Kernels for Graph Data
You can refer to our demo for semi-supervised learning for a simple usage of kernels for graph data.
And there is also a demo for graph kernel using an example of propagation kernel.
Kernels on Graph
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pyGPs.GraphExtensions.nodeKernels.VNDKernel(A, alpha=0.5)[source]
Von Neumann Diffusion Kernel on graph (Zhou et al., 2004)
(also label spreading kernel)
K = (I - alpha*S)^-1, where S = D^-1/2*A*D^-1/2
| Parameters: |
- A – adjacency matrix
- alpha – hyperparameter alpha
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| Returns: | kernel matrix
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pyGPs.GraphExtensions.nodeKernels.cosKernel(A)[source]
Cosine Kernel (also Inverse Cosine Kernel)
K = cos (L*pi/4), where L is the normalized Laplacian
| Parameters: | A – adjacency matrix |
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| Returns: | kernel matrix |
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pyGPs.GraphExtensions.nodeKernels.diffKernel(A, beta=0.5)[source]
Diffusion Process Kernel
K = exp(beta * H), where H = -L = A-D
K = Q exp(beta * Lambda) Q.T
| Parameters: |
- A – adjacency matrix
- beta – hyperparameter beta
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| Returns: | kernel matrix
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pyGPs.GraphExtensions.nodeKernels.normLap(A)[source]
Normalized Laplacian
| Parameters: | A – adjacency matrix |
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| Returns: | kernel matrix |
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pyGPs.GraphExtensions.nodeKernels.psInvLapKernel(A)[source]
Pseudo inverse of the normalized Laplacian.
| Parameters: | A – adjacency matrix |
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| Returns: | kernel matrix |
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pyGPs.GraphExtensions.nodeKernels.regLapKernel(A, sigma=1)[source]
Regularized Laplacian Kernel
| Parameters: |
- A – adjacency matrix
- sigma – hyperparameter sigma
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| Returns: | kernel matrix
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pyGPs.GraphExtensions.nodeKernels.rwKernel(A, p=1, a=2)[source]
p-step Random Walk Kernel with a>1
K = (aI-L)^p, p>1 and L is the normalized Laplacian
| Parameters: |
- A – adjacency matrix
- p – step parameter
- a – hyperparameter a
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| Returns: | kernel matrix
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Graph Kernels
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pyGPs.GraphExtensions.graphKernels.propagationKernel(A, l, gr_id, h_max, w, p, ktype=None, SUM=True, VIS=False, showEachStep=False)[source]
Propagation kernel for graphs as described in:
Neumann, M., Patricia, N., Garnett, R., Kersting, K.: Efficient Graph Kernels by
Randomization. In: P.A. Flach, T.D. Bie, N. Cristianini (eds.) ECML/PKDD, Notes in
Computer Science, vol. 7523, pp. 378-393. Springer (2012).
| Parameters: |
- A – adjacency matrix (num_nodes x num_nodes)
- l – label array (num_nodes x 1); values [1,...,k] or -1 for unlabeled nodes
OR label array (num_nodes x num_labels); values [0,1], unlabeled nodes have only 0 entries
- gr_id – graph indicator array (num_nodes x 1); values [0,..,n]
- h_max – number of iterations
- w – bin widths parameter
- p – distance (‘tv’, ‘hellinger’, ‘L1’, ‘L2’)
- ktype – type of propagation kernel [‘diffusion’, ‘label_propagation’, ‘label_spreading’, ‘belief_propagation’]
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| Returns: | kernel matrix
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