philentropy

Similarity and Distance Quantification between Probability Functions

Describe and understand the world through data.

Data collection and data comparison are the foundations of scientific research. Mathematics provides the abstract framework to describe patterns we observe in nature and Statistics provides the framework to quantify the uncertainty of these patterns. In statistics, natural patterns are described in form of probability distributions which either follow a fixed pattern (parametric distributions) or more dynamic patterns (non-parametric distributions).

The `philentropy` package implements fundamental distance and similarity measures to quantify distances between probability density functions as well as traditional information theory measures. In this regard, it aims to provide a framework for comparing natural patterns in a statistical notation.

This project is born out of my passion for statistics and I hope that it will be useful to the people who share it with me.

Installation

``````# install philentropy version 0.3.0 from CRAN
install.packages("philentropy")``````

Citation

I am developing `philentropy` in my spare time and would be very grateful if you would consider citing the following paper in case `philentropy` was useful for your own research. I plan on maintaining and extending the `philentropy` functionality and usability in the next years and require citations to back up these efforts. Many thanks in advance :)

HG Drost, (2018). Philentropy: Information Theory and Distance Quantification with R. Journal of Open Source Software, 3(26), 765. https://doi.org/10.21105/joss.00765

Examples

``````library(philentropy)
# retrieve available distance metrics
getDistMethods()``````
`````` [1] "euclidean"         "manhattan"         "minkowski"
[4] "chebyshev"         "sorensen"          "gower"
[7] "soergel"           "kulczynski_d"      "canberra"
[10] "lorentzian"        "intersection"      "non-intersection"
[13] "wavehedges"        "czekanowski"       "motyka"
[16] "kulczynski_s"      "tanimoto"          "ruzicka"
[19] "inner_product"     "harmonic_mean"     "cosine"
[22] "hassebrook"        "jaccard"           "dice"
[25] "fidelity"          "bhattacharyya"     "hellinger"
[28] "matusita"          "squared_chord"     "squared_euclidean"
[31] "pearson"           "neyman"            "squared_chi"
[34] "prob_symm"         "divergence"        "clark"
[40] "k_divergence"      "topsoe"            "jensen-shannon"
[43] "jensen_difference" "taneja"            "kumar-johnson"
[46] "avg"``````
``````# define a probability density function P
P <- 1:10/sum(1:10)
# define a probability density function Q
Q <- 20:29/sum(20:29)

# combine P and Q as matrix object
x <- rbind(P,Q)

# compute the jensen-shannon distance between
# probability density functions P and Q
distance(x, method = "jensen-shannon")``````
``````jensen-shannon using unit 'log'.
jensen-shannon
0.02628933``````

Alternatively, users can also retrieve values from all available distance/similarity metrics using `dist.diversity()`:

``dist.diversity(x, p = 2, unit = "log2")``
``````        euclidean         manhattan
0.12807130        0.35250464
minkowski         chebyshev
0.12807130        0.06345083
sorensen             gower
0.17625232        0.03525046
soergel      kulczynski_d
0.29968454        0.42792793
canberra        lorentzian
2.09927095        0.49712136
intersection  non-intersection
0.82374768        0.17625232
wavehedges       czekanowski
3.16657887        0.17625232
motyka      kulczynski_s
0.58812616        2.33684211
tanimoto           ruzicka
0.29968454        0.70031546
inner_product     harmonic_mean
0.10612245        0.94948528
cosine        hassebrook
0.93427641        0.86613103
jaccard              dice
0.13386897        0.07173611
fidelity     bhattacharyya
0.97312397        0.03930448
hellinger          matusita
0.32787819        0.23184489
squared_chord squared_euclidean
0.05375205        0.01640226
pearson            neyman
0.16814418        0.36742465
squared_chi         prob_symm
0.10102943        0.20205886
divergence             clark
1.49843905        0.86557468
0.53556883        0.13926288
jeffreys      k_divergence
0.31761069        0.04216273
topsoe    jensen-shannon
0.07585498        0.03792749
jensen_difference            taneja
0.03792749        0.04147518
kumar-johnson               avg
0.62779644        0.20797774``````

