This workspace contains c# solution of the problem 'histogram cells to servers' and Python project of the generation of simulated data and related figures.
The c# solution 'histogram cells to servers' includes lp_solve as a compiled library which is a Linear Programming system (see: http://web.mit.edu/lpsolve/doc). The citation information is available below.
Description : Open source (Mixed-Integer) Linear Programming system
Language : Multi-platform, pure ANSI C / POSIX source code, Lex/Yacc based parsing
Official name : lp_solve (alternatively lpsolve)
Release data : Version 5.1.0.0 dated 1 May 2004
Co-developers : Michel Berkelaar, Kjell Eikland, Peter Notebaert
Licence terms : GNU LGPL (Lesser General Public Licence)
Citation policy : General references as per LGPL Module specific references as specified therein
The Python project for simulating and plotting data includes scikit-learn (see: http://scikit-learn.org/stable/index.html) for usage of MDS algorithm for sophisticated color management of figure generation. The citation information is available below.
Scikit-learn: Machine Learning in Python, Pedregosa et al., JMLR 12, pp. 2825-2830, 2011.
This c# solution 'spectral clustering for directed network' is based on the below-mentioned articles (see: References). This will be used for another approach of the original problem. It depends on MathNet.Numerics (see: http://numerics.mathdotnet.com/) which is used for tasks of Linear Algebra topics.
See Notations for the followings:
- Input: file which contains weights
- Output: clusters of the directed network
- Form the matrix
- Compute the eigenvector which belongs to the second largest eigenvalue. Thereafter split the node set into two parts based on this vector. (If a coordinate of the vector is non-negative the related node will belong to the one part otherwise to the other part.)
- Repeat steps 1. and 2. for the parts while the needed condition is satisfied.
- Gleich, David. "Hierarchical directed spectral graph partitioning." Tech. rep., Stanford University (2006).
- Malliaros, Fragkiskos D., and Michalis Vazirgiannis. "Clustering and community detection in directed networks: A survey." Physics Reports 533.4 (2013): 95-142.