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Computer Science Review 37 (2020) 100254
Contents lists available at ScienceDirect
Computer Science Review
journal homepage: www.elsevier.com/locate/cosrev
Review article
Julia language in machine learning: Algorithms, applications, and open
issues
Kaifeng Gao a, Gang Mei a,∗, Francesco Piccialli b,∗, Salvatore Cuomo b,∗, Jingzhi Tu a,
Zenan Huo a
aSchool of Engineering and Technology, China University of Geosciences (Beijing), 100083, Beijing, China
bDepartment of Mathematics and Applications R. Caccioppoli, University of Naples Federico II, Naples, Italy
article info
Article history:
Received 27 February 2020
Received in revised form 25 April 2020
Accepted 6 May 2020
Available online xxxx
Keywords:
Julia language
Machine learning
Supervised learning
Unsupervised learning
Deep learning
Artificial neural networks
abstract
Machine learning is driving development across many fields in science and engineering. A simple and
efficient programming language could accelerate applications of machine learning in various fields.
Currently, the programming languages most commonly used to develop machine learning algorithms
include Python, MATLAB, and C/C ++. However, none of these languages well balance both efficiency
and simplicity. The Julia language is a fast, easy-to-use, and open-source programming language that
was originally designed for high-performance computing, which can well balance the efficiency and
simplicity. This paper summarizes the related research work and developments in the applications of
the Julia language in machine learning. It first surveys the popular machine learning algorithms that are
developed in the Julia language. Then, it investigates applications of the machine learning algorithms
implemented with the Julia language. Finally, it discusses the open issues and the potential future
directions that arise in the use of the Julia language in machine learning.
©2020 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND
license (http://creativecommons.org/licenses/by-nc- nd/4.0/).
Contents
1. Introduction......................................................................................................................................................................................................................... 2
2. A brief introduction to the Julia language ...................................................................................................................................................................... 3
3. Julia in machine learning: Algorithms ............................................................................................................................................................................. 3
3.1. Overview ................................................................................................................................................................................................................. 3
3.2. Supervised learning algorithms developed in Julia ........................................................................................................................................... 3
3.3. Unsupervised learning algorithms developed in Julia....................................................................................................................................... 5
3.4. Other main algorithms.......................................................................................................................................................................................... 7
3.5. List of commonly used Julia packages ................................................................................................................................................................ 7
4. Julia in machine learning: Applications........................................................................................................................................................................... 7
4.1. Overview ................................................................................................................................................................................................................. 7
4.2. Analysis of IoT data ............................................................................................................................................................................................... 8
4.3. Computer vision..................................................................................................................................................................................................... 8
4.4. Natural language processing (NLP)...................................................................................................................................................................... 9
4.5. Autonomous driving .............................................................................................................................................................................................. 9
4.6. Graph analytics ...................................................................................................................................................................................................... 9
4.7. Signal processing ................................................................................................................................................................................................... 9
4.8. Pattern recognition ................................................................................................................................................................................................ 9
5. Julia in machine learning: Open issues ........................................................................................................................................................................... 10
5.1. Overview ................................................................................................................................................................................................................. 10
5.2. A developing language .......................................................................................................................................................................................... 10
5.3. Lack of stable development tools ........................................................................................................................................................................ 10
5.4. Interfacing with other languages......................................................................................................................................................................... 10
5.5. Limited number of third-party packages............................................................................................................................................................ 10
6. Conclusions.......................................................................................................................................................................................................................... 10
∗Corresponding authors.
E-mail addresses: gang.mei@cugb.edu.cn (G. Mei), francesco.piccialli@unina.it (F. Piccialli), salvatore.cuomo@unina.it (S. Cuomo).
https://doi.org/10.1016/j.cosrev.2020.100254
1574-0137/©2020 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-
nc-nd/4.0/).
2K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254
Declaration of competing interest.................................................................................................................................................................................... 11
Acknowledgments .............................................................................................................................................................................................................. 11
References ........................................................................................................................................................................................................................... 11
List of Abbreviations
AD Algorithmic Differentiation
APIs Application Programming Interfaces
CNN Convolutional Neural Network
DPMM Dirichlet Process Mixture Model
ELM Extreme Learning Machine
FFGs Forney-style Factor Graphs
GBDT Gradient-Boosting Decision Tree
GMMs Gaussian Mixture Models
GPU Graphics Processing Unit
ICA Independent Component Analysis
IoT Internet of Things
JIT Just-In-Time
kNN k-Nearest Neighbors
LLVM Low-Level Virtual Machine
NLP Natural Language Processing
ODPS Open Data Processing Service
PCA Principal Component Analysis
RNN Recurrent Neural Network
SVD Singular Value Decomposition
SVM Support Vector Machine
1. Introduction
Machine learning is currently one of the most rapidly growing
technical fields, lying at the intersection of computer science
and statistics and at the core of artificial intelligence and data
science [1–4]. Machine learning technology powers many aspects
of modern society, from web searches to content filtering on
social networks to recommendations on electronic commerce
websites. Recent advances in machine learning methods promise
powerful new tools for practicing scientists. Modern machine
learning methods are closely related to scientific application [5,6];
see Fig. 1.
Python, MATLAB, Go, R, and C/C++ are widely used program-
ming languages in machine learning. Python has proven to be
a very effective programming language and is used in many
scientific computing applications [7]. MATLAB combines the func-
tions of numerical analysis, matrix calculation, and scientific data
visualization in an easy-to-use manner. Both Python and MATLAB
are ‘‘Plug-and-Play’’ programming languages; the algorithms are
prepackaged and mostly do not require learning processes, but
they are used to solve large-scale tasks at a slow speed and have
very strict requirements for memory and computing power [8].
In addition, MATLAB is commercial.
