Neighborhood Components Analysis
Neighborhood Component Analysis (NCA) is a machine learning algorithm for metric learning. It learns a linear transformation in a supervised fashion to improve the classification accuracy of a stochastic nearest neighbors rule in the transformed space.
Read more in the :ref:`User Guide <nca>`.
Parameters ---------- n_components : int, optional (default=None) Preferred dimensionality of the projected space. If None it will be set to ``n_features``.
init : string or numpy array, optional (default='auto') Initialization of the linear transformation. Possible options are 'auto', 'pca', 'lda', 'identity', 'random', and a numpy array of shape (n_features_a, n_features_b).
'auto' Depending on ``n_components``, the most reasonable initialization will be chosen. If ``n_components <= n_classes`` we use 'lda', as it uses labels information. If not, but ``n_components < min(n_features, n_samples)``, we use 'pca', as it projects data in meaningful directions (those of higher variance). Otherwise, we just use 'identity'.
'pca' ``n_components`` principal components of the inputs passed to :meth:`fit` will be used to initialize the transformation. (See :class:`~sklearn.decomposition.PCA`)
'lda' ``min(n_components, n_classes)`` most discriminative components of the inputs passed to :meth:`fit` will be used to initialize the transformation. (If ``n_components > n_classes``, the rest of the components will be zero.) (See :class:`~sklearn.discriminant_analysis.LinearDiscriminantAnalysis`)
'identity' If ``n_components`` is strictly smaller than the dimensionality of the inputs passed to :meth:`fit`, the identity matrix will be truncated to the first ``n_components`` rows.
'random' The initial transformation will be a random array of shape `(n_components, n_features)`. Each value is sampled from the standard normal distribution.
numpy array n_features_b must match the dimensionality of the inputs passed to :meth:`fit` and n_features_a must be less than or equal to that. If ``n_components`` is not None, n_features_a must match it.
warm_start : bool, optional, (default=False) If True and :meth:`fit` has been called before, the solution of the previous call to :meth:`fit` is used as the initial linear transformation (``n_components`` and ``init`` will be ignored).
max_iter : int, optional (default=50) Maximum number of iterations in the optimization.
tol : float, optional (default=1e-5) Convergence tolerance for the optimization.
callback : callable, optional (default=None) If not None, this function is called after every iteration of the optimizer, taking as arguments the current solution (flattened transformation matrix) and the number of iterations. This might be useful in case one wants to examine or store the transformation found after each iteration.
verbose : int, optional (default=0) If 0, no progress messages will be printed. If 1, progress messages will be printed to stdout. If > 1, progress messages will be printed and the ``disp`` parameter of :func:`scipy.optimize.minimize` will be set to ``verbose - 2``.
random_state : int or numpy.RandomState or None, optional (default=None) A pseudo random number generator object or a seed for it if int. If ``init='random'``, ``random_state`` is used to initialize the random transformation. If ``init='pca'``, ``random_state`` is passed as an argument to PCA when initializing the transformation.
Attributes ---------- components_ : array, shape (n_components, n_features) The linear transformation learned during fitting.
n_iter_ : int Counts the number of iterations performed by the optimizer.
random_state_ : numpy.RandomState Pseudo random number generator object used during initialization.
Examples -------- >>> from sklearn.neighbors import NeighborhoodComponentsAnalysis >>> from sklearn.neighbors import KNeighborsClassifier >>> from sklearn.datasets import load_iris >>> from sklearn.model_selection import train_test_split >>> X, y = load_iris(return_X_y=True) >>> X_train, X_test, y_train, y_test = train_test_split(X, y, ... stratify=y, test_size=0.7, random_state=42) >>> nca = NeighborhoodComponentsAnalysis(random_state=42) >>> nca.fit(X_train, y_train) NeighborhoodComponentsAnalysis(...) >>> knn = KNeighborsClassifier(n_neighbors=3) >>> knn.fit(X_train, y_train) KNeighborsClassifier(...) >>> print(knn.score(X_test, y_test)) 0.933333... >>> knn.fit(nca.transform(X_train), y_train) KNeighborsClassifier(...) >>> print(knn.score(nca.transform(X_test), y_test)) 0.961904...
References ---------- .. 1
J. Goldberger, G. Hinton, S. Roweis, R. Salakhutdinov. "Neighbourhood Components Analysis". Advances in Neural Information Processing Systems. 17, 513-520, 2005. http://www.cs.nyu.edu/~roweis/papers/ncanips.pdf
.. 2
Wikipedia entry on Neighborhood Components Analysis https://en.wikipedia.org/wiki/Neighbourhood_components_analysis