Install Developer Version

``````# install.packages("devtools")
# install the current version of philentropy on your system
library(devtools)
install_github("HajkD/philentropy", build_vignettes = TRUE, dependencies = TRUE)``````

NEWS

The current status of the package as well as a detailed history of the functionality of each version of `philentropy` can be found in the NEWS section.

Important Functions

Distance Measures

• `distance()` : Implements 46 fundamental probability distance (or similarity) measures
• `getDistMethods()` : Get available method names for ‘distance’
• `dist.diversity()` : Distance Diversity between Probability Density Functions
• `estimate.probability()` : Estimate Probability Vectors From Count Vectors

Information Theory

• `H()` : Shannon’s Entropy H(X)
• `JE()` : Joint-Entropy H(X,Y)
• `CE()` : Conditional-Entropy H(X | Y)
• `MI()` : Shannon’s Mutual Information I(X,Y)
• `KL()` : Kullback–Leibler Divergence
• `JSD()` : Jensen-Shannon Divergence
• `gJSD()` : Generalized Jensen-Shannon Divergence

Studies that successfully applied the `philentropy` package

• Single cell census of human kidney organoids shows reproducibility and diminished off-target cells after transplantation A Subramanian et al. - Nature Communications, 2019

• Different languages, similar encoding efficiency: Comparable information rates across the human communicative niche C Coupé, YM Oh, D Dediu, F Pellegrino - Science Advances, 2019

• Loss of adaptive capacity in asthmatic patients revealed by biomarker fluctuation dynamics after rhinovirus challenge A Sinha et al. - eLife, 2019

• Evacuees and Migrants Exhibit Different Migration Systems after the Great East Japan Earthquake and Tsunami M Hauer, S Holloway, T Oda – 2019

• Robust comparison of similarity measures in analogy based software effort estimation P Phannachitta - 11th International Conference on Software, 2017

• Expression variation analysis for tumor heterogeneity in single-cell RNA-sequencing data EF Davis-Marcisak, P Orugunta et al. - BioRxiv, 2018

• SEDE-GPS: socio-economic data enrichment based on GPS information T Sperlea, S Füser, J Boenigk, D Heider - BMC bioinformatics, 2018

• How the Choice of Distance Measure Influences the Detection of Prior-Data Conflict K Lek, R Van De Schoot - Entropy, 2019

• Concept acquisition and improved in-database similarity analysis for medical data I Wiese, N Sarna, L Wiese, A Tashkandi, U Sax - Distributed and Parallel Databases, 2019

• Differential variation analysis enables detection of tumor heterogeneity using single-cell RNA-sequencing data EF Davis-Marcisak, TD Sherman et al. - Cancer research, 2019

• Dynamics of Vaginal and Rectal Microbiota over Several Menstrual Cycles in Female Cynomolgus Macaques MT Nugeyre, N Tchitchek, C Adapen et al. - Frontiers in Cellular and Infection Microbiology, 2019

• Inferring the quasipotential landscape of microbial ecosystems with topological data analysis WK Chang, L Kelly - BioRxiv, 2019

• Shifts in the nasal microbiota of swine in response to different dosing regimens of oxytetracycline administration KT Mou, HK Allen, DP Alt, J Trachsel et al. - Veterinary microbiology, 2019

• The Patchy Distribution of Restriction–Modification System Genes and the Conservation of Orphan Methyltransferases in Halobacteria MS Fullmer, M Ouellette, AS Louyakis et al. - Genes, 2019

• Genetic differentiation and intrinsic genomic features explain variation in recombination hotspots among cocoa tree populations EJ Schwarzkopf, JC Motamayor, OE Cornejo - BioRxiv, 2019

• Metastable regimes and tipping points of biochemical networks with potential applications in precision medicine SS Samal, J Krishnan, AH Esfahani et al. - Reasoning for Systems Biology and Medicine, 2019

• Genome‐wide characterization and developmental expression profiling of long non‐coding RNAs in Sogatella furcifera ZX Chang, OE Ajayi, DY Guo, QF Wu - Insect science, 2019

• Loss of adaptive capacity in asthmatics revealed by biomarker fluctuation dynamics upon experimental rhinovirus challenge A Sinha, R Lutter, B Xu, T Dekker, B Dierdorp et al. - BioRxiv, 2019

• Development of a simulation system for modeling the stock market to study its characteristics P Mariya – 2018

• The Tug1 Locus is Essential for Male Fertility JP Lewandowski, G Dumbović, AR Watson, T Hwang et al. - BioRxiv, 2019

• Microbiotyping the sinonasal microbiome A Bassiouni, S Paramasivan, A Shiffer et al. - BioRxiv, 2019

• Critical search: A procedure for guided reading in large-scale textual corpora J Guldi - Journal of Cultural Analytics, 2018

• A Bibliography of Publications about the R, S, and S-Plus Statistics Programming Languages NHF Beebe – 2019

• Improved state change estimation in dynamic functional connectivity using hidden semi-Markov models H Shappell, BS Caffo, JJ Pekar, MA Lindquist - NeuroImage, 2019

• A Smart Recommender Based on Hybrid Learning Methods for Personal Well-Being Services RM Nouh, HH Lee, WJ Lee, JD Lee - Sensors, 2019

• Cognitive Structural Accuracy V Frenz – 2019

• Kidney organoid reproducibility across multiple human iPSC lines and diminished off target cells after transplantation revealed by single cell transcriptomics A Subramanian, EH Sidhom, M Emani et al. - BioRxiv, 2019

• Multi-classifier majority voting analyses in provenance studies on iron artefacts G Żabiński et al. - Journal of Archaeological Science, 2020

Discussions and Bug Reports

I would be very happy to learn more about potential improvements of the concepts and functions provided in this package.

Furthermore, in case you find some bugs or need additional (more flexible) functionality of parts of this package, please let me know:

https://github.com/HajkD/philentropy/issues

or find me on twitter: HajkDrost