Go is an open-source programming language that makes it
easy to build simple, reliable, and efficient software. Go is syntac-
tically similar to C, but with memory safety, garbage collection,
and structural typing. Rather than call out to libraries written
in other languages, developers can work with machine learning
libraries written directly in Go. However, the current machine
learning libraries written in Go are not extensive. R is a language
and environment for statistical computing and graphics. R pro-
vides a wide variety of statistical and graphical techniques, and
is highly extensible. One of the advantages of R is that it can easily
produce high-quality drawings. However, R stores data in system
memory (RAM), which is a constraint when analyzing big data.
Fig. 1. Main applications of machine learning.
C/C++ is one of the main programming languages in machine
learning. It is of high efficiency and strong portability. However,
the development and implementation of machine learning algo-
rithms with C/C++ is not easy due to the difficulties in learning
and using C/C++. In machine learning, the availability of large data
sets is increasing, and the demand for general large-scale parallel
analysis tools is also increasing [9]. Therefore, it is necessary to
choose a programming language with both simplicity and good
performance.
Julia is a simple, fast, and open-source language [10]. The
efficiency of Julia is almost comparable to that of static program-
ming languages such as C/C++ and Fortran [11]. Julia is rapidly
becoming a highly competitive language in data science and
general scientific computing. Julia is as easy to use as R, Python,
and MATLAB.
Julia was originally designed for high-performance scientific
computing and data analysis. Julia can call many other mature
high-performance basic codes, such as linear algebra and fast
Fourier transforms. Similarly, Julia can call C++ language functions
directly without packaging or special application programming
interfaces (APIs). In addition, Julia has special designs for par-
allel computing and distributed computing. In high-dimensional
computing, Julia has more advantages than C++ [9]. In the field of
machine learning, Julia has developed many third-party libraries,
including some for machine learning.
In this paper, we systematically review and summarize the
development of the Julia programming language in the field of
machine learning by focusing on the following three aspects:
(1) Machine learning algorithms developed in the Julia lan-
guage.
(2) Applications of the machine learning algorithms imple-
mented with the Julia language.
(3) Open issues that arise in the use of the Julia language in
machine learning.
The rest of the paper is organized as follows. Section 2gives
a brief introduction to the Julia language. Section 3summarizes
K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254 3
Fig. 2. Julia benchmarks (the benchmark data shown above were computed with Julia v1.0.0, Go 1.9, Javascript V8 6.2.414.54, MATLAB R2018a, Anaconda Python
3.6.3, and R 3.5.0. C and Fortran are compiled with gcc 7.3.1, taking the best timing from all optimization levels. C performance =1.0, smaller is better [12]).
the machine learning algorithms developed in Julia language. Sec-
tion 4introduces applications of the machine learning algorithms
implemented with Julia language. Section 5presents open issues
occurring in the use of Julia language in machine learning. Finally,
Section 6concludes this survey.
2. A brief introduction to the Julia language
Julia is a modern, expressive, and high-performance program-
ming language for scientific computing and data processing. Its
development started in 2009, and the current stable release as of
April 2020 is v1.4.0. Although this low version number indicates
that the language is still developing rapidly, it is stable enough
to enable the development of research code. Julia’s grammar is
as readable as that of MATLAB or Python, and it can approach
the C/C++ language in performance by compiling in real time. In
addition, Julia is a free, open-source language that runs on all
popular operation systems.
With the low-level virtual machine (LLVM)-based just-in-
time (JIT) compiler, Julia provides powerful computing perfor-
mance. [13,14]; see Fig. 2. Julia also incorporates some important
features from the beginning of its design, such as excellent sup-
port for parallelism [15] and a practical functional programming
orientation, which were not fully implemented in the develop-
ment of scientific computing languages decades ago. Julia can also
be embedded in other programming languages. These advantages
make Julia a universal language.
Julia successfully combines the high performance of a static
programming language with the flexibility of a dynamic program-
ming language [14]. It provides built-in primitives for parallel
computing at every level: instruction level parallelism, multi-
threading and distributed computing. The Julia modules allow
users to suspend and resume computations with full control
of communication without having to manually interface with
the operating system’s scheduler. Besides, Julia provides a mul-
tiprocessing environment based on message passing to allow
programs to run on multiple processes in separate memory do-
mains at once [16]. Moreover, the use of the high-level Julia
programming language enables new and dynamic approaches for
graphics processing unit (GPU) programming, and Julia GPU code
can be highly generic and flexible, without sacrificing perfor-
mance [15,17]. However, parallel computing has not yet reached
the required level of richness and interactivity [10]. The Julia
language could further improve the efficiency of data division and
combination, and optimize the parallel algorithms.
3. Julia in machine learning: Algorithms
3.1. Overview
This section describes machine learning algorithm packages
and toolkits written either in or for Julia. Most applications of ma-
chine learning algorithms in Julia can be divided into supervised
learning and unsupervised learning algorithms. However, more
complex algorithms, such as deep learning, artificial neural net-
works, and extreme learning machines, include both supervised
learning and unsupervised learning, and these require separate
classification; see Fig. 3.
Supervised learning learns the training samples with class
labels and then predicts the classes of data outside the train-
ing samples. All the markers in supervised learning are known;
therefore, the training samples have low ambiguity. Unsuper-
vised learning learns the training samples without class labels
to discover the structural knowledge in the training sample set.
All categories in unsupervised learning are unknown; thus, the
training samples are highly ambiguous.
3.2. Supervised learning algorithms developed in Julia
Supervised learning infers a model from labeled training data.
Supervised learning algorithms developed in Julia mainly include
classification and regression algorithms; see Fig. 4.
Bayesian model
There are two key points in the definition of Bayesian model:
independence between features and the Bayesian theorem.
One of the most important research areas of Bayesian model
is Bayesian linear regression. Bayesian linear regression solves
the problem of overfitting in maximum likelihood estimation.
Moreover, it makes full use of data samples and is suitable
for modeling complex data [18,19]. In addition to regression,
Bayesian reasoning can also be applied in other fields. Some
researchers have conducted research on naive Bayes in image
recognition and text classification.
4K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254
Fig. 3. Main machine learning algorithms.
Fig. 4. Main supervised learning algorithms developed in Julia.
