# 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 0.8.0 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
philentropy::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
philentropy::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 `philentropy::dist.diversity()`:

``philentropy::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

• Annelid functional genomics reveal the origins of bilaterian life cycles FM Martín-Zamora, Y Liang, K Guynes et al.- Nature, 2023

• An atlas of gene regulatory elements in adult mouse cerebrum YE Li, S Preissl, X Hou, Z Zhang, K Zhang et al.- Nature, 2021

• Convergent somatic mutations in metabolism genes in chronic liver disease S Ng, F Rouhani, S Brunner, N Brzozowska et al. Nature, 2021

• Antigen dominance hierarchies shape TCF1+ progenitor CD8 T cell phenotypes in tumors ML Burger, AM Cruz, GE Crossland et al. - Cell, 2021

• High-content single-cell combinatorial indexing R Mulqueen et al. - Nature Biotechnology, 2021

• A comparative atlas of single-cell chromatin accessibility in the human brain YE Li, S Preissl, M Miller, ND Johnson, Z Wang et al. - Science, 2023

• Extinction at the end-Cretaceous and the origin of modern Neotropical rainforests MR Carvalho, C Jaramillo et al. - Science, 2021

• sciCSR infers B cell state transition and predicts class-switch recombination dynamics using single-cell transcriptomic data JCF Ng, G Montamat Garcia, AT Stewart et al. - Nature Methods, 2023

• HERMES: a molecular-formula-oriented method to target the metabolome R Giné, J Capellades, JM Badia et al. - Nature Methods, 2021

• The genetic architecture of temperature adaptation is shaped by population ancestry and not by selection regime KA Otte, V Nolte, F Mallard et al. - Genome Biology, 2021

• The Tug1 lncRNA locus is essential for male fertility JP Lewandowski et al. - Genome Biology, 2020

• Transcriptional vulnerabilities of striatal neurons in human and rodent models of Huntington’s disease A Matsushima, SS Pineda, JR Crittenden et al. - Nature Communications, 2023

• Resolving the structure of phage–bacteria interactions in the context of natural diversity KM Kauffman, WK Chang, JM Brown et al. - Nature Communications, 2022

• Gut microbiome-mediated metabolism effects on immunity in rural and urban African populations M Stražar, GS Temba, H Vlamakis et al. - Nature Communications, 2021

• Aging, inflammation and DNA damage in the somatic testicular niche with idiopathic germ cell aplasia M Alfano, AS Tascini, F Pederzoli et al. - Nature Communications, 2021

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

• A single-cell multi-omic atlas spanning the adult rhesus macaque brain KL Chiou, X Huang, MO Bohlen et al. - Science Advances, 2023

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

• Single-cell deletion analyses show control of pro–T cell developmental speed and pathways by Tcf7, Spi1, Gata3, Bcl11a, Erg, and Bcl11b W Zhou, F Gao, M Romero-Wolf, S Jo, EV Rothenberg - Science Immunology, 2022

• Large-scale iterated singing experiments reveal oral transmission mechanisms underlying music evolution M Anglada-Tort, PMC Harrison, H Lee, N Jacoby - Current Biology, 2023

• TAS-Seq is a robust and sensitive amplification method for bead-based scRNA-seq S Shichino, S Ueha, S Hashimoto, T Ogawa et al. - Communications biology, 2022

• Mapping hormone-regulated cell-cell interaction networks in the human breast at single-cell resolution LM Murrow, RJ Weber, JA Caruso et al. - Cell Systems, 2022

• Large-scale chromatin reorganization reactivates placenta-specific genes that drive cellular aging Z Liu, Q Ji, J Ren, P Yan, Z Wu, S Wang, L Sun, Z Wang et al. - Developmental Cell, 2022

• Direct epitranscriptomic regulation of mammalian translation initiation through N4-acetylcytidine D Arango, D Sturgill, R Yang, T Kanai, P Bauer et al. - Molecular Cell, 2022

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

• Sex and hatching order modulate the association between MHC‐II diversity and fitness in early‐life stages of a wild seabird M Pineaux et al - Molecular Ecology, 2020

• BELMM: Bayesian model selection and random walk smoothing in time-series clustering O Sarala, T Pyhäjärvi, MJ Sillanpää - Bioinformatics, 2023

• Cellsig plug-in enhances CIBERSORTx signature selection for multi-dataset transcriptomes with sparse multilevel modelling MA Al Kamran Khan, J Wu, S Yuhan et al. - Bioinformatics, 2023

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

• Multi-Omics Investigation of Innate Navitoclax Resistance in Triple-Negative Breast Cancer Cells M Marczyk et al. - Cancers, 2020

• Impact of Gut Microbiome on Hypertensive Patients with Low-Salt Intake: Shika Study Results S Nagase et al. - Frontiers in Medicine, 2020

• Children’s social networks in developmental psychology: A network approach to capture and describe early social environments N Burke, N Brezack, A Woodward - Frontiers in psychology, 2022

• Combined TCR Repertoire Profiles and Blood Cell Phenotypes Predict Melanoma Patient Response to Personalized Neoantigen Therapy plus Anti-PD-1 A Poran et al. - Cell Reports Medicine, 2020

