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Hubness reduction and analysis tools

Project description

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scikit-hubness comprises tools for the analysis and reduction of hubness in high-dimensional data. Hubness is an aspect of the curse of dimensionality and is detrimental to many machine learning and data mining tasks.

The skhubness.analysis and skhubness.reduction packages allow to

  • analyze, whether your data sets show hubness
  • reduce hubness via a variety of different techniques
  • perform downstream analysis (performance assessment) with scikit-learn due to compatible data structures

The skhubness.neighbors package acts as a drop-in replacement for sklearn.neighbors. In addition to the functionality inherited from scikit-learn, it also features

  • approximate nearest neighbor search
  • hubness reduction
  • and combinations,

which allows for fast hubness-reduced neighbor search in large datasets (tested with >1M objects).

We follow the API conventions and code style of scikit-learn.


Make sure you have a working Python3 environment (at least 3.7).

Use pip to install the latest stable version of scikit-hubness from PyPI:

pip install scikit-hubness

Dependencies are installed automatically, if necessary. scikit-hubness requires numpy, scipy and scikit-learn. Approximate nearest neighbor search and approximate hubness reduction additionally requires at least one of the following packges:

  • nmslib for hierachical navigable small-world graphs ('hnsw')
  • ngtpy for nearest neighbor graphs ('nng'), and variants (ANNG, ONNG)
  • puffinn for locality-sensitive hashing ('lsh')
  • falconn for alternative LSH ('falconn_lsh') , or
  • annoy for random projection forests ('rptree').

Some modules require tqdm or joblib. All these packages are available from open repositories, such as PyPI.

For more details and alternatives, please see the Installation instructions.


Documentation is available online:

What's new

See the changelog to find what's new in the latest package version.


Users of scikit-hubness may want to

  1. analyse, whether their data show hubness
  2. reduce hubness
  3. perform learning (classification, regression, ...)

The following example shows all these steps for an example dataset from the text domain (dexter). (Please make sure you have installed scikit-hubness).

# load the example dataset 'dexter'
from import load_dexter
X, y = load_dexter()

# dexter is embedded in a high-dimensional space,
# and could, thus, be prone to hubness
print(f'X.shape = {X.shape}, y.shape={y.shape}')

# assess the actual degree of hubness in dexter
from skhubness import Hubness
hub = Hubness(k=10, metric='cosine')
k_skew = hub.score()
print(f'Skewness = {k_skew:.3f}')

# additional hubness indices are available, for example:
print(f'Robin hood index: {hub.robinhood_index:.3f}')
print(f'Antihub occurrence: {hub.antihub_occurrence:.3f}')
print(f'Hub occurrence: {hub.hub_occurrence:.3f}')

# There is considerable hubness in dexter.
# Let's see, whether hubness reduction can improve
# kNN classification performance 
from sklearn.model_selection import cross_val_score
from skhubness.neighbors import KNeighborsClassifier

# vanilla kNN
knn_standard = KNeighborsClassifier(n_neighbors=5,
acc_standard = cross_val_score(knn_standard, X, y, cv=5)

# kNN with hubness reduction (mutual proximity)
knn_mp = KNeighborsClassifier(n_neighbors=5,
acc_mp = cross_val_score(knn_mp, X, y, cv=5)

print(f'Accuracy (vanilla kNN): {acc_standard.mean():.3f}')
print(f'Accuracy (kNN with hubness reduction): {acc_mp.mean():.3f}')

# Accuracy was considerably improved by mutual proximity.
# Did it actually reduce hubness?
hub_mp = Hubness(k=10, metric='cosine',
k_skew_mp = hub_mp.score()
print(f'Skewness after MP: {k_skew_mp:.3f} '
      f'(reduction of {k_skew - k_skew_mp:.3f})')
print(f'Robin hood: {hub_mp.robinhood_index:.3f} '
      f'(reduction of {hub.robinhood_index - hub_mp.robinhood_index:.3f})')

# The neighbor graph can also be created directly,
# with or without hubness reduction
from skhubness.neighbors import kneighbors_graph
neighbor_graph = kneighbors_graph(X, n_neighbors=5, hubness='mutual_proximity')

Check the User Guide for additional example usage.


The developers of scikit-hubness welcome all kinds of contributions! Get in touch with us if you have comments, would like to see an additional feature implemented, would like to contribute code or have any other kind of issue. Don't hesitate to file an issue here on GitHub.

For more information about contributing, please have a look at the contributors guidelines.

(c) 2018-2019, Roman Feldbauer
Austrian Research Institute for Artificial Intelligence (OFAI) and
University of Vienna, Division of Computational Systems Biology (CUBE)
Contact: <>


A software publication paper is currently in preparation. Until then, if you use scikit-hubness in your scientific publication, please cite:

author={R. {Feldbauer} and M. {Leodolter} and C. {Plant} and A. {Flexer}},
booktitle={2018 IEEE International Conference on Big Knowledge (ICBK)},
title={Fast Approximate Hubness Reduction for Large High-Dimensional Data},
keywords={computational complexity;data analysis;data mining;mobile computing;public domain software;software packages;mobile device;open source software package;high-dimensional data mining;fast approximate hubness reduction;massive mobility data;linear complexity;quadratic algorithmic complexity;dimensionality curse;Complexity theory;Indexes;Estimation;Data mining;Approximation algorithms;Time measurement;curse of dimensionality;high-dimensional data mining;hubness;linear complexity;interpretability;smartphones;transport mode detection},

The technical report Fast approximate hubness reduction for large high-dimensional data is available at OFAI.

Additional reading

Local and Global Scaling Reduce Hubs in Space, Journal of Machine Learning Research 2012, Link.

A comprehensive empirical comparison of hubness reduction in high-dimensional spaces, Knowledge and Information Systems 2018, DOI.


scikit-hubness is licensed under the terms of the BSD-3-Clause license. The skhubness.neighbors package was modified from sklearn.neighbors, distributed under the same license. Users can, therefore, safely use scikit-hubness in the same way they use scikit-learn.

Note: Individual files contain the following tag instead of the full license text.

    SPDX-License-Identifier: BSD-3-Clause

This enables machine processing of license information based on the SPDX License Identifiers that are here available:


Several parts of scikit-hubness adapt code from scikit-learn. We thank all the authors and contributors of this project for the tremendous work they have done.

PyVmMonitor is being used to support the development of this free open source software package. For more information go to

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