There are some Bayesian model packages and algorithms de-
veloped in mature languages. Strickland et al. [20] developed
the Python package Pyssm, which was developed for time se-
ries analysis using a linear Gaussian state-space model. Mertens
et al. [21] developed a user-friendly Python package Abrox for ap-
proximate Bayesian computation with a focus on model compar-
ison. There are also Python packages BAMSE [22], BayesPy [23],
PyMC [24] and so on. Moreover, Vanhatalo et al. [25] devel-
oped the MATLAB toolbox GPstuff for Bayesian modeling with
Gaussian processes, and Zhang et al. [26] developed the MATLAB
toolbox BSmac, which implements a Bayesian spatial model for
brain activation and connectivity.
The Julia language is also used to develop packages for the
Bayesian model. Gen [27] is a probabilistic programming lan-
guage proposed by Cusumano and Mansinghka that can be em-
bedded in Julia. This language provides a structure for the opti-
mization of the automatic generation of custom reasoning strate-
gies for static analysis based on an objective probability model.
They described Gen’s language design informally and used an
example Bayesian statistical model for robust regression to show
that Gen is more expressive than Stan, a widely used language for
hierarchical Bayesian modeling. Cox et al. [28] explored a specific
probabilistic programming paradigm, namely, message passing in
Forney-style factor graphs (FFGs), in the context of the automated
design of efficient Bayesian signal processing algorithms. More-
over, they developed ForneyLab.jl as a Julia Toolbox for message
passing-based inference in FFGs.
Due to the increasing availability of large data sets, the need
for a general-purpose massively parallel analysis tool is becoming
ever greater. Bayesian nonparametric mixture models, exempli-
fied by the Dirichlet process mixture model (DPMM), provide a
principled Bayesian approach to adapt model complexity to the
data. Dinari et al. [9] used Julia to implement efficient and easily
modifiable distributed inference in DPMMs.
K -nearest neighbors (kNN)
The kNN algorithm has been widely used in data mining and
machine learning due to its simple implementation and distin-
guished performance. A training data set with a known label
category is used, and for a new data set, the kinstances closest to
the new data are found in the feature space of the training data
set. If most of the instances belong to a category, the new data
set belongs to this category.
At present, there are many packages developed for the kNN
algorithm in the Python language. Among these, scikit-learn and
Pypl are the most commonly used packages. It should be noted
that scikit-learn and Pypl are not specially developed for the kNN
algorithm; they contain many other machine learning algorithms.
In addition, Bergstra et al. [29] developed Hyperopt to define a
search space that encompasses many standard components and
common patterns of composing them.
Julia is also used to develop packages for the kNN algorithm.
NearestNeighbors.jl [30] is a package written in Julia to perform
high-performance nearest neighbor searches in arbitrarily high
dimensions. This package can realize kNN searches and range
searches.
Decision tree, regression tree, and random forest
Mathematically, a decision tree is a graph that evaluates a
limited number of probabilities to determine a reliable classifi-
cation for each data point. A regression tree is the opposite of a
K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254 5
decision tree and is suitable for solving regression problems. It
does not predict labels but predicts a continuous change value.
Random forests are a set of decision trees or regression trees
that work together [31]. The set of decision trees (or continuous
y regression trees) is constructed by performing bootstrapping
on the data sets and averaging or acquiring pattern prediction
(called ‘‘bagging’’) from the trees. Subsampling of features is used
to reduce generalization errors [32]. An ancillary result of the
bootstrapping procedure is that the data not sampled in each
bootstrap (called ‘‘out-of-bag’’ data) can be used to estimate the
generalization error as an alternative to cross-validation [33].
Many packages have been developed for decision trees, re-
gression trees, and random forests. For example, the above three
algorithms are implemented in Spark2 ML and scikit-learn using
Python. In addition, Upadhyay et al. [34] proposed land-use and
land-cover classification technology based on decision trees and
k-nearest neighbors, and the proposed techniques are imple-
mented using the scikit-learn data mining package for python.
Keck [35] proposed a speed-optimized and cache-friendly imple-
mentation for multivariate classification called FastBDT, which
provides interfaces to C/C++, Python, and TMVA. Yang et al. [36]
used the open data processing service (ODPS) and Python to
implement the gradient-boosting decision tree (GBDT) model.
DecisionTree.jl [37], written in the Julia language, is a pow-
erful package that can realize decision tree, regression tree, and
random forest algorithms very well. The package has two func-
tions, and the ingenious use of these functions can help us realize
these three algorithms.
Support vector machine (SVM)
In SVM, the objective is to find a hyperplane in high-
dimensional space, which represents the maximum margin be-
tween any two instances of two types of training data points
(support vectors) or maximizes the correlation function when it
cannot be separated. The so-called kernel similarity function is
used to design the non-linear SVM [38].
Currently, there are textbook style implementations of two
popular linear SVM algorithms: Pegasos [39], Dual Coordinate
Descent. LIBSVM developed by the Information Engineering Insti-
tute of Taiwan University is the most widely used SVM tool [40].
LIBSVM includes standard SVM algorithm, probability output,
support vector regression, multi-classification SVM and other
functions. Its source code is originally written by C. It pro-
vides Java, Python, R, MATLAB, and other language invocation
interfaces.
SVM.jl [41], MLJ.jl [42], and LIBSVM.jl [43] are native Julia
implementations of SVM algorithm. However, LIBSVM.jl is more
comprehensive than SVM.jl.LIBSVM.jl supports all libsvm mod-
els: classification c-svc, nu-svc, regression: epsilon-svr, nu-svr
and distribution estimation: a class of support vector machines
and ScikitLearn.jl [44] API. In addition, the model object is rep-
resented by a support vector machine of Julia type. The SVM can
easily access the model features and can be saved as a JLD file.
Regression analysis
Regression analysis is an important supervised learning algo-
rithm in machine learning. It is a predictive modeling technique,
which constructs the optimal solution to estimate unknown data
through the sample and weight calculation. Regression analysis
is widely used in the fields of the stock market and medical data
analysis.
