{"id":22039546,"url":"https://github.com/mpolinowski/fisher-discriminant-analysis","last_synced_at":"2026-05-10T02:40:45.176Z","repository":{"id":234831418,"uuid":"627398941","full_name":"mpolinowski/fisher-discriminant-analysis","owner":"mpolinowski","description":"LDA is a widely used dimensionality reduction technique built on Fisher’s linear discriminant.","archived":false,"fork":false,"pushed_at":"2023-04-13T11:43:26.000Z","size":858,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"master","last_synced_at":"2025-01-28T19:17:57.984Z","etag":null,"topics":["linear-discriminant-analysis","matplotlib-pyplot","python","scikit-learn"],"latest_commit_sha":null,"homepage":"https://mpolinowski.github.io/docs/IoT-and-Machine-Learning/ML/2023-04-13-fisher-discriminant-analysis/2023-04-13","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/mpolinowski.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null}},"created_at":"2023-04-13T11:43:17.000Z","updated_at":"2023-04-13T12:10:15.000Z","dependencies_parsed_at":"2024-04-21T02:03:08.613Z","dependency_job_id":"ed4b52fd-fe54-411a-b11b-a72c490d7bbf","html_url":"https://github.com/mpolinowski/fisher-discriminant-analysis","commit_stats":null,"previous_names":["mpolinowski/fisher-discriminant-analysis"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mpolinowski%2Ffisher-discriminant-analysis","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mpolinowski%2Ffisher-discriminant-analysis/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mpolinowski%2Ffisher-discriminant-analysis/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/mpolinowski%2Ffisher-discriminant-analysis/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/mpolinowski","download_url":"https://codeload.github.com/mpolinowski/fisher-discriminant-analysis/tar.gz/refs/heads/master","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":245104529,"owners_count":20561380,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["linear-discriminant-analysis","matplotlib-pyplot","python","scikit-learn"],"created_at":"2024-11-30T11:11:11.702Z","updated_at":"2026-05-10T02:40:40.149Z","avatar_url":"https://github.com/mpolinowski.png","language":"Jupyter 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# Fisher Linear Discriminant Analysis (LDA)\n\nLDA is a widely used dimensionality reduction technique built on Fisher’s linear discriminant.\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.discriminant_analysis import LinearDiscriminantAnalysis\n```\n\n## Dataset\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```\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```python\n# normalize data columns\ndata_norm = data.copy()\ndata_norm[data_columns] = MinMaxScaler().fit_transform(data[data_columns])\n\ndata_norm.describe().T\n```\n\n## 2-Dimensional Plot\n\n```python\nno_components = 2\n\nlda = LinearDiscriminantAnalysis(n_components = no_components)\ndata_lda = lda.fit_transform(data_norm[data_columns].values , y=data_norm['Class'])\n\ndata_norm[['LDA1', 'LDA2']] = data_lda\n\ndata_norm.head(1)\n```\n\n|  | Species | Sex | Index | Frontal Lobe | Rear Width | Carapace Midline | Maximum Width | Body Depth | Class | LDA1 | LDA2 |\n| -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |\n| 0 | Blue | Male | 1 | 0.056604 | 0.014599 | 0.042553 | 0.050667 | 0.058065 | BlueMale | 1.538869 | -0.808137 |\n\n```python\nfig = plt.figure(figsize=(10, 8))\nsns.scatterplot(x='LDA1', y='LDA2', hue='Class', data=data_norm)\n```\n\n![Fisher Linear Discriminant Analysis (LDA)](https://github.com/mpolinowski/fisher-discriminant-analysis/blob/master/assets/Linear_Discriminant_Analysis_01.png)\n\n![Fisher Linear Discriminant Analysis (LDA)](https://github.com/mpolinowski/fisher-discriminant-analysis/blob/master/assets/nice.gif)\n\n\n## 3-Dimensional Plot\n\n```python\nno_components = 3\n\nlda = LinearDiscriminantAnalysis(n_components = no_components)\ndata_lda = lda.fit_transform(data_norm[data_columns].values , y=data_norm['Class'])\n\ndata_norm[['LDA1', 'LDA2', 'LDA3']] = data_lda\n\ndata_norm.head(1)\n```\n\n|  | Species | Sex | Index | Frontal Lobe | Rear Width | Carapace Midline | Maximum Width | Body Depth | Class | LDA1 | LDA2 | LDA3 |\n| -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- | -- |\n| 0 | Blue | Male | 1 | 0.056604 | 0.014599 | 0.042553 | 0.050667 | 0.058065 | BlueMale | 1.538869 | -0.808137 | 1.18642 |\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.LDA1\ny=data_norm.LDA2\nz=data_norm.LDA3\n\nfig = plt.figure(figsize=(10,10))\nplt.title('Linear Discriminant Analysis')\nax = fig.add_subplot(projection='3d')\n\nax.scatter(xs=x, ys=y, zs=z, s=50, c=colours)\n```\n\n![Fisher Linear Discriminant Analysis (LDA)](https://github.com/mpolinowski/fisher-discriminant-analysis/blob/master/assets/Linear_Discriminant_Analysis_02.png)","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmpolinowski%2Ffisher-discriminant-analysis","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fmpolinowski%2Ffisher-discriminant-analysis","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fmpolinowski%2Ffisher-discriminant-analysis/lists"}