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FSCNMF

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Abstract

<p align="justify"> An implementation of Fusing Structure and Content via Non-negative Matrix Factorization for Embedding Information Networks. Analysis and visualization of an information network can be facilitated better using an appropriate embedding of the network. Network embedding learns a compact low-dimensional vector representation for each node of the network, and uses this lower dimensional representation for different network analysis tasks. Only the structure of the network is considered by a majority of the current embedding algorithms. However, some content is associated with each node, in most of the practical applications, which can help to understand the underlying semantics of the network. It is not straightforward to integrate the content of each node in the current state-of-the-art network embedding methods. In this paper, we propose a nonnegative matrix factorization based optimization framework, namely FSCNMF which considers both the network structure and the content of the nodes while learning a lower dimensional representation of each node in the network. Our approach systematically regularizes structure based on content and vice versa to exploit the consistency between the structure and content to the best possible extent. We further extend the basic FSCNMF to an advanced method, namely FSCNMF++ to capture the higher order proximities in the network. We conduct experiments on real world information networks for different types of machine learning applications such as node clustering, visualization, and multi-class classification. The results show that our method can represent the network significantly better than the state-of-the-art algorithms and improve the performance across all the applications that we consider. </p> <div style="text-align:center"><img src ="fscnmf.png" ,width=720/></div>

The model is now also available in the package Karate Club.

This repository provides an implementation for FSCNMF as described in the paper:

FSCNMF: Fusing Structure and Content via Non-negative Matrix Factorization for Embedding Information Networks. Sambaran Bandyopadhyay, Harsh Kara, Aswin Kannan and M N Murty arXiv, 2018. https://arxiv.org/pdf/1804.05313.pdf

Alternative implementations are available [here] and [here].

Requirements

The codebase is implemented in Python 3.5.2. package versions used for development are just below.

networkx          2.4
tqdm              4.28.1
numpy             1.15.4
pandas            0.23.4
texttable         1.5.0
scipy             1.1.0
argparse          1.1.0

Datasets

<p align="justify"> The code takes an input graph in a csv file. Every row indicates an edge between two nodes separated by a comma. The first row is a header. Nodes should be indexed starting with 0. Sample graphs for the `Wikipedia Chameleons` and `Wikipedia Giraffes` are included in the `input/` directory. </p>

The feature matrix can be stored two ways:

If the feature matrix is a sparse binary one it is stored as a json. Nodes are keys of the json and features are the values. For each node feature column ids are stored as elements of a list. The feature matrix is structured as:

{ 0: [0, 1, 38, 1968, 2000, 52727],
  1: [10000, 20, 3],
  2: [],
  ...
  n: [2018, 10000]}

If the feature matrix is dense it is assumed that it is stored as csv with comma separators. It has a header, the first column contains node identifiers and it is sorted by these identifers. It should look like this:

NODE ID	Feature 1	Feature 2	Feature 3	Feature 4
0	3	0	1.37	1
1	1	1	2.54	-11
2	2	0	1.08	-12
3	1	1	1.22	-4
...	...	...	...	...
n	5	0	2.47	21

Options

Learning of the embedding is handled by the src/main.py script which provides the following command line arguments.

Input and output options

  --edge-path    STR        Input graph path.           Default is `input/chameleon_edges.csv`.
  --feature-path STR        Input Features path.        Default is `input/chameleon_features.json`.
  --output-path  STR        Embedding path.             Default is `output/chameleon_fscnmf.csv`.

Model options

  --features       STR         Structure of the feature matrix.                   Default is `sparse`. 
  --dimensions     INT         Number of embeding dimensions.                     Default is 32.
  --order          INT         Order of adjacency matrix powers.                  Default is 3.
  --iterations     INT         Number of power interations.                       Default is 500.
  --alpha_1        FLOAT       Alignment parameter for adjacency matrix.          Default is 1000.0.
  --alpha_2        FLOAT       Adjacency basis regularization.                    Default is 1.0.
  --alpha_3        FLOAT       Adjacency features regularization.                 Default is 1.0.
  --beta_1         FLOAT       Alignment parameter for feature matrix.            Default is 1000.0.
  --beta_2         FLOAT       Attribute basis regularization .                   Default is 1.0.
  --beta_3         FLOAT       Attribute feature regularization.                  Default is 1.0.
  --gamma          FLOAT       Embedding mixing parameter.                        Default is 0.5.  
  --lower-control  FLOAT       Overflow control parameter.                        Default is 10**-15.

Examples

The following commands learn a graph embedding and write the embedding to disk. The node representations are ordered by the ID.

Creating an FSCNMF embedding of the default dataset with the default hyperparameter settings. Saving the embedding at the default path.

$ python src/main.py

Creating an FSCNMF embedding of the default dataset with 128 dimensions and approximation order 1.

$ python src/main.py --dimensions 128 --order 1

Creating an FSCNMF embedding of the default dataset with asymmetric mixing.

$ python src/main.py --gamma 0.1

Creating an embedding of an other dense structured dataset the Wikipedia Giraffes. Saving the output in a custom folder.

$ python src/main.py --edge-path input/giraffe_edges.csv --feature-path input/giraffe_features.csv --output-path output/giraffe_fscnmf.csv --features dense