Analysis code for "Scale-variant Topological Information for Characterizing Complex Networks" manuscript.
Preprint at https://arxiv.org/abs/1811.03573
Authors:
- Quoc Hoan Tran: zoro@biom.t.u-tokyo.ac.jp
- Van Tuan Vo: tuan@biom.t.u-tokyo.ac.jp
- Yoshihiko Hasegawa: hasegawa@biom.t.u-tokyo.ac.jp
Hasegawa Lab, Department of Information and Communication Engineering, Graduate School of Information Science and Technology, The University of Tokyo
We describe source code used in our experiments to generate network data from network models.
Generate networks from Girvan-Newman network model.
Number of nodes N = 128
Four communities of size 32 and the average degree of 16.
p_in, p_out: the probability of intra-community and inter-community links.
r = p_out/p_in = 0.01, 0.02,..., 1.0
Generate networks from Watts-Strogatz model.
Number of nodes N = 128
Rewiring probability beta = 0.00, 0.01,..., 1.0
Generate networks from Erdos-Renyi model.
Number of nodes N = 128
The pair-link probability p_link = 0.020, 0.021,..., 0.1
Generate networks from Sales-Pardo model.
Number of nodes N = 640 nodes
Three community structures nested in one another.
64 communities of 10 nodes at the small-scale level,
16 communities of 40 nodes at the medium-scale level,
4 communities of 160 nodes at the large-scale level.
The average degree k_bar = 16
The separations between the three scales: rho = 0.05, 0.10,..., 2.0
For the classification task, we test on ten real-world network datasets of bioinformatics and social networks. We save these datasets into two format-types *_adj.mat (adjacency matrix) and *.graphml file (see folder real-networks/{dataname}).
The first dataset is MUTAG; it consists of 188 networks of chemical compounds divided into two classes according to their mutagenic effect on a bacterium, i.e. mutagenic aromatic and heteroaromatic nitro compounds.
BZR, COX2, DHFR datasets consist of 405 ligands for the benzodiazepine receptor (BZR), 467 cyclooxygenase-2 inhibitors (COX2) and 756 inhibitors of the dihydrofolate reductase (DHFR) come with 3D coordinates. In each of these datasets, the chemical compounds are divided into active and inactive compounds that we need to classify.
FRANKENSTEIN is a modified version of BURSI dataset made of 4337 molecules with 2401 mutagens and 1936 nonmutagens to classify. Each molecule is represented as a small network whose vertices are labelled by the chemical atom symbol and edges by the bond type.
PROTEINS is a dataset of 1113 proteins represented as networks, where the nodes are secondary structure elements and the edges represent the neighbourhood within the 3-D structure or along the amino acid chain. We classify the proteins into enzymes and non-enzymes.
NCI1 and NCI109 are datasets of chemical compounds with 4110 and 4127 compounds, respectively. We classify the compounds with the ability to suppress or inhibit the growth of a panel of human tumour cell lines.
IMDB--BINARY is a dataset of 1000 movie collaboration ego-networks for each actor (actress) in Action and Romance genres from IMDB.com. For each network, two nodes representing actors or actresses are connected if they appear in the same movie. The task is to identify whether a given ego-network of an actor (actress) belongs to the Action or Comedy genre.
IMDB--MULTI is the multi-class version of IMDB--BINARY and contains 1500 ego-networks belonging to Comedy, Romance and Sci-Fi genres.
Generate diffusion distance matrix from network adjency matrix.
Options:
--matpath : input directory consisting of the collection of adjency matrices
(nodes_*_index_{}_adj.mat --> for ER, GN, SP, WS, Drosophila-Melanogaster networks
nodes_*_index_{}_adj.nse --> for LFR, LFR-H networks )
--outpath : output directory to save diffusion matrices
(*.npy file with matrix size of K x N x N, K: number of tau, N: number of nodes)
--normflag : normalize (=1) the diffusion matrix by its maximum element or not
--avgflag : average (=1) the diffusion matrix for K values of tau or not
--idxbg : start index of adjency matrices file to divide in multi processing
--idxed : end index of adjency matrices file to divide in multi processing
--taubg : start value of tau
--taued : end value of tau
--interval : sampling interval for tau from taubg to taued
--nproc : number of processes using in this program
Example: python generate_diffusion_mat.py
--matpath get-networks\mat\GN-net --outpath distmat\GN-net
--normflag 0 --avgflag 0 --idxbg 1 --idxed 1
--taubg 1.0 --taued 10.0 --interval 1.0 --nproc 8
Download ph-compute folder and launch ScaleVariantTopo\TopolologyAnalysis.sln
Calculate persistence diagrams from point clouds.
