ML Docs: Start pca notebook

Author: xhlulu

doc/python/ml-pca.md

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+  plotly:
+    description: Visualize Principle Component Analysis (PCA) of your high-dimensional
+      data with Plotly on Python.
+    display_as: ai_ml
+    language: python
+    layout: base
+    name: PCA Visualization
+    order: 4
+    page_type: example_index
+    permalink: python/pca-visualization/
+    thumbnail: thumbnail/ml-pca.png
+---
+
+## Basic PCA Scatter Plot
+
+This example shows you how to simply visualize the first two principal components of a PCA, by reducing a dataset of 4 dimensions to 2D. It uses scikit-learn's `PCA`.
+
+```python
+import plotly.express as px
+from sklearn.decomposition import PCA
+
+df = px.data.iris()
+X = df[['sepal_length', 'sepal_width', 'petal_length', 'petal_width']]
+
+pca = PCA(n_components=2)
+components = pca.fit_transform(X)
+
+fig = px.scatter(x=components[:, 0], y=components[:, 1], color=df['species'])
+fig.show()
+```
+
+## Visualize PCA with `px.scatter_3d`
+
+Just like the basic PCA plot, this let you visualize the first 3 dimensions. This additionally displays the total variance explained by those components.
+
+```python
+import plotly.express as px
+from sklearn.decomposition import PCA
+
+df = px.data.iris()
+X = df[['sepal_length', 'sepal_width', 'petal_length', 'petal_width']]
+
+pca = PCA(n_components=3)
+components = pca.fit_transform(X)
+
+total_var = pca.explained_variance_ratio_.sum() * 100
+
+fig = px.scatter_3d(
+    x=components[:, 0], y=components[:, 1], z=components[:, 2],
+    color=df['species'], 
+    title=f'Total Explained Variance: {total_var:.2f}%',
+    labels={'x': 'PC 1', 'y': 'PC 2', 'z': 'PC 3'},
+)
+fig.show()
+```
+
+## Plot high-dimensional components with `px.scatter_matrix`
+
+If you need to visualize more than 3 dimensions, you can use scatter plot matrices.
+
+```python
+import pandas as pd
+from sklearn.decomposition import PCA
+from sklearn.datasets import load_boston
+
+boston = load_boston()
+df = pd.DataFrame(boston.data, columns=boston.feature_names)
+
+pca = PCA(n_components=5)
+components = pca.fit_transform(df)
+
+total_var = pca.explained_variance_ratio_.sum() * 100
+
+labels = {str(i): f"PC {i+1}" for i in range(5)}
+labels['color'] = 'Median Price'
+
+fig = px.scatter_matrix(
+    components, 
+    color=boston.target,
+    dimensions=range(5),
+    labels=labels,
+    title=f'Total Explained Variance: {total_var:.2f}%',
+)
+fig.update_traces(diagonal_visible=False)
+fig.show()
+```
+
+## Plotting explained variance
+
+Often, you might be interested in seeing how much variance the PCA is able to explain as you increase the number of components, in order to decide how many dimensions to ultimately keep or analyze. This example shows you how to quickly plot the cumulative sum of explained variance for a high-dimensional dataset like [Diabetes](https://scikit-learn.org/stable/datasets/index.html#diabetes-dataset).
+
+```python
+import numpy as np
+import pandas as pd
+from sklearn.decomposition import PCA
+from sklearn.datasets import load_diabetes
+
+boston = load_diabetes()
+df = pd.DataFrame(boston.data, columns=boston.feature_names)
+
+pca = PCA()
+pca.fit(df)
+exp_var_cumul = np.cumsum(pca.explained_variance_ratio_)
+
+px.area(
+    x=range(1, exp_var_cumul.shape[0] + 1),
+    y=exp_var_cumul, 
+    labels={"x": "# Components", "y": "Explained Variance"}
+)
+```
+
+## Visualize loadings