Python has been widely used to develop a variety of third-
party packages for regression analysis, including scikit-learn and
orange. The scikit-learn package is a powerful Python module,
which supports mainstream machine learning algorithms such as
regression, clustering, classification and neural network [45–47].
Fig. 5. Main unsupervised learning algorithms developed in Julia.
The orange package is a component-based data mining software,
which can be used as a module of Python programming lan-
guage, especially suitable for classification, clustering, regression
and other work [48,49]. MATLAB also supports the regression
algorithm. By invoking commands such as regress and stepwise
in the statistical toolbox of MATLAB, regression operation can be
performed conveniently on the computer.
The Julia language is also used to develop a package, Re-
gression.jl [50], to perform the regression analysis. The Regres-
sion.jl package seeks to minimize empirical risk based on Empir-
icalRisk.jl [51] and provides a set of algorithms for performing
regression analysis. It supports multiple linear regression, non-
linear regression, and other regression algorithms. In addition, the
Regression.jl package also provides a variety of solvers such as
analytical solution (for linear and ridge regression) and gradient
descent.
3.3. Unsupervised learning algorithms developed in Julia
Unsupervised learning is a type of self-organized learning that
can help find previously unknown patterns in a dataset without
the need for pre-existing labels. Two of the main methods used
in unsupervised learning are dimensionality reduction and cluster
analysis; see Fig. 5.
Gaussian mixture models (GMMs)
GMMs are probabilistic models for representing normally dis-
tributed subpopulations within an overall population. GMMs
use Gaussian distribution as the basic parameter model, accu-
rately characterizes the data distribution by combining multiple
Gaussian distributions, and use the expectation–maximization
algorithm for training. Compared with the Gaussian models, the
GMMs provide greater flexibility and precision in modeling the
underlying statistics of sample data [52]. Generally, the GMMs are
used to solve problems such as image segmentation and dynamic
target detection [53].
Currently, there are many libraries that can implement Gaus-
sian mixture models; these include packages developed with
Python, such as PyBGMM and numpy-ml, and packages devel-
oped with C++, such as Armadillo. There are also some GMM
packages for specialized fields. Bruneau et al. [54] proposed a new
Python package for nucleotide sequence clustering, which im-
plements a Gaussian mixture model for DNA clustering. Holoien
et al. [55] developed a new open-source tool, EmpiriciSN, writ-
ten in Python, for performing extreme deconvolution Gaussian
mixture modeling.
To the best of the authors’ knowledge, there is no mature Julia
package for the GMMs. GmmFlow.jl [56] is a Julia library that
can implement some simple functions of the GMMs, including
6K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254
model generation and cluster mapping. But the algorithm opti-
mization could be improved. GaussianMixtures.jl [57] is another
Julia package for the GMMs. This package has implemented both
diagonal covariance and full covariance GMMs, and full covari-
ance variational Bayes GMMs. However, the package is slightly
strict with data types. ScikitLearn.jl implements the popular
scikit-learn interface and algorithms in Julia, and it can access
approximately 150 Julia and Python models, including the Gaus-
sian mixture model. Moreover, Srajer et al. [58] used algorithmic
differentiation (AD) tools in a GMM fitting algorithm.
K -means
The k-means clustering algorithm is an iterative clustering
algorithm. It first randomly selects kobjects as the initial clus-
tering center, then calculates the distance between each object
and each seed clustering center, and assigns each object to the
nearest clustering center. Cluster centers and the objects assigned
to them represent a cluster. As an unsupervised clustering al-
gorithm, k-means is widely used because of its simplicity and
effectiveness.
The k-means algorithm is a classic clustering method, and
many programming languages have developed packages related
to it. The third-party package scikit-learn in Python implements
the k-means algorithm [47,59]. The Kmeans function in MATLAB
can also implement a k-means algorithm [60]. In addition, many
researchers have implemented the k-means algorithm in the
C/C++ programming language.
Julia has also been used to develop a specific package, Clus-
tering.jl [61], for clustering. Clustering.jl provides several func-
tions for data clustering and clustering quality evaluation. Be-
cause Clustering.jl has comprehensive and powerful functions,
this package is a good choice for k-means.
Hierarchical clustering
Hierarchical clustering is a kind of clustering algorithm that
performs clustering by calculating the similarity between data
points of different categories [62–64]. The strategy of cohesive
hierarchical clustering is to first treat each object as a cluster and
then merge these clusters into larger and larger clusters until
all objects are in one cluster or some termination condition is
satisfied.
The commonly used Python packages for hierarchical clus-
tering are scikit-learn and scipy. Hierarchical clustering within
the scikit-learn package is implemented in the sklearn.cluster
method, which includes three important parameters: the num-
ber of clusters, the connection method, and connection mea-
surement options [47]. scipy implements hierarchical clustering
with the scipy.cluster method [65]. In addition, programming lan-
guages such as MATLAB and C/C++ can also perform hierarchical
clustering [66].
The package QuickShiftClustering.jl [67], written using Julia,
can realize hierarchical clustering algorithms. This package is
quite easy to use. It provides three functions: clustering matrix
data, clustering labels, and creating hierarchical links to achieve
hierarchical clustering [68].
Bi-clustering
Bi-Clustering algorithm is based on traditional clustering. Its
basic idea is to cluster rows and columns of matrices through
traditional clustering, and then merge the clustering results.
Bi-Clustering algorithm solves the bottleneck problem of tradi-
tional clustering in high-dimensional data. Data sets in reality
are mostly high-dimensional and inherently sparse. Traditional
clustering algorithms often fail to detect meaningful clustering
in high-dimensional data sets. However, Bi-Clustering can detect
clusters of any shape and position in space, and it is an effective
method to solve the problem of subspace clustering in high-
dimensional data sets [69,70]. To search for local information
better in the data matrix, researchers put forward the concept
of bi-clustering.
