soft-brownian-offset

Soft Brownian Offset (SBO) defines an iterative approach to translate points by a most likely distance from a given dataset.

Background

The technique is described in detail within the paper TBA. For citations please see cite.

Installation

This project is hosted on PyPI and can therefore be installed easily through pip:

pip install sbo

Dependending on your setup you may need to add --user after the install.

Demonstration

The following code creates the plot seen above:

#!/usr/bin/env python3
# Creates a plot for Soft Brownian Offset (SBO)

import numpy as np
import pylab as plt
import itertools
import sys

from matplotlib import cm
from sklearn.datasets import make_moons

from sbo import soft_brownian_offset, gaussian_hyperspheric_offset

plt.rc('text', usetex=True)

c = cm.tab10.colors

def plot_data(X, y, ax=plt):
    ax.scatter(X[:, 0], X[:, 1], marker='x', s=20, label='ID', alpha=alpha, c=[c[-1]])
    ax.scatter(y[:, 0], y[:, 1], marker='+', label='SBO', alpha=alpha, c=[c[-6]])

def plot_mindist(X, y, ax=plt):
    if len(X.shape) == 1:
        X = X[:, None]
    if len(y.shape) == 1:
        y = y[:, None]
    ax.hist(pairwise_distances(y, X).min(axis=1), bins=len(y) // 10)
    ax.set_xlabel("Minimum distance from ood to id")
    ax.set_ylabel("Count")

def plot_data_mindist(X, y):
    fig, ax = plt.subplots(1, 2)
    plot_data(X, y, ax=ax[0])
    plot_mindist(X, y, ax=ax[1])
    plt.show()


n_samples_id = 60
n_samples_ood = 150
noise = .08
show_progress = False
alpha = .6

n_colrow = 3
d_min = np.linspace(.25, .45, n_colrow)
softness = np.linspace(0, 1, n_colrow)
fig, ax = plt.subplots(n_colrow, n_colrow, sharex=True, sharey=True, figsize=(8.5, 9))

X, _ = make_moons(n_samples=n_samples_id, noise=noise)
for i, (d_min_, softness_) in enumerate(itertools.product(d_min, softness)):
    xy = i // n_colrow, i % n_colrow
    d_off_ = d_min_ * .7
    ax[xy].set_title(f"$d^- = {d_min_:.2f}\ d^+ = {d_off_:.2f}\ \sigma = {softness_}$")
    if softness_ == 0:
        softness_ = False
    y = soft_brownian_offset(X, d_min_, d_off_, n_samples=n_samples_ood, softness=softness_, show_progress=show_progress)
    plot_data(X, y, ax=ax[xy])
    if i // n_colrow == len(d_min) - 1:
        ax[xy].set_xlabel("$x_1$")
    if i % n_colrow == 0:
        ax[xy].set_ylabel("$x_2$")
ax[0, n_colrow - 1].legend(loc='upper right')

plt.tight_layout()
plt.savefig('assets/sbo-demo.svg')

Cite

Please cite SBO in your paper if it helps your research TBA:

@article{name2020sbo,
  Author = {TBA},
  Journal = {arXiv preprint arXiv:TBA},
  Title = {TBA},
  Year = {2020}
}