• Identification of a glioma functional network from gene fitness data using machine learning C Xiang, X Liu, D Zhou, Y Zhou, X Wang, F Chen - Journal of Cellular and Molecular Medicine, 2022

• Whole genome assemblies of Zophobas morio and Tenebrio molitor S Kaur, SA Stinson, GC diCenzo - G3: Genes, Genomes, Genetics, 2023

• Prediction of New Risk Genes and Potential Drugs for Rheumatoid Arthritis from Multiomics Data AM Birga, L Ren, H Luo, Y Zhang, J Huang - Computational and Mathematical Methods in Medicine, 2022

• Phenotyping of acute and persistent COVID-19 features in the outpatient setting: exploratory analysis of an international cross-sectional online survey S Sahanic, P Tymoszuk, D Ausserhofer et al. - medRxiv, 2021

• A two-part evaluation approach for measuring the usability and user experience of an Augmented Reality-based assistance system to support the temporal coordination of spatially dispersed teams L Thomaschewski, B Weyers, A Kluge - Cognitive Systems Research, 2021

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

• Longitudinal analysis on the ecological dynamics of the cervicovaginal microbiome in hrHPV infection MA Molina, WJG Melchers, et al. - Computational and structural biotechnology, 2023

• Spatial and molecular anatomy of germ layers in the gastrulating primate embryo G Cui, S Feng, Y Yan, L Wang, X He, X Li, et al. - bioRxiv, 2022

• 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

• RUNIMC - An R-based package for imaging mass cytometry data analysis and pipeline validation L Dolcetti, PR Barber, G Weitsman, S Thavarajet al. - bioRxiv, 2021

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

• 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

• 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

• 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

• Identifying inhibitors of epithelial–mesenchymal plasticity using a network topology-based approach K Hari et al. - NPJ systems biology and applications, 2020

• Genetic differentiation and intrinsic genomic features explain variation in recombination hotspots among cocoa tree populations EJ Schwarzkopf et al. - BMC Genomics, 2020

• Enhancing Card Sorting Dendrograms through the Holistic Analysis of Distance Methods and Linkage Criteria. JA Macías - Journal of Usability Studies, 2021

• Pattern-based identification and mapping of landscape types using multi-thematic data J Nowosad, TF Stepinski - International Journal of Geographical Information, 2021

• Motif Analysis in k-mer Networks: An Approach towards Understanding SARS-CoV-2 Geographical Shifts S Biswas, S Saha, S Bandyopadhyay, M Bhattacharyya - bioRxiv, 2020

• Motif: an open-source R tool for pattern-based spatial analysis J Nowosad - Landscape Ecology, 2021

• New effective spectral matching measures for hyperspectral data analysis C Kumar, S Chatterjee, T Oommen, A Guha - International Journal of Remote Sensing, 2021

• Innovative activity of Polish enterprises–a strategic aspect. The similarity of NACE divisions E Bielińska-Dusza, M Hamerska - Journal of Entrepreneurship, Management and innovation, 2021

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

• Unraveling the record of a tropical continental Cretaceous-Paleogene boundary in northern Colombia, South America F de la Parra, C Jaramillo, P Kaskes et al. - Journal of South American Earth Sciences, 2022

• A roadmap to reconstructing muscle architecture from CT data J Katzke, P Puchenkov, H Stark, EP Economo - Integrative Organismal Biology, 2022

• Pandemonium: a clustering tool to partition parameter space—application to the B anomalies U Laa, G Valencia - The European Physical Journal Plus, 2022

• Identification of a glioma functional network from gene fitness data using machine learning C Xiang, X Liu, D Zhou, Y Zhou, X Wang, F Chen - Journal of Cellular and Molecular Medicine, 2022

• Cross compatibility in intraspecific and interspecific hybridization in yam (Dioscorea spp.) JM Mondo, PA Agre, A Edemodu et al. - Scientific reports, 2022

• A Modular and Expandable Ecosystem for Metabolomics Data Annotation in R J Rainer, A Vicini, L Salzer, J Stanstrup et al. - Metabolites, 2022

• Single-Cell Transcriptome Integration Analysis Reveals the Correlation Between Mesenchymal Stromal Cells and Fibroblasts C Fan, M Liao, L Xie, L Huang, S Lv, S Cai et al. - Frontiers in genetics, 2022

• Phenotypic regionalization of the vertebral column in the thorny skate Amblyraja radiata: Stability and variation F Berio, Y Bayle, C Riley, O Larouche, R Cloutier - Journal of Anatomy, 2022

• Community assembly during vegetation succession after metal mining is driven by multiple processes with temporal variation T Li, H Yang, X Yang, Z Guo, D Fu, C Liu, S Li et al. - Ecology and evolution, 2022

• Integrative Organismal Biology J Katzke, P Puchenkov, H Stark, EP Economo - 2022

• Optimizing use of US Ex-PVP inbred lines for enhancing agronomic performance of tropical Striga resistant maize inbred lines ARS Maazou, M Gedil, VO Adetimirin et al. - BMC Plant Biology, 2022

## 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/drostlab/philentropy/issues

or find me on twitter: HajkDrost