grakel.RandomWalk

class grakel.RandomWalk(n_jobs=None, normalize=False, verbose=False, lamda=0.1, method_type='fast', kernel_type='geometric', p=None)

The random walk kernel class.

See [KTI03], [GartnerFW03] and [VBS07].

Parameters

lambdafloat

A lambda factor concerning summation.

method_typestr, valid_values={“baseline”, “fast”}

The method to use for calculating random walk kernel:

• “baseline” Complexity: \(O(|V|^6)\) (see [KTI03], [GartnerFW03])

• “fast” Complexity: \(O((|E|+|V|)|V||M|)\) (see [VBS07])

kernel_typestr, valid_values={“geometric”, “exponential”}

Defines how inner summation will be applied.

pint or None

If initialised defines the number of steps.

Attributes

mu_list

List of coefficients concerning a finite sum, in case p is not None.

Methods

diagonal(self)	Calculate the kernel matrix diagonal of the fit/transformed data.
fit(self, X[, y])	Fit a dataset, for a transformer.
fit_transform(self, X)	Fit and transform, on the same dataset.
get_params(self[, deep])	Get parameters for this estimator.
initialize(self)	Initialize all transformer arguments, needing initialization.
pairwise_operation(self, X, Y)	Calculate the random walk kernel.
parse_input(self, X)	Parse and create features for random_walk kernel.
set_params(self, \*\*params)	Call the parent method.
transform(self, X)	Calculate the kernel matrix, between given and fitted dataset.

Initialise a random_walk kernel.

Attributes

X

Methods

diagonal(self)	Calculate the kernel matrix diagonal of the fit/transformed data.
fit(self, X[, y])	Fit a dataset, for a transformer.
fit_transform(self, X)	Fit and transform, on the same dataset.
get_params(self[, deep])	Get parameters for this estimator.
initialize(self)	Initialize all transformer arguments, needing initialization.
pairwise_operation(self, X, Y)	Calculate the random walk kernel.
parse_input(self, X)	Parse and create features for random_walk kernel.
set_params(self, \*\*params)	Call the parent method.
transform(self, X)	Calculate the kernel matrix, between given and fitted dataset.

__init__(self, n_jobs=None, normalize=False, verbose=False, lamda=0.1, method_type='fast', kernel_type='geometric', p=None)

Initialise a random_walk kernel.

diagonal(self)

Calculate the kernel matrix diagonal of the fit/transformed data.

Parameters

None.

Returns

X_diagnp.array

The diagonal of the kernel matrix between the fitted data. This consists of each element calculated with itself.

Y_diagnp.array

The diagonal of the kernel matrix, of the transform. This consists of each element calculated with itself.

fit(self, X, y=None)

Fit a dataset, for a transformer.

Parameters

Xiterable

Each element must be an iterable with at most three features and at least one. The first that is obligatory is a valid graph structure (adjacency matrix or edge_dictionary) while the second is node_labels and the third edge_labels (that fitting the given graph format). The train samples.

yNone

There is no need of a target in a transformer, yet the pipeline API requires this parameter.

Returns

selfobject

Returns self.

fit_transform(self, X)

Fit and transform, on the same dataset.

Parameters

Xiterable

Each element must be an iterable with at most three features and at least one. The first that is obligatory is a valid graph structure (adjacency matrix or edge_dictionary) while the second is node_labels and the third edge_labels (that fitting the given graph format). If None the kernel matrix is calculated upon fit data. The test samples.

yNone

There is no need of a target in a transformer, yet the pipeline API requires this parameter.

Returns

Knumpy array, shape = [n_targets, n_input_graphs]

corresponding to the kernel matrix, a calculation between all pairs of graphs between target an features

get_params(self, deep=True)

Get parameters for this estimator.

Parameters

deepbool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

paramsmapping of string to any

Parameter names mapped to their values.

initialize(self)

Initialize all transformer arguments, needing initialization.

pairwise_operation(self, X, Y)

Calculate the random walk kernel.

Fast: Spectral demoposition algorithm as presented in [VBS07] p.13, s.4.4, with complexity of \(O((|E|+|V|)|E||V|^2)\) for graphs witout labels.

Baseline: Algorithm presented in [KTI03], [GartnerFW03] with complexity of \(O(|V|^6)\)

Parameters

X, YObjects

Objects as produced from parse_input.

Returns

kernelnumber

The kernel value.

parse_input(self, X)

Parse and create features for random_walk kernel.

Parameters

Xiterable

For the input to pass the test, we must have: Each element must be an iterable with at most three features and at least one. The first that is obligatory is a valid graph structure (adjacency matrix or edge_dictionary) while the second is node_labels and the third edge_labels (that correspond to the given graph format). A valid input also consists of graph type objects.

Returns

outlist

The extracted adjacency matrices for any given input.

set_params(self, **params)

Call the parent method.

transform(self, X)

Calculate the kernel matrix, between given and fitted dataset.

Parameters

Xiterable

Each element must be an iterable with at most three features and at least one. The first that is obligatory is a valid graph structure (adjacency matrix or edge_dictionary) while the second is node_labels and the third edge_labels (that fitting the given graph format). If None the kernel matrix is calculated upon fit data. The test samples.

Returns

Knumpy array, shape = [n_targets, n_input_graphs]

corresponding to the kernel matrix, a calculation between all pairs of graphs between target an features

Bibliography

GartnerFW03(1,2,3)

Thomas Gärtner, Peter Flach, and Stefan Wrobel. On Graph Kernels: Hardness Results and Efficient Alternatives. In Learning Theory and Kernel Machines, 129–143. 2003.

KTI03(1,2,3)

Hisashi Kashima, Koji Tsuda, and Akihiro Inokuchi. Marginalized Kernels Between Labeled Graphs. In Proceedings of the 20th Conference in Machine Learning, 321–328. 2003.

VBS07(1,2,3)

S.V.N. Vishwanathan, Karsten M. Borgwardt, and Nicol N. Schraudolph. Fast Computation of Graph Kernels. In Advances in Neural Information Processing Systems, 1449–1456. 2007.