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Hubness reduction and analysis tools

Project description Documentation Status


The Hub Toolbox is a collection of scripts for the analysis and reduction of hubness in high-dimensional data.

It allows you to

  • analyze, whether your datasets show hubness
  • reduce hubness via a variety of different techniques (including scaling and centering approaches) and obtain secondary distances for downstream analysis inside or outside the Hub Toolbox
  • perform evaluation tasks with both internal and external measures (e.g. Goodman-Kruskal index and k-NN classification)


Make sure you have a working Python3 environment (at least 3.4) with numpy, scipy and scikit-learn packages. Use pip3 to install the latest stable version:

pip3 install hub-toolbox

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


Documentation is available online:


To run a full hubness analysis on the example dataset (DEXTER) using some of the provided hubness reduction methods, simply run the following in a Python shell:

>>> from hub_toolbox.HubnessAnalysis import HubnessAnalysis
>>> ana = HubnessAnalysis()
>>> ana.analyze_hubness()

See how you can conduct the individual analysis steps:

import hub_toolbox

# load the DEXTER example dataset
D, labels, vectors = hub_toolbox.IO.load_dexter()

# calculate intrinsic dimension estimate
d_mle = hub_toolbox.IntrinsinDim.intrinsic_dimension(vectors)

# calculate hubness (here, skewness of 5-occurence)
S_k, _, _ = hub_toolbox.Hubness.hubness(D=D, k=5, metric='distance')

# perform k-NN classification LOO-CV for two different values of k
acc, _, _ = hub_toolbox.KnnClassification.score(
        D=D, target=labels, k=[1,5], metric='distance')

# calculate Goodman-Kruskal index
gamma = hub_toolbox.GoodmanKruskal.goodman_kruskal_index(
        D=D, classes=labels, metric='distance')

# Reduce hubness with Mutual Proximity (Empiric distance distribution)
D_mp = hub_toolbox.MutualProximity.mutual_proximity_empiric(
        D=D, metric='distance')

# Reduce hubness with Local Scaling variant NICDM
D_nicdm = hub_toolbox.LocalScaling.nicdm(D=D, k=10, metric='distance')

# Check whether indices improve after hubness reduction
S_k_mp, _, _ = hub_toolbox.Hubness.hubness(D=D_mp, k=5, metric='distance')
acc_mp, _, _ = hub_toolbox.KnnClassification.score(
        D=D_mp, target=labels, k=[1,5], metric='distance')
gamma_mp = hub_toolbox.GoodmanKruskal.goodman_kruskal_index(
        D=D_mp, classes=labels, metric='distance')

# Repeat the last steps for all secondary distances you calculated

Check the Tutorial for in-depth explanations of the same.


The Hub Toolbox is a work in progress. 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. Please don’t hesitate to file an issue here on GitHub.

(c) 2011-2016, Dominik Schnitzer and Roman Feldbauer
Austrian Research Institute for Artificial Intelligence (OFAI)
Contact: <>


If you use the Hub Toolbox in your scientific publication, please cite:

                 title={Centering Versus Scaling for Hubness Reduction},
                 author={Feldbauer, Roman and Flexer, Arthur},
                 book={Artificial Neural Networks and Machine Learning - ICANN 2016},


                 title={Local and global scaling reduce hubs in space},
                 author={Schnitzer, Dominik and Flexer, Arthur and
                                 Schedl, Markus and Widmer, Gerhard},
                 journal={Journal of Machine Learning Research},


The HUB TOOLBOX is licensed under the terms of the GNU GPLv3.


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

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