.. only:: html .. note:: :class: sphx-glr-download-link-note Click :ref:`here ` to download the full example code or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_neighbors_plot_nca_dim_reduction.py: ============================================================== Dimensionality Reduction with Neighborhood Components Analysis ============================================================== Sample usage of Neighborhood Components Analysis for dimensionality reduction. This example compares different (linear) dimensionality reduction methods applied on the Digits data set. The data set contains images of digits from 0 to 9 with approximately 180 samples of each class. Each image is of dimension 8x8 = 64, and is reduced to a two-dimensional data point. Principal Component Analysis (PCA) applied to this data identifies the combination of attributes (principal components, or directions in the feature space) that account for the most variance in the data. Here we plot the different samples on the 2 first principal components. Linear Discriminant Analysis (LDA) tries to identify attributes that account for the most variance *between classes*. In particular, LDA, in contrast to PCA, is a supervised method, using known class labels. Neighborhood Components Analysis (NCA) tries to find a feature space such that a stochastic nearest neighbor algorithm will give the best accuracy. Like LDA, it is a supervised method. One can see that NCA enforces a clustering of the data that is visually meaningful despite the large reduction in dimension. .. rst-class:: sphx-glr-horizontal * .. image:: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_001.png :alt: PCA, KNN (k=3) Test accuracy = 0.52 :class: sphx-glr-multi-img * .. image:: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_002.png :alt: LDA, KNN (k=3) Test accuracy = 0.66 :class: sphx-glr-multi-img * .. image:: /auto_examples/neighbors/images/sphx_glr_plot_nca_dim_reduction_003.png :alt: NCA, KNN (k=3) Test accuracy = 0.70 :class: sphx-glr-multi-img .. code-block:: default # License: BSD 3 clause import numpy as np import matplotlib.pyplot as plt from sklearn import datasets from sklearn.model_selection import train_test_split from sklearn.decomposition import PCA from sklearn.discriminant_analysis import LinearDiscriminantAnalysis from sklearn.neighbors import (KNeighborsClassifier, NeighborhoodComponentsAnalysis) from sklearn.pipeline import make_pipeline from sklearn.preprocessing import StandardScaler print(__doc__) n_neighbors = 3 random_state = 0 # Load Digits dataset X, y = datasets.load_digits(return_X_y=True) # Split into train/test X_train, X_test, y_train, y_test = \ train_test_split(X, y, test_size=0.5, stratify=y, random_state=random_state) dim = len(X[0]) n_classes = len(np.unique(y)) # Reduce dimension to 2 with PCA pca = make_pipeline(StandardScaler(), PCA(n_components=2, random_state=random_state)) # Reduce dimension to 2 with LinearDiscriminantAnalysis lda = make_pipeline(StandardScaler(), LinearDiscriminantAnalysis(n_components=2)) # Reduce dimension to 2 with NeighborhoodComponentAnalysis nca = make_pipeline(StandardScaler(), NeighborhoodComponentsAnalysis(n_components=2, random_state=random_state)) # Use a nearest neighbor classifier to evaluate the methods knn = KNeighborsClassifier(n_neighbors=n_neighbors) # Make a list of the methods to be compared dim_reduction_methods = [('PCA', pca), ('LDA', lda), ('NCA', nca)] # plt.figure() for i, (name, model) in enumerate(dim_reduction_methods): plt.figure() # plt.subplot(1, 3, i + 1, aspect=1) # Fit the method's model model.fit(X_train, y_train) # Fit a nearest neighbor classifier on the embedded training set knn.fit(model.transform(X_train), y_train) # Compute the nearest neighbor accuracy on the embedded test set acc_knn = knn.score(model.transform(X_test), y_test) # Embed the data set in 2 dimensions using the fitted model X_embedded = model.transform(X) # Plot the projected points and show the evaluation score plt.scatter(X_embedded[:, 0], X_embedded[:, 1], c=y, s=30, cmap='Set1') plt.title("{}, KNN (k={})\nTest accuracy = {:.2f}".format(name, n_neighbors, acc_knn)) plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** ( 0 minutes 2.021 seconds) .. _sphx_glr_download_auto_examples_neighbors_plot_nca_dim_reduction.py: .. only :: html .. container:: sphx-glr-footer :class: sphx-glr-footer-example .. container:: binder-badge .. image:: https://mybinder.org/badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/0.23.X?urlpath=lab/tree/notebooks/auto_examples/neighbors/plot_nca_dim_reduction.ipynb :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_nca_dim_reduction.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_nca_dim_reduction.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_