Robust Euclidean Embedding
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Robust Euclidean Embedding

This package is a python implementation of Robust Euclidean Embedding (REE). REE is an algorithm that takes as input a set of n interpoint dissimilarities (distances) and tries to find n points whose Euclidean distances match the input. This basic task is known as an embedding or multidimensional scaling. The algorithm is described in this paper:

L. Cayton and S. Dasgupta. Robust Euclidean embedding. Twenty-Third International Conference on Machine Learning (ICML), 2006.

This implementation is based on the subgradient algorithm described in that paper. It also has an implementation of classical multidimensional scaling (cMDS).

Note that this implementation is not what was used to produce the results in the original paper; that was a matlab implementation that is long gone. It differs in at least one respect: in default usage, the algorithm will attempt to set the step size via a line search on each iteration. If the line search fails, it will fall back to using a step size of c / sqrt(i), where i is the iteration number.


Basic usage.

import ree

# D is a n-by-n numpy array
X = ree(D)
# X will be a n-by-n numpy array. The rows correspond to points; the columns to their attributes. 
# To get a d-dimensional embedding, simply do:
X_lowdim = X[:, :d]


  • Set a limit on the number of iterations:
X = ree(D, max_num_its=1000)
  • Turn off the line search (always use a step size of c/sqrt(n)):
X = ree(D, no_line_search=True)
  • Turn off verbosity:
X = ree(D, verbosity=False)
  • Initialize solution to the zeros-matrix (otherwise a random n-by-2 dimensional configuration will be used):
X = ree(D, init_zeros=True)

Requirements and limitations

This is currently only tested under Python 2.7. It requires only scipy and numpy.