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توضیحات

Cutnorm approximation via Gaussian Rounding and Optimization with Orthogonality Constraints

ویژگی	مقدار
سیستم عامل	-
نام فایل	cutnorm-0.1.9
نام	cutnorm
نسخه کتابخانه	0.1.9
نگهدارنده	[]
ایمیل نگهدارنده	[]
نویسنده	Ping-Ko Chiu, Peter Diao, Olewasanmi Koyejo
ایمیل نویسنده	pchiu5@illinois.edu, peter.z.diao@gmail.com, sanmi@illinois.edu
آدرس صفحه اصلی	https://github.com/pingkoc/cutnorm
آدرس اینترنتی	https://pypi.org/project/cutnorm/
مجوز	MIT

======= Cutnorm ======= Approximation via Gaussian Rounding and Optimization with Orthogonality Constraints ----------------------------------------------------------------------------------- This package computes the approximations to the cutnorm of matrices using some of the techniques detailed by Alon and Noar [ALON2004]_ and a fast optimization algorithm by Wen and Yin [WEN2013]_. Read the documentation_. .. _documentation: https://pingkoc.github.io/cutnorm/cutnorm.html Installation ------------ Use pip_ to install the package. Install from terminal as follows:: $ pip install cutnorm .. _pip: http://www.pip-installer.org/en/latest/ Example Usage ------------- Given the adjacency matrices of two simple graphs A and B, we wish to compute a norm for the difference matrix (A - B) between the two graphs. An obvious display of the advantages of using a cutnorm over l1 norm is to consider the value of the norms on `Erdos-Renyi random graphs`_. .. _`Erdos-Renyi random graphs`: https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93R%C3%A9nyi_model Given two Erdos-Renyi random graphs with constant n and p=0.5, the edit distance (l1 norm) of the difference (after normalization) is 0.5 with large probability. An l1 norm of 1 implies the two matrices are completely different, 0 implies identity, and 0.5 is somewhere in between. However, these two graphs have the same global structure. As n approaches infinity, A and B converges to the same graphon object that is 0.5 everywhere. The edit distance fails as a notion of 'distance' between the two graphs in the perspective of global structural similarity as discussed by Lovasz [LOVASZ2009]_. The cutnorm is a measure of distance that reflects global structural similarity. In fact, the cutnorm of the difference for this example approaches 0 as n grows. Below is an example of using the cutnorm package and tools. .. code:: python import numpy as np from cutnorm import compute_cutnorm, tools # Generate Erdos Renyi Random Graph (Simple/Undirected) n = 100 p = 0.5 erdos_renyi_a = tools.sbm.erdos_renyi(n, p, symmetric=True) erdos_renyi_b = tools.sbm.erdos_renyi(n, p, symmetric=True) # Compute l1 norm normalized_diff = (erdos_renyi_a - erdos_renyi_b) / n**2 l1 = np.linalg.norm(normalized_diff.flatten(), ord=1) # Compute cutnorm cutn_round, cutn_sdp, info = compute_cutnorm(erdos_renyi_a, erdos_renyi_b) print("l1 norm: ", l1) # prints l1 norm value near ~0.5 print("cutnorm rounded: ", cutn_round) # prints cutnorm rounded solution near ~0 print("cutnorm sdp: ", cutn_sdp) # prints cutnorm sdp solution near ~0 ---- .. [ALON2004] Noga Alon and Assaf Naor. 2004. Approximating the cut-norm via Grothendieck's inequality. In Proceedings of the thirty-sixth annual ACM symposium on Theory of computing (STOC '04). ACM, New York, NY, USA, 72-80. DOI: http://dx.doi.org/10.1145/1007352.1007371 .. [WEN2013] Zaiwen Wen and Wotao Yin. 2013. A feasible method for optimization with orthogonality constraints. Math. Program. 142, 1-2 (December 2013), 397-434. DOI: https://doi.org/10.1007/s10107-012-0584-1 .. [LOVASZ2009] Lovasz, L. 2009. Very large graphs. ArXiv:0902.0132 [Math]. Retrieved from http://arxiv.org/abs/0902.0132

نحوه نصب

نصب پکیج whl cutnorm-0.1.9:

pip install cutnorm-0.1.9.whl

نصب پکیج tar.gz cutnorm-0.1.9:

pip install cutnorm-0.1.9.tar.gz