The package scikit-learn can implement bi-clustering, and
the implementation module is sklearn.cluster.bicluster. At present,
bi-clustering is mainly applied to highthroughput detection tech-
nologies such as gene chips and DNA microarrays.
The Julia language is also used to develop packages that imple-
ment bi-clustering. For example, Kpax3 [71] is a Bayesian method
for multi-cluster multi-sequence alignment. Bezanson et al. [10]
used a Bayesian dual clustering model, which extended and im-
proved the model originally introduced by Pessia et al. [71]. They
wrote the kpax3.jl library package in Julia and the output con-
tains multiple text files containing a cluster of rows and columns
of the input dataset.
Principal component analysis (PCA)
PCA is a method of statistical analysis and a simplified data
set. It uses an orthogonal transformation to linearly transform
observations of a series of possibly related variables and then
project them into a series of linearly uncorrelated variables. These
uncorrelated variables are called principal components. PCA is
often used to reduce the dimensionality of a data set while main-
taining the features that have the largest variance contribution in
the data set.
Python is the most frequently used language for develop-
ing PCA algorithms. The scikit-learn package provides a class,
sklearn.decomposition.PCA [72], to implement PCA algorithms in
the sklearn.decomposition module. Generally, the PCA class does
not need to adjust parameters very much but needs to specify the
target dimension or the variance of the principal components af-
ter dimensionality reduction. In addition, many researchers have
developed related application packages using the C++ program-
ming language. These include the ALGLIB [73] package and the
class cv :: PCA [74] in OpenCV.
To the best of the authors’ knowledge, there is no mature Julia
package specifically for PCA. However, MultivariateStats.jl [75]
is a Julia package for multivariate statistics and data analysis.
This package defines a PCA type to represent a PCA model and
provides a set of methods to access properties.
Independent component analysis (ICA)
ICA is a new signal processing technology developed in recent
years. The ICA method is based on mutual statistical indepen-
dence between sources. In the practical applications of signal
processing, especially in communication and biomedicine, it is
important to eliminate noise data. Traditional signal process-
ing techniques for noise cancellation include band-pass filtering,
fast Fourier transform, autocorrelation, autoregressive modeling,
adaptive filtering, Kalman filtering and singular value decompo-
sition. The traditional filtering technology is based on the as-
sumption that noise is the only additive, which is not suitable for
multi-sensor observation of mixed signals [76]. However, the ICA
algorithm has strong robustness to additive noise, and it is one of
the most promising methods to solve the problem of blind noise
suppression [77,78]. Moreover, in contrast to traditional signal
separation methods based on feature analysis, such as singular
value decomposition (SVD) and PCA, ICA is an analysis method
based on higher-order statistical characteristics. In many appli-
cations, the analysis of higher-order statistical characteristics is
more practical.
Python is the most frequently used language in develop-
ing ICA algorithms. The scikit-learn package has developed a
class, FastICA [79], to implement ICA algorithms in the sklearn.
decomposition module. In addition, Brian Moore [80] developed a
K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254 7
PCA and ICA Package using the MATLAB programming language.
The PCA and ICA algorithms are implemented as functions in this
package, and it includes multiple examples to demonstrate their
usage.
To the best of the authors’ knowledge, ICA does not have a ma-
ture software package developed in the Julia language. However,
MultivariateStats.jl [75], like a Julia package for multivariate
statistics and data analysis, defines an ICA type representing the
ICA model and provides a set of methods to access the attributes.
3.4. Other main algorithms
In addition to supervised learning algorithms and unsuper-
vised learning algorithms, machine learning algorithms include
a class of algorithms that are more complex and cannot be cat-
egorized into a specific category. For example, artificial neu-
ral networks can implement supervised learning, unsupervised
learning, reinforcement learning, and self-learning. Deep learn-
ing algorithms are based on artificial neural network algorithms
and can perform supervised learning, unsupervised learning, and
semisupervised learning. Extreme learning machines were pro-
posed for supervised learning algorithms but were extended to
unsupervised learning in subsequent developments.
Deep learning
Deep learning allows computational models that are com-
posed of multiple processing layers to learn representations of
data with multiple levels of abstraction [5]. Several deep learning
frameworks, such as the depth neural network, the convolutional
neural network, the depth confidence network and the recursive
neural network, have been applied to computer vision, speech
recognition, natural language processing, image recognition, and
bioinformatics and have achieved excellent results.
It has been several years since the birth of deep learning
algorithms. Many researchers have improved and developed deep
learning algorithms. Python is the most frequently used lan-
guage in developing deep learning algorithms. For example, Py-
Torch [81,82] and ALiPy [83] are Python packages with many
deep learning algorithms. Moreover, Tang et al. developed GCNv2
[84] using C++ and Python, Huang et al. wrote Mask Scoring R-
CNN [85] using Python, Hanson and Frazier-Logue compared the
Dropout [86] algorithm with the SDR [87] algorithm, and Luo
et al. [88] proposed and used Python to write AdaBound (a new
adaptive optimization algorithm).
Julia has also been used to develop various deep learning
algorithms. For example, AD allows the exact computation of
derivatives given only an implementation of an objective func-
tion, and Srajer et al. [58] wrote an AD tool and used it in a
hand-tracking algorithm.
Augmentor is a software package available in both Python and
Julia that provides a high-level API for the expansion of image
data using a stochastic, pipeline-based approach that effectively
allows images to be sampled from a distribution of augmented
images at runtime [89]. To demonstrate the API and to highlight
the effectiveness of augmentation on a well-known dataset, a
short experiment was performed. In the experiment, the package
is used on a convolutional neural network (CNN) [90].
MXNet.jl [91], Knet.jl [92], Flux.jl [93], and TensorFlow.jl [94]
are deep learning frameworks with both efficiency and flexibility.
At its core, MXNet.jl contains a dynamic dependency scheduler
that automatically parallelizes both symbolic and imperative op-
erations on the fly. MXNet.jl is portable and lightweight, scaling
effectively to multiple GPUs and multiple machines.
