Port grasp_show_transform from GraSP to thgsp

[bwdeng20]

The function grasp_show_transform by Benjamin Girault and Antonio Ortega is a visualization tool of GFT already implemented in GraSP. This note summarizes the current state of grasp_show_transform implementation provided in thgsp.

• Embedding Algorithm
  • The eigenvector of Lrw's second smallest eigenvalue
  • Equispaced embbedding
• Sampling Method: implemented here
• grasp_show_transform : implemented here
• Examples: An example with USC toy graph is below.
• Better consistence between embedding and clustering results

import numpy as np
from scipy.sparse import lil_matrix
from thgsp.datasets import Toy
from thgsp.sampling import ess_sampling
from thgsp.visual import show_transform
g = Toy()[0]
fs, U = g.spectral(lap_type="comb")
bands = np.linspace(fs[0], fs[-1], num=9) 
bands2= np.hstack([bands[:-1, None], bands[1:, None]]) # both two kinds of bands are supported
N, M = U.shape 
print(bands)
print(bands2)
sampled_nodes = ess_sampling(g.L("comb"), g.n_node, k=4)
highlights = lil_matrix((M, N))
highlights[range(M), sampled_nodes] = 1
fig, _, _ = show_transform(g, U.t(), fs, highlights, cluster=2, bands=bands)

# Before showing the figure, you can adjust the figure on many aspects, including but not limited to
# font, text, colors of axes, using APIs provided by `plotly.go.Figure` class.
fig.show()

The interactive figure will be displayed in a browser window, and one can download the static png version like the following one.

Gaussian-kernel-weighted USCToy Graph with GFT based on normalized Laplacian.

Gaussian-kernel-weighted USCToy Graph with GFT based on combinatorial Laplacian.