MoDE-embeddings 0.0.3

Source code for Multi-objective n-dimensional embeddings

Python implementation for MoDE (Multi-objective 2D Embeddings)

Important modules

• "MoDE": Contains the main class that implements MoDE.
• "metrics": Contains the functions to compute the three metrics introduced in the paper, i.e, distance, correlation, and order preservation metrics.
• "waterfilling_compression": Contains the implementation of waterfilling algorithm.

Usage

MoDE embeddings can be trained on exact or inexact distance matrices. In the case of inexact distance information, ranges of lower and upper bounds on the distances in the form of seperate lower and upper bound distance matrices should be given to the fit_transform function. The resulting embeddings are in 2D dimensions and the data points are placed in the embedding space such that samples with higher scores are placed in higher angles (in polar coordinates).

from MoDE import MoDE
mode = MoDE(n_neighbor=20, max_iter=100000, tol=0.0001, verbose=True)
x_2d = mode.fit_transform(data, score, dm_ub, dm_lb)

Once the MoDE embeddings are trained, you can measure the fidelity of the embedded dataset to the original dataset in terms of preserving distances, correlations and orders. To do so, you can use the metric functions available from metrics module.

from metrics import distance_metric, correlation_metric, order_preservation
dm_avg = (dm_ub+dm_lb) / 2
R_d = distance_metric(data, x_2d, dm_avg, n_neighbor=20)
R_c = correlation_metric(data, x_2d, dm_avg, n_neighbor=20)
R_o = order_preservation(x_2d, dm_avg, n_neighbor=20, score=score.squeeze())

Waterfilling algorithm (for data compression)

With waterfilling algorithm you can find tight lower and upper bounds on the pair-wise distances between data points that have been compressed using orthonormal transforms, e.g, fourier transform. Using the WaterfillingCompression class you can compress the data by keeping only a small portion of fourier transform coefficients. Then by calling the compute_distance_bounds method you are able to compute tight lower and upper bounds on pair-wise distances. For more information on the waterfilling algorithm check out the paper: https://arxiv.org/pdf/1405.5873.pdf

from waterfilling_compression import WaterfillingCompression
comp = WaterfillingCompression(num_coeffs=4, coeffs_to_keep='optimal')
dm_ub, dm_lb = comp.compute_distance_bounds(data)