Artificial neural networks
A neural network is a feedforward network consisting of nodes
(‘‘neurons’’), each side of which has weights. These allow the
network to form a mapping between the input and output [95].
Each neuron that receives input from a previous neuron consists
of the following components: the activation, a threshold, the time
at which the newly activated activation function is calculated and
the output function of the activation output.
At present, the framework of a neural network model is usu-
ally developed in C++ or Python. DLL is a machine learning
framework written in C++ [96]. It supports a variety of neural net-
work layers and standard backpropagation algorithms. It can train
artificial neural networks and CNNs and support basic learning
options such as momentum and weight attenuation. scikit-learn,
a machine learning library based on Python, also supports neural
network models [47].
Employing the Julia language, Diffiqflux.jl [97] is a pack-
age that integrates neural networks and differential equations.
Rackauckas et al. [97] described differential equations from the
perspective of data science and discuss the complementarity be-
tween machine learning models and differential equations. These
authors demonstrated the ability to combine DifferentialEqua-
tions.jl [98] defined differential equations into Flux-defined neu-
ral networks. Backpropneuralnet.jl [58] is an easy-to-use neural
network package.
Extreme learning machine (ELM)
ELM [99] is a variant of Single Hidden Layer Feedforward
Networks (SLFNs). Because its weight is not adjusted iteratively, it
deviates greatly. This significantly improves the efficiency when
training the neural networks.
The basic algorithm of ELM and Multi-Layer [100]/Hierarchical
[101] ELM have been implemented in HP-ELM. Meanwhile, C/C++,
MATLAB, Python and JAVA versions are provided. HP-ELM in-
cludes GPU acceleration and memory optimization, which is suit-
able for large data processing. HP-ELM supports LOO (Leave One
Out) and k-fold cross-validation to dynamically select the number
of hidden layer nodes. The available feature maps include linear
function, Sigmoid function, hyperbolic sinusoidal function, and
three radial basis functions.
According to ELM, parameters of hidden nodes or neurons are
not only independent of training data but also independent of
each other. Standard feedforward neural networks with hidden
nodes have universal approximation and separation capabilities.
These hidden nodes and their related maps are terminologically
ELM random nodes, ELM random neurons or ELM random fea-
tures. Unlike traditional learning methods, which need to see
training data before generating hidden nodes or neuron parame-
ters, ELM could generate hidden nodes or neuron parameters ran-
domly before seeing training data. Elm.jl [102] is an easy-to-use
extreme learning machine package.
3.5. List of commonly used Julia packages
We summarize the commonly used Julia language packages
and the machine learning algorithms that these packages primar-
ily support; see the investigation in Table 1.
4. Julia in machine learning: Applications
4.1. Overview
Machine learning is one of the fastest-growing technical fields
nowadays. It is a cross-cutting field of statistics and computer
science [1–3]. Machine learning specializes in how computers
simulate or implement human learning behaviors. By acquiring
8K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254
Table 1
Commonly used Julia language packages.
Julia packages Ref. Supervised learning Unsupervised learning Other
Bayesian
model
kNN Random
forest
SVM Regression
analysis
GMM k-means Hierarchical
Clustering
Bi-
Clustering
PCA ICA Deep
Learning
ANN ELM
ForneyLab.jl [28]
NearestNeighbors.jl [30]
DecisionTree.jl [37]
SVM.jl [41]
MLJ.jl [42]
LIBSVM.jl [43]
ScikitLearn.jl [44]
Regression.jl [50]
EmpiricalRisk.jl [51]
Clustering.jl [61]
QuickShiftClustering.jl [67]
kpax3.jl [8]
MultivariateStats.jl [75]
MXNet.jl [91]
Knet.jl [92]
Flux.jl [93]
TensorFlow.jl [94]
Diffiqflux.jl [97]
DifferentialEquations.jl [98]
Backpropneuralnet.jl [58]
Elm.jl [102]
GmmFlow.jl [56]
GaussianMixtures.jl [57]
Fig. 6. Major applications of machine learning using Julia language.
new knowledge and skills, the existing knowledge structure is
reorganized to improve its performance.
Julia, as a programming language with the rise of machine
learning, has corresponding algorithmic library packages in most
machine learning applications. In the following, we summarize
the applications of Julia in machine learning. As shown in Fig. 6,
the current applications of Julia programming language in ma-
chine learning mainly focus on the Internet of Things (IoT), com-
puter vision, autonomous driving, pattern recognition, etc.
4.2. Analysis of IoT data
The IoT, also called the Internet of Everything or the Industrial
Internet, is a new technology paradigm envisioned as a global
network of machines and devices capable of interacting with each
other [103]. The application of the IoT in industry, agriculture, the
environment, transportation, logistics, security, and other infras-
tructure fields effectively promotes the intelligent development
of these areas and more rationally uses and allocates limited
resources, thus improving the efficiency of these fields [104–
106]. Machine learning has brought enormous development op-
portunities for the IoT and has a significant impact on existing
industries [107,108].
Invenia Technical Computing used the Julia language to ex-
pand its energy intelligence system [109]. They optimized the
entire North American grid and used the energy intelligent sys-
tem (EIS) and various signals to directly improve the day-ahead
planning process. They used the latest research in machine learn-
ing, complex systems, risk analysis, and energy systems. In ad-
dition, Julia provided Invenia Technical Computing with versa-
tility in terms of programming style, parallelism, and language
interoperability [109].
Fugro Roames engineers [110] used the Julia language to im-
plement machine learning algorithms to identify network faults
and potential faults, achieving a 100-fold increase in speed. Pro-
tecting the grid means ensuring that all power lines, poles, and
wires are in good repair, which used to be a laborious manual
task that required thousands of hours to travel along the power
line. Fugro Roames engineers have developed a more effective
way to identify threats to wires, poles, and conductors. Using
a combination of LiDAR and high-resolution aerial photography,
they created a detailed three-dimensional map of the physical
conditions of the grid and possible intrusions. Then, they used
machine learning algorithms to identify points on the network
that have failed or are at risk of failure [110].
