Python implementation of ACD algorithm described in:

[1] Safdari, H., De Bacco, C. Anomaly detection and community detection in networks. J Big Data 9, 122 (2022).

This is a probabilistic generative model and efficient algorithm to model anomalous edges in networks. It assigns latent variables as community memberships to nodes and anomaly parameter to the edges.

If you use this code please cite [1].

The paper can be found at https://doi.org/10.1186/s40537-022-00669-1.

Copyright (c) 2020 Hadiseh Safdari and Caterina De Bacco.

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON INFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

• code : Contains the Python implementation of ACD algorithm, the code for performing the cross-validation procedure and the code for generating benchmark synthetic data with intrinsic community structure and anomalous edges.
• data/input : Contains an example of a network having an intrinsic community structure and anomalous edges, and some example files to initialize the latent variables. They are synthetic data.
• data/output : Contains some results to test the code.

To test the program on the given example file, type:

cd code
python main.py

It will use the sample network contained in ./data/input. The adjacency matrix syn_data.dat represents a directed, weighted network with N=500 nodes, K=3 equal-size unmixed communities with an assortative structure $\rho_a$ =0.3, and **$ \pi$ = 0.2 **..

• -K : Number of communities, (default=3).
• -A : Input file name of the adjacency matrix, (default='syn_data.dat').
• -f : Path of the input folder, (default='../data/input/').
• -o : Path of the output folder, (default='../data/output/').
• -E : Anomaly flag, (default=1).
• -e: name of the source of the edge,(default='source').
• -t : Name of the target of the edge, (default='target').

You can find a list by running (inside code directory):

python main.py --help

The network should be stored in a .dat file. An example of rows is

node1 node2 3
node1 node3 1

where the first and second columns are the source and target nodes of the edge, respectively; the third column tells if there is an edge and the weight. In this example the edge node1 --> node2 exists with weight 3, and the edge node1 --> node3 exists with weight 1.

Other configuration settings can be set by modifying the setting_*_.yaml files:

• setting_syn_data.yaml : contains the setting to generate synthetic data
• setting_inference.yaml : contains the setting to run the algorithm ACD

The algorithm returns a compressed file inside the data/output folder. To load and print the out-going membership matrix:

import numpy as np  
theta = np.load('theta_data.npz')
print(theta['u'])

theta contains the two NxK membership matrices u ('u') and v ('v'), the 1xKxK (or 1xK if assortative=True) affinity tensor w ('w'), the anomaly parameter $\pi$ ('pi'), the prior $\mu$ ('mu'),, the total number of iterations ('max_it'), the value of the maximum pseudo log-likelihood ('maxPSL') and the nodes of the network ('nodes').

For an example jupyter notebook importing the data, see code/AnomalyDetection_Inf_debug.ipynb.