | -- | -- | -- | -- | -- |\n| count | 200.000000 | 200.000000 | 200.000000 | 200.000000 | 200.000000 | 200.000000 |\n| mean | 25.500000 | 0.527233 | 0.455365 | 0.529043 | 0.515053 | 0.511645 |\n| std | 14.467083 | 0.219832 | 0.187835 | 0.216382 | 0.209919 | 0.220953 |\n| min | 1.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 | 0.000000 |\n| 25% | 13.000000 | 0.358491 | 0.328467 | 0.382219 | 0.384000 | 0.341935 |\n| 50% | 25.500000 | 0.525157 | 0.459854 | 0.528875 | 0.525333 | 0.503226 |\n| 75% | 38.000000 | 0.682390 | 0.569343 | 0.684650 | 0.664000 | 0.677419 |\n| max | 50.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 | 1.000000 |\n\n\n## 2-Dimensional Plot\n\n```python\nno_components = 2\nk_nearest_neighbors = 10\n\nisomap = Isomap(\n    n_components=no_components,\n    n_neighbors=k_nearest_neighbors)\n\ndata_isomap = isomap.fit_transform(data_norm[data_columns])\nprint('Reconstruction Error: ', isomap.reconstruction_error())\n# Reconstruction Error:  0.009501240251169362\n\ndata_norm[['ISOMAP1', 'ISOMAP2']] = data_isomap\ndata_norm.head(1)\n```\n\n|    | Species | Sex | Index | Frontal Lobe | Rear Width | Carapace Midline | Maximum Width | Body Depth | Class | MDS1 | MDS2 | ISOMAP1 | ISOMAP2 |\n| -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |\n| 0 | Blue | Male | 1 | 0.056604 | 0.014599 | 0.042553 | 0.050667 | 0.058065 | BlueMale | -0.482199 | -0.917839 | 1.091359 | 0.00803 |\n\n```python\nfig = plt.figure(figsize=(10, 8))\nsns.scatterplot(x='ISOMAP1', y='ISOMAP2', hue='Class', data=data_norm)\n```\n\n![Isometric Mapping (ISOMAP)](https://github.com/mpolinowski/isometric-mapping/blob/master/assets/Isometric_Mapping_01.png)\n\n\n## 3-Dimensional Plot\n\n```python\nno_components = 3\nk_nearest_neighbors = 10\n\nisomap = Isomap(\n    n_components=no_components,\n    n_neighbors=k_nearest_neighbors)\n\ndata_isomap = isomap.fit_transform(data_norm[data_columns])\nprint('Reconstruction Error: ', isomap.reconstruction_error())\n# Reconstruction Error:  0.007640087707465774\n\ndata_norm[['ISOMAP1', 'ISOMAP2', 'ISOMAP3']] = data_isomap\ndata_norm.head(1)\n```\n\n|    | Species | Sex | Index | Frontal Lobe | Rear Width | Carapace Midline | Maximum Width | Body Depth | Class | ISOMAP1 | ISOMAP2 | ISOMAP3 |\n| -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |\n| 0 | Blue | Male | 1 | 0.056604 | 0.014599 | 0.042553 | 0.050667 | 0.058065 | BlueMale | 1.091359 | 0.00803 | 0.117078 |\n\n```python\nclass_colours = {\n    'BlueMale': '#0027c4', #blue\n    'BlueFemale': '#f18b0a', #orange\n    'OrangeMale': '#0af10a', # green\n    'OrangeFemale': '#ff1500', #red\n}\n\ncolours = data_norm['Class'].apply(lambda x: class_colours[x])\n\nx=data_norm.ISOMAP1\ny=data_norm.ISOMAP2\nz=data_norm.ISOMAP3\n\nfig = plt.figure(figsize=(10,10))\nplt.title('ISOMAP Data Analysis')\nax = fig.add_subplot(projection='3d')\n\nax.scatter(xs=x, ys=y, zs=z, s=50, c=colours)\n```\n\n![Isometric Mapping (ISOMAP)](https://github.com/mpolinowski/isometric-mapping/blob/master/assets/Isometric_Mapping_02.png)","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmpolinowski%2Fisometric-mapping","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmpolinowski%2Fisometric-mapping","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmpolinowski%2Fisometric-mapping/lists"}