4.3. Computer vision
Computer vision is a simulation of biological vision using
computers and related equipment. Its main task is to obtain
the three-dimensional information of the corresponding scene
by processing collected pictures or videos. Computer vision in-
cludes image processing and pattern recognition. In addition,
it also includes geometric modeling and recognition processes.
The realization of image understanding is the ultimate goal of
computer vision. Machine learning is developing, and computer
vision research has gradually shifted from traditional models to
deep learning models represented by CNNs and deep Boltzmann
machines.
Computer vision is currently widely applied in the fields of bi-
ological and medical image analysis [111], urban streetscapes [37,
112], rock type identification [113], automated pavement distress
detection and classification [114], structural damage detection
in buildings [115], and other fields. The development language
used in current research is usually Python or another mature
language. In contrast, when dealing with large-scale data sets,
K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254 9
the Julia language has inherent advantages in high-performance
processing. Therefore, many scholars and engineers use Julia to
develop packages for the applications of computer vision. The
Metalhead.jl [116] package provides computer vision models
that run on top of the Flux machine learning library. The package
ImageProjectiveGeometry.jl [117] is intended as a starting point
for the development of a library of projective geometry functions
for computer vision in Julia. Currently, the package consists of a
number of components that could ultimately be separated into
individual packages or added to other existing packages.
4.4. Natural language processing (NLP)
NLP employs computational techniques for the purpose of
learning, understanding, and producing human language con-
tent [118]. It is an important research direction in the field
of computer science and artificial intelligence. Modern NLP al-
gorithms are based on machine learning algorithms, especially
statistical machine learning algorithms. Many different machine
learning algorithms have been applied to NLP tasks, the most
representative of which are deep learning algorithms exemplified
by CNN [119–122].
Currently, one of the main research tasks of NLP is to inves-
tigate the characteristics of human language and establish the
cognitive mechanism of understanding and generating language.
In addition, new practical applications for processing human lan-
guage through computer intelligence have been developed. Many
researchers and engineers have developed practical application
tools or software packages using the Julia language. For exam-
ple, LightNLP.jl [123] is a lightweight NLP toolkit for the Julia
language. However, to the best of the authors’ knowledge, there
are currently no stable library packages developed in the Julia
language specifically for NLP.
4.5. Autonomous driving
Machine learning is widely used in autonomous driving, and
it mainly focuses on the environmental perception and behav-
ioral decision-making of autonomous vehicles. The application
of machine learning in environmental perception belongs to the
category of supervised learning. When performing object recogni-
tion on images obtained from the surrounding environment of a
vehicle, a large number of images with solid objects are required
as training data, and then deep learning methods can identify
objects from the new images [41,42,102,124]. The application
of machine learning in behavioral decision-making generally in-
volves reinforcement learning. Autonomous vehicles need to in-
teract with the environment, and reinforcement learning learns
the mapping relationship between the environment and behavior
that interacts with the environment from a large amount of
sample data. Thus, whenever an autonomous vehicle perceives
the environment, it can act intelligently [125,126].
To the best of the authors’ knowledge, there are no software
packages or solutions specially developed in Julia for autonomous
driving. However, the machine learning algorithms used in au-
tonomous driving are currently implemented by researchers in
the Julia language. The amount of data obtained by autonomous
vehicles is huge, and the processing is complex, but autonomous
vehicles have strict requirements for data processing time. High-
level languages such as Python and MATLAB are not as efficient
in computing as the Julia language, which was specifically devel-
oped for high-performance computing. Therefore, we believe that
Julia has strong competitiveness as a programming language for
autonomous vehicle platforms.
4.6. Graph analytics
Graph analytics is a rapidly developing research field. It com-
bines graph-theoretic, statistics and database technology to
model, store, retrieve and analyze graph-structured data. Samsi
[127] used subgraph isomorphism to solve the previous scal-
ability difficulties in machine learning, high-performance com-
puting, and visual analysis. The serial implementations of C++,
Python, and Pandas and MATLAB are implemented, and their
single-thread performance is measured.
LightGraphs.jl is currently the most comprehensive library
developed in Julia for graph analysis [128]. LightGraphs.jl pro-
vides a set of simple, concrete graphical implementations (in-
cluding undirected and directed graphs) and APIs for developing
more complex graphical implementations under the Abstract-
Graph type.
4.7. Signal processing
The signal processing in communications is the cornerstones
of electrical engineering research and other related fields [129,
130]. Python has natural advantages in analyzing complex signal
data due to its numerous packages. In addition, the actually
collected signals need to be processed before they can be used
for analysis. MATLAB provides many signal processing toolboxes,
such as spectrum analysis toolbox, waveform viewer, filter design
toolbox. Therefore, MATLAB is also a practical tool for signal data
processing.
Current and emerging means of communication increasingly
rely on the ability to extract patterns from large data sets to
support reasoning and decision-making using machine learn-
ing algorithms. This calls the use of the Julia language. For ex-
ample, Srivastava Prakalp et al. [131] designed an end-to-end
programmable hybrid signal accelerator, PROMISE, for machine
learning algorithms. PROMISE can use machine learning algo-
rithms described by Julia and generate PROMISE code. PROMISE
can combine multiple signals and accelerate machine learning
algorithms.
4.8. Pattern recognition
Pattern recognition is the automatic processing and interpre-
tation of patterns by means of a computer using mathematical
technology [132]. With the development of computer technol-
ogy, it is possible for humans to study the complex process
of information-processing, an important form of which is the
recognition of the environment and objects by living organisms.
The main research directions of pattern recognition are image
processing and computer vision, speech information processing,
medical diagnosis and biometric authentication technology [133].
Pattern recognition is generally categorized according to the
type of learning procedure used to generate the output value.
Medical diagnosis is a typical field of pattern recognition ap-
plications. Rajsavi et al. [134] used the Julia libraries packages
such as GLM.jl [135] to predict the mortality rate of diabetic ICU
patients through severity indicators. The application case of this
pattern recognition was completely written by Julia language.