Options:
--nthreads : number of threads using for multi-processing (-1 for all possible threads)
--modulus : coefficient in the prime field Z/<p>Z to compute homology
--maxdim : maximum holes dimension to compute homology
--thres : maximum diameter to construct Rips complex
--format : format of the input (point-cloud, lower-distance, upper-distance, distance, dipha)
--outdir : directory for the output
--input : input file or file contains list of input files
--multi : compute single input file (0) or multi files in one input file (1)
--help : print usage option
Example: (see more at ph-compute\ScaleVariantTopo\run-compute-persistent.bat)
Release\PersistentRunner_D64.exe --nthreads 16 --maxdim 1 --format point-cloud --outdir output --input data\pcl_1.txt --multi 0
Release\PersistentRunner_D64.exe --nthreads -1 --maxdim 1 --format point-cloud --outdir output --input data\pcl_list.txt --multi 1
Notice that this is the wrapper module for Ripser, which is also available under an MIT license and copyright to Ulrich Baeur.
Bauer, Ulrich. "Ripser: a lean C++ code for the computation of Vietoris–Rips persistence barcodes."
Software available at https ://github. com/Ripser/ripser (2017).
Calculate persistence diagrams from diffusion distance matrix.
Options:
--nthreads : number of threads using for multi-processing (-1 for all possible threads)
--modulus : coefficient in the prime field Z/<p>Z to compute homology
--maxdim : maximum holes dimension to compute homology
--thres : maximum diameter to construct Rips complex
--outdir : directory for the output
--input : input folder which contains distance matrices
--taumax : compute with diffusion time up to taumax
--help : print usage option
See example at run-diffusion-persistence.bat.
Calculate kernel for persistence diagrams.
Calculate kernel for 3-dimensional persistence diagrams.
Options:
--timehold : parameter sigmal in the kernel (=0 for optimal value)
--timetau : ratio of xi vs. sigmal in the kernel
--left : (left) input as list of barcodes
--right : (right) input as list of barcodes
--dim : dimension of holes to compute kernel
--skipinf : skip holes which have infinity death-scale (default=True)
--infval : replace infinity death-scales with a default value
--thres : threshold to skip holes with death-birth < thres (default=0 to use all holes)
--output : output filename for gram matrix
--posfix : posfix for output file
--method : method to compute kernel
0: L2_inner_multi_sse, 1: L2_squared_distance,
2: Slice Wasserstein, 3:L2_inner_multi_nosse, 4:riemmannian_metric
--theta_ndirs : number of direction in wasserstein slice distance for theta
--phi_ndirs : number of direction in wasserstein slice distance for phi
--alltau : use all tau (True), or single tau (False)
--opttau : specify single tau (enable if alltau=0)
if opttau > 0 -> calculate single-delay kernel with tau=opttau
if opttau <= 0 -> calculate single-delay kernel with tau specified in barcode list file
--help : print usage option
Example of list of barcodes for input (see more at run-compute-kernel.bat):
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_1.10e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_1.30e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_1.20e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_5.70e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_7.30e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_9.00e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_5.90e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_8.20e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_8.50e-01_index_1_dim_1.txt
demo\ph_GN_norm_0\diffusion_barcode_nodes_32_group_4_avgdeg_16_rate_5.50e-01_index_1_dim_1.txt
Generate igraph database files from .graphml files. Example:
genigraph("MUTAG")
to convert all *.graphml files in data/MUTAG/graphml to list of graphs: jointddf_MUTAG.RData.
Calculate graph-kernels from igraph database files. Example:
datname <- "MUTAG"
calckernel()
Calculate common features from network adjency matrix
16 common features:
avg_deg_centrality, avg_clustering_coeff, avg_shortest_paths,
avg_eccentricity, avg_node_closeness_centrality,
avg_node_betweeness_centrality, avg_edge_betweeness_centrality,
avg_local_efficiency, avg_triangles,
density, transitivity, diameter, radius,
assortiative_coef, global_efficiency, nums_connected_parts
Usage: python make_common_features.py -d dataname -i infolder -o outfolder
Example: python make_common_features.py -d MUTAG -i real-networks -o common-features