# SpectralClustering

class hana_ml.algorithms.pal.clustering.SpectralClustering(n_clusters, n_components=None, gamma=None, affinity=None, n_neighbors=None, cut=None, eigen_tol=None, krylov_dim=None, distance_level=None, minkowski_power=None, category_weights=None, max_iter=None, init=None, tol=None)

This is the Python wrapper for PAL Spectral Clustering.

Spectral clustering is an algorithm evolved from graph theory, and has been widely used in clustering. Its main idea is to treat all data as points in space, which can be connected by edges. The edge weight between two points farther away is low, while the edge weight between two points closer is high. Cutting the graph composed of all data points to make the edge weight sum between different subgraphs after cutting as low as possible, while make the edge weight sum within the subgraph as high as possible to achieve the purpose of clustering.

It performs a low-dimension embedding of the affinity matrix between samples, followed by k-means clustering of the components of the eigenvectors in the low dimensional space.

Parameters
n_clustersint

The number of clusters for spectral clustering.

The valid range for this parameter is from 2 to the number of records in the input data.

n_componentsint, optional

The number of eigenvectors used for spectral embedding.

Defaults to the value of n_clusters.

gammafloat, optional

RBF kernel coefficient $$\gamma$$ used in constructing affinity matrix with distance metric d, illustrated as $$\exp(-\gamma * d^2)$$.

Defaults to 1.0.

affinitystr, optional

Specifies the type of graph used to construct the affinity matrix. Valid options include:

• 'knn' : binary affinity matrix constructed from the graph of k-nearest-neighbors(knn).

• 'mutual-knn' : binary affinity matrix constructed from the graph of mutual k-nearest-neighbors(mutual-knn).

• 'fully-connected' : affinity matrix constructed from fully-connected graph, with weights defined by RBF kernel coefficients.

Defaults to 'fully-connected'.

n_neighborsint, optional

The number neighbors to use when constructing the affinity matrix using nearest neighbors method.

Valid only when graph is 'knn' or 'mutual-knn'.

Defaults to 10.

cutstr, optional

Specifies the method to cut the graph.

• 'ratio-cut' : Ratio-Cut.

• 'n-cut' : Normalized-Cut.

Defaults to 'ratio-cut'.

eigen_tolfloat, optional

Stopping criterion for eigendecomposition of the Laplacian matrix.

Defaults to 1e-10.

krylov_dimint, optional

Specifies the dimension of Krylov subspaces used in Eigenvalue decomposition. In general, this parameter controls the convergence speed of the algorithm. Typically a larger krylov_dim means faster convergence, but it may also result in greater memory use and more matrix operations in each iteration.

Defaults to 2*n_components.

Note

This parameter must satisfy

n_components < krylov_dim $$\leq$$ the number of training records.

distance_levelstr, optional

Specifies the method for computing the distance between data records and cluster centers:

• 'manhattan' : Manhattan distance.

• 'euclidean' : Euclidean distance.

• 'minkowski' : Minkowski distance.

• 'chebyshev' : Chebyshev distance.

• 'cosine' : Cosine distance.

Defaults to 'euclidean'.

minkowski_powerfloat, optional

Specifies the power parameter in Minkowski distance.

Valid only when distance_level is 'minkowski'.

Defaults to 3.0.

category_wightsfloat, optional

Represents the weight of category attributes.

Defaults to 0.707.

max_iterint, optional

Maximum number of iterations for K-Means algorithm.

Defaults to 100.

init{'first_k', 'replace', 'no_replace', 'patent'}, optional

Controls how the initial centers are selected in K-Means algorithm:

• 'first_k': First k observations.

• 'replace': Random with replacement.

• 'no_replace': Random without replacement.

• 'patent': Patent of selecting the init center (US 6,882,998 B1).

Defaults to 'patent'.

tolfloat, optional

Specifies the exit threshold for K-Means iterations.

Defaults to 1e-6.

Attributes
labels_DataFrame

DataFrame that holds the cluster labels.

Set to None if not fitted.

stats_DataFrame

DataFrame that holds the related statistics for spectral clustering.

Set to None if not fitted.

Methods

 fit(data[, key, features, thread_ratio]) Perform spectral clustering for the given dataset. fit_predict(data[, key, features, thread_ratio]) Given data, perform spectral clustering and return the corresponding cluster labels.

Perform spectral clustering for the given dataset.

Parameters

DataFrame containing the input data for spectral clustering.

keystr, optional

Name of ID column in data.

Mandatory if data is not indexed, or indexed by multiple columns.

Defaults to the index column of data if there is one.

featuresa list of str, optional

Names of the feature columns.

If features is not provided, it defaults to all non-key columns of data.

Specifies the ratio of total number of threads that can be used by spectral clustering.

The value range is from 0 to 1, where 0 means only using 1 thread, and 1 means using at most all the currently available threads. Values outside the range will be ignored and this function heuristically determines the number of threads to use.

Defaults to 0.

Given data, perform spectral clustering and return the corresponding cluster labels.

Parameters

DataFrame containing the input data for spectral clustering.

keystr, optional

Name of ID column in data.

Mandatory if data is not indexed, or indexed by multiple columns.

Defaults to the index column of data if there is one.

featuresa list of str, optional

Names of the feature columns.

If features is not provided, it defaults to all non-key columns of data.

Specifies the ratio of total number of threads that can be used by spectral clustering.

The value range is from 0 to 1, where 0 means only using 1 thread, and 1 means using at most all the currently available threads. Values outside the range will be ignored and this function heuristically determines the number of threads to use.

Defaults to 0.

Returns
DataFrame

The cluster labels of all records in data, structured as follows:

• 1st column : column name and type same as the key column of data, representing record IDs.

• 2nd column : CLUSTER_ID, type INTEGER, representing the cluster IDs assigned to all records in data.

property fit_hdbprocedure

Returns the generated hdbprocedure for fit.

property predict_hdbprocedure

Returns the generated hdbprocedure for predict.

## Inherited Methods from PALBase

Besides those methods mentioned above, the SpectralClustering class also inherits methods from PALBase class, please refer to PAL Base for more details.