msmbuilder.cluster.SpectralClustering

class msmbuilder.cluster.SpectralClustering(n_clusters=8, eigen_solver=None, random_state=None, n_init=10, gamma=1.0, affinity='rbf', n_neighbors=10, eigen_tol=0.0, assign_labels='kmeans', degree=3, coef0=1, kernel_params=None, n_jobs=1)

Apply clustering to a projection to the normalized laplacian.

In practice Spectral Clustering is very useful when the structure of the individual clusters is highly non-convex or more generally when a measure of the center and spread of the cluster is not a suitable description of the complete cluster. For instance when clusters are nested circles on the 2D plan.

If affinity is the adjacency matrix of a graph, this method can be used to find normalized graph cuts.

When calling fit, an affinity matrix is constructed using either kernel function such the Gaussian (aka RBF) kernel of the euclidean distanced d(X, X):

np.exp(-gamma * d(X,X) ** 2)

or a k-nearest neighbors connectivity matrix.

Alternatively, using precomputed, a user-provided affinity matrix can be used.

Read more in the User Guide.

Parameters:
n_clusters : integer, optional

The dimension of the projection subspace.

eigen_solver : {None, ‘arpack’, ‘lobpcg’, or ‘amg’}

The eigenvalue decomposition strategy to use. AMG requires pyamg to be installed. It can be faster on very large, sparse problems, but may also lead to instabilities

random_state : int, RandomState instance or None, optional, default: None

A pseudo random number generator used for the initialization of the lobpcg eigen vectors decomposition when eigen_solver == ‘amg’ and by the K-Means initialization. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

n_init : int, optional, default: 10

Number of time the k-means algorithm will be run with different centroid seeds. The final results will be the best output of n_init consecutive runs in terms of inertia.

gamma : float, default=1.0

Kernel coefficient for rbf, poly, sigmoid, laplacian and chi2 kernels. Ignored for affinity='nearest_neighbors'.

affinity : string, array-like or callable, default ‘rbf’

If a string, this may be one of ‘nearest_neighbors’, ‘precomputed’, ‘rbf’ or one of the kernels supported by sklearn.metrics.pairwise_kernels.

Only kernels that produce similarity scores (non-negative values that increase with similarity) should be used. This property is not checked by the clustering algorithm.

n_neighbors : integer

Number of neighbors to use when constructing the affinity matrix using the nearest neighbors method. Ignored for affinity='rbf'.

eigen_tol : float, optional, default: 0.0

Stopping criterion for eigendecomposition of the Laplacian matrix when using arpack eigen_solver.

assign_labels : {‘kmeans’, ‘discretize’}, default: ‘kmeans’

The strategy to use to assign labels in the embedding space. There are two ways to assign labels after the laplacian embedding. k-means can be applied and is a popular choice. But it can also be sensitive to initialization. Discretization is another approach which is less sensitive to random initialization.

degree : float, default=3

Degree of the polynomial kernel. Ignored by other kernels.

coef0 : float, default=1

Zero coefficient for polynomial and sigmoid kernels. Ignored by other kernels.

kernel_params : dictionary of string to any, optional

Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.

n_jobs : int, optional (default = 1)

The number of parallel jobs to run. If -1, then the number of jobs is set to the number of CPU cores.

Notes

If you have an affinity matrix, such as a distance matrix, for which 0 means identical elements, and high values means very dissimilar elements, it can be transformed in a similarity matrix that is well suited for the algorithm by applying the Gaussian (RBF, heat) kernel:

np.exp(- dist_matrix ** 2 / (2. * delta ** 2))

Where delta is a free parameter representing the width of the Gaussian kernel.

Another alternative is to take a symmetric version of the k nearest neighbors connectivity matrix of the points.

If the pyamg package is installed, it is used: this greatly speeds up computation.

References

Attributes:
affinity_matrix_ : array-like, shape (n_samples, n_samples)

Affinity matrix used for clustering. Available only if after calling fit.

labels_ : list of arrays, each of shape [sequence_length, ]

The label of each point is an integer in [0, n_clusters).

Methods

fit(sequences[, y]) Fit the clustering on the data
fit_predict(sequences[, y]) Performs clustering on X and returns cluster labels.
fit_transform(sequences[, y]) Alias for fit_predict
get_params([deep]) Get parameters for this estimator.
partial_predict(X[, y]) Predict the closest cluster each sample in X belongs to.
partial_transform(X) Alias for partial_predict
predict(sequences[, y]) Predict the closest cluster each sample in each sequence in sequences belongs to.
set_params(**params) Set the parameters of this estimator.
summarize() Return some diagnostic summary statistics about this Markov model
transform(sequences) Alias for predict
__init__(n_clusters=8, eigen_solver=None, random_state=None, n_init=10, gamma=1.0, affinity='rbf', n_neighbors=10, eigen_tol=0.0, assign_labels='kmeans', degree=3, coef0=1, kernel_params=None, n_jobs=1)

Initialize self. See help(type(self)) for accurate signature.

Methods

__init__([n_clusters, eigen_solver, …]) Initialize self.
fit(sequences[, y]) Fit the clustering on the data
fit_predict(sequences[, y]) Performs clustering on X and returns cluster labels.
fit_transform(sequences[, y]) Alias for fit_predict
get_params([deep]) Get parameters for this estimator.
partial_predict(X[, y]) Predict the closest cluster each sample in X belongs to.
partial_transform(X) Alias for partial_predict
predict(sequences[, y]) Predict the closest cluster each sample in each sequence in sequences belongs to.
set_params(**params) Set the parameters of this estimator.
summarize() Return some diagnostic summary statistics about this Markov model
transform(sequences) Alias for predict
fit(sequences, y=None)

Fit the clustering on the data

Parameters:
sequences : list of array-like, each of shape [sequence_length, n_features]

A list of multivariate timeseries. Each sequence may have a different length, but they all must have the same number of features.
Returns:
self
fit_predict(sequences, y=None)

Performs clustering on X and returns cluster labels.

Parameters:
sequences : list of array-like, each of shape [sequence_length, n_features]

A list of multivariate timeseries. Each sequence may have a different length, but they all must have the same number of features.
Returns:
Y : list of ndarray, each of shape [sequence_length, ]

Cluster labels
fit_transform(sequences, y=None)

Alias for fit_predict

get_params(deep=True)

Get parameters for this estimator.

Parameters:
deep : boolean, optional

If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:
params : mapping of string to any

Parameter names mapped to their values.
partial_predict(X, y=None)

Predict the closest cluster each sample in X belongs to.

In the vector quantization literature, cluster_centers_ is called the code book and each value returned by predict is the index of the closest code in the code book.

Parameters:
X : array-like shape=(n_samples, n_features)

A single timeseries.
Returns:
Y : array, shape=(n_samples,)

Index of the cluster that each sample belongs to
partial_transform(X)

Alias for partial_predict

predict(sequences, y=None)

Predict the closest cluster each sample in each sequence in sequences belongs to.

In the vector quantization literature, cluster_centers_ is called the code book and each value returned by predict is the index of the closest code in the code book.

Parameters:
sequences : list of array-like, each of shape [sequence_length, n_features]

A list of multivariate timeseries. Each sequence may have a different length, but they all must have the same number of features.
Returns:
Y : list of arrays, each of shape [sequence_length,]

Index of the closest center each sample belongs to.
set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns:
self
summarize()

Return some diagnostic summary statistics about this Markov model

transform(sequences)

Alias for predict