Other typical applications of pattern recognition techniques are
automatic speech recognition, text classification , face recog-
nition. Languages.jl [136] is a Julia package for working with
human languages. Script detection model works by checking the
Unicode character ranges present within the input text. But the
package was supported only for English and German currently.
10 K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254
Fig. 7. Open issues of Julia language.
5. Julia in machine learning: Open issues
5.1. Overview
Since its release, the advantages of Julia language, such as
simplicity and efficiency, have been recognized by developers in
various fields. However, with the promotion of the Julia language
and the steady increase in the number of users, it also faces
several open issues; see Fig. 7.
5.2. A developing language
Although Julia has developed rapidly, its influence is far less
than that of other popular programming languages. After sev-
eral versions of updates, Julia has become relatively stable, but
there are still several problems to be solved. Julia’s grammar
has changed considerably, and although these changes are for
the sake of performance or ease of expression, these differences
also make it difficult for different programs to work together.
One of Julia’s obvious advantages is its satisfactory efficiency; but
to write efficient code, one needs to transform the method of
thinking in programming and not just copy code into Julia. For
people who have just come into contact with Julia, the ease of
use can also cause them to ignore this problem and ultimately
lead to unsatisfactory code efficiency.
5.3. Lack of stable development tools
Currently, the commonly used editors and IDEs for the Julia
language include (1) Juno (Atom Plugin), (2) Visual Studio Code
(VS Code Extension), (3) Jupyter (Jupyter kernel), and (4) Jet
Brains (IntelliJ IDEA Plugin). According to [137], Juno is currently
the most popular editor. These editors and IDEs are extensions
based on third-party platforms, which can quickly build develop-
ment environments for Julia in its early stages of development,
but in the long run, this is not a wise approach. Users need to
configure Julia initially, but the final experience is not satisfactory.
Programming languages such as MATLAB, Python and C/C++ each
have their own IDE, which integrates the functions of code writ-
ing, analysis, compilation and debugging. Although editors and
IDEs have achieved many excellent functions, it is very important
to have a complete and Julia-specific IDE.
5.4. Interfacing with other languages
In the process of using Julia for development, although most
of the code can be written in Julia, many high-quality, mature
numerical computing libraries have been written in C and Fortran.
To facilitate the use of existing code, Julia should also make it easy
and effective to call C/C++ and Fortran functions. In the field of
machine learning, Python has been used to write a large quantity
of excellent code. If one desires to transplant code into Julia in a
short time for maintenance, simple calls are necessary, which can
greatly reduce the learning curve.
Currently, PyCall and Call are used in Julia to invoke these
existing libraries, but Julia still needs a more concise and general
invocation method. More important is finding a method to ensure
that the parts of these calls can maintain the original execution
efficiency or the execution efficiency of the native Julia language.
At the same time, it is also very important to embed Julia’s code
in other languages, which would not only popularize the use of
Julia more quickly but also combine the characteristics of Julia to
enable researchers to accomplish tasks more quickly.
5.5. Limited number of third-party packages
For good programming languages, the quantity and quality
of third-party libraries are very important. For Python, there are
194,934 projects registered in PyPI [11], while the number of Julia
third-party packages registered in Julia Observer is approximately
3000. The number of third-party libraries in Julia is increasing, but
there are still relatively few compared with other programming
languages, and there may not be suitable libraries available in
some unpopular areas.
Because Julia is still in the early stage of development, version
updates are faster, and the interface and grammar of the program
are greatly changed in each version upgrade. After the release of
Julia 1.0, the Julia language has become more mature and stable
than in the past. However, many excellent third-party machine
learning libraries were written before the release of Julia 1.0
and failed to update to the new version in time. Users need to
carefully evaluate whether a third-party library has been updated
to the latest version of Julia to ensure its normal use. In addition,
Julia is designed for parallel programming, but there are not
many third-party libraries for parallel programming. Currently,
the more commonly used third-party packages of Julia are CUD-
Anative.jl,CuArrays.jl, and juliaDB.jl. However, many functions
in these packages are still in the testing stage.
Although Julia libraries are not as rich as those of Python, the
prospects for development are optimistic. Officials have provided
statistical trends in the number of repositories. Many scholars and
technicians are committed to improving the Julia libraries. Rong
Hongbo et al. [138] used Julia, Intel MKL and the SPMP library
to implement Sparso, which is a sparse linear algebra context-
driven optimization tool that can accelerate machine learning
algorithms. Plumb Gregory et al. [139] compiled a library package
for fast Fourier analysis using Julia, which made it easier for fast
Fourier analysis to be employed in statistical machine learning
algorithms.
6. Conclusions
This paper has systematically investigated the development
status of the Julia language in the field of machine learning,
including machine learning algorithms written in Julia, the appli-
cation of the Julia language in machine learning, and the potential
challenges faced by Julia. We find that: (1) Machine learning algo-
rithms written in Julia are mainly supervised learning algorithms,
and there are fewer algorithms for unsupervised learning. (2) The
K. Gao, G. Mei, F. Piccialli et al. / Computer Science Review 37 (2020) 100254 11
Julia language is widely used in seven popular machine learn-
ing research topics: pattern recognition, NLP, IoT data analysis,
computer vision, autonomous driving, graph analytics, and signal
processing. (3) There are far fewer available application packages
than there are for other high-level languages, such as Python,
which is Julia’s greatest challenge. This survey provides a com-
prehensive investigation of the applications of Julia in machine
learning. We believe that with the gradual maturing of the Julia
language and the development of related third-party packages,
the Julia language will be a highly competitive programming
language for machine learning.
Declaration of competing interest
The authors declare that they have no known competing finan-
cial interests or personal relationships that could have appeared
to influence the work reported in this paper.
Acknowledgments
This research was jointly supported by the National Natural
Science Foundation of China (11602235), the Fundamental Re-
search Funds for China Central Universities (2652018091), and
the Major Project for Science and Technology (2020AA002). The
authors would like to thank the editor and the reviewers for their
valuable comments.
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