Figure 2
Illustration of loop/circle-based clustering using four one-dimensional (1D) homology generators (a) and spectral clustering using four zero-dimensional (0D) non-homology generators (b). The Dirac matrices \(\textbf{D}_1\) are generated from the Vietoris Rips complex of the C\(_\alpha\) atoms in PDBID: 1AXC at 10Å. (a) Here 1D homology generators \(\textbf{w}_1^{\top}\) are taken from the homology generators of \(\textbf{D}_1\) with eigenvalues as 0. A thick edge with dark blue color indicates large magnitude of the value, while a thinner edge with light blue color means the corresponding the 1D homology generator has a value with small magnitude on this 1-simplex. Each 1D homology generator forms an individual loop or circle. (b) The four 0D non-homology generators \(\textbf{w}_0^{\top}\) are taken from the non-homology generators of \(\textbf{D}_1\) with the four smallest positive eigenvalues. Note that these 0D non-homology generators are defined on nodes (0-simplices). Nodes with negative values are colored in red while nodes with positive values are of blue color. It can be seen that the nodes in the structure can be naturally clustered into groups based on the signs of these 0D non-homology generators.
