🔬Data Science: Deep Learning (Definitions)

"Deep learning is an area of machine learning that emerged from the intersection of neural networks, artificial intelligence, graphical modeling, optimization, pattern recognition and signal processing." (N D Lewis, "Deep Learning Made Easy with R: A Gentle Introduction for Data Science", 2016)

"Methods that are used to train models with several levels of abstraction from the raw input to the output. For example, in visual recognition, the lowest level is an image composed of pixels. In layers as we go up, a deep learner combines them to form strokes and edges of different orientations, which can then be combined to detect longer lines, arcs, corners, and junctions, which in turn can be combined to form rectangles, circles, and so on. The units of each layer may be thought of as a set of primitives at a different level of abstraction." (Ethem Alpaydın, "Machine learning : the new AI", 2016)

"A branch of machine learning to whose architectures belong deep ANNs. The term “deep” denotes the application of multiple layers with a complex structure." (Iva Mihaylova, "Applications of Artificial Neural Networks in Economics and Finance", 2018)

"A deep-learning model is a neural network that has multiple (more than two) layers of hidden units (or neurons). Deep networks are deep in terms of the number of layers of neurons in the network. Today many deep networks have tens to hundreds of layers. The power of deep-learning models comes from the ability of the neurons in the later layers to learn useful attributes derived from attributes that were themselves learned by the neurons in the earlier layers." (John D Kelleher & Brendan Tierney, "Data science", 2018)

"Also known as deep structured learning or hierarchical learning is part of a broader family of machine learning methods based on learning data representations, as opposed to task-specific algorithms." (Soraya Sedkaoui, "Big Data Analytics for Entrepreneurial Success", 2018)

"Deep learning broadly describes the large family of neural network architectures that contain multiple, interacting hidden layers." (Benjamin Bengfort et al, "Applied Text Analysis with Python: Enabling Language-Aware Data Products with Machine Learning", 2018)

"It is a part of machine learning approach used for learning data representations." (Dharmendra S Rajput et al, "Investigation on Deep Learning Approach for Big Data: Applications and Challenges", 2018)

"The ability of a neural network to improve its learning process." (David Natingga, "Data Science Algorithms in a Week" 2nd Ed., 2018)

"A learning algorithm using a number of layers for extracting and learning feature hierarchies before providing an output for any input." (Tanu Wadhera & Deepti Kakkar, "Eye Tracker: An Assistive Tool in Diagnosis of Autism Spectrum Disorder", 2019)

"a machine-learning technique that extends standard artificial neural network models to many layers representing different levels of abstraction, say going from individual pixels of an image through to recognition of objects." (David Spiegelhalter, "The Art of Statistics: Learning from Data", 2019)

"A part of a broader family of machine learning methods based on learning data representations." (Nil Goksel & Aras Bozkurt, "Artificial Intelligence in Education: Current Insights and Future Perspectives", 2019)

"A recent method of machine learning based on neural networks with more than one hidden layer." (Samih M Jammoul et al, "Open Source Software Usage in Education and Research: Network Traffic Analysis as an Example", 2019)

"A subbranch of machine learning which inspires from the artificial neural network. It has eliminated the need to design handcrafted features as in deep learning features are automatically learned by the model from the data." (Aman Kamboj et al, "Ear Localizer: A Deep-Learning-Based Ear Localization Model for Side Face Images in the Wild", 2019)

"It is class of one machine learning algorithms that can be supervised, unsupervised, or semi-supervised. It uses multiple layers of processing units for feature extraction and transformation." (Siddhartha Kumar Arjaria & Abhishek S Rathore, "Heart Disease Diagnosis: A Machine Learning Approach", 2019)

"Is the complex, unsupervised processing of unstructured data in order to create patterns used in decision making, patterns that are analogous to those of the human brain." (Samia H Rizk, "Risk-Benefit Evaluation in Clinical Research Practice", 2019)

"The ability for machines to autonomously mimic human thought patterns through artificial neural networks composed of cascading layers of information." (Kirti R Bhatele et al, "The Role of Artificial Intelligence in Cyber Security", 2019)

"The method for solving problems that have more probabilistic calculations based on artificial neural networks." (Tolga Ensari et al, "Overview of Machine Learning Approaches for Wireless Communication", 2019)

"A category of machine learning methods which is inspired by the artificial neural networks" (Shouvik Chakraborty & Kalyani Mali, "An Overview of Biomedical Image Analysis From the Deep Learning Perspective", 2020)

"A sub-field of machine learning which is based on the algorithms and layers of artificial networks." (S Kayalvizhi & D Thenmozhi, "Deep Learning Approach for Extracting Catch Phrases from Legal Documents", 2020)

"A type of machine learning based on artificial neural networks. It can be supervised, unsupervised, or semi-supervised, and it uses an artificial neural network with multiple layers between the input and output layers." (Timofei Bogomolov et al, "Identifying Patterns in Fresh Produce Purchases: The Application of Machine Learning Techniques", 2020)

"An extension of machine learning approach, which uses neural network." (Neha Garg & Kamlesh Sharma, "Machine Learning in Text Analysis", 2020)

"Deep learning (also known as deep structured learning or hierarchical learning) is part of a broader family of machine learning methods based on learning data representations, as opposed to task-specific algorithms. Learning can be supervised, semi-supervised or unsupervised." (R Murugan, "Implementation of Deep Learning Neural Network for Retinal Images", 2020)

 "Deep learning is a collection of algorithms used in machine learning, used to model high-level abstractions in data through the use of model architectures, which are composed of multiple nonlinear transformations. It is part of a broad family of methods used for machine learning that are based on learning representations of data." (Edward T Chen, "Deep Learning and Sustainable Telemedicine", 2020)

"Deep learning is a collection of neural-network techniques that generally use multiple layers." (Alex Thomas, "Natural Language Processing with Spark NLP", 2020)

"Deep learning is a kind of machine learning technique with automatic image interpretation and feature learning facility. The different deep learning algorithms are convolutional neural network (CNN), deep neural network (DNN), recurrent neural network (RNN), genetic adversarial networks (GAN), etc." (Rajandeep Kaur & Rajneesh Rani, "Comparative Study on ASD Identification Using Machine and Deep Learning", 2020)

"Deep learning is a subset of machine learning that models high-level abstractions in data by means of network architectures, which are composed of multiple nonlinear transformations." (Loris Nanni et al, "Digital Recognition of Breast Cancer Using TakhisisNet: An Innovative Multi-Head Convolutional Neural Network for Classifying Breast Ultrasonic Images", 2020)

"In contradistinction to surface or superficial learning, deep learning is inextricably associated with long-term retention of pertinent and solid knowledge, based on a thorough and critical understanding of the object of study, be it curricular content or not." (Leonor M Martínez-Serrano, "The Pedagogical Potential of Design Thinking for CLIL Teaching: Creativity, Critical Thinking, and Deep Learning", 2020)

"Is a group of methods that allow multilayer computing models to work with data that has an abstraction hierarchy." (Heorhii Kuchuk et al, "Application of Deep Learning in the Processing of the Aerospace System's Multispectral Images", 2020)

"It is a part of machine learning intended for learning form large amounts of data, as in the case of experience-based learning. It can be considered that feature engineering in deep learning-based models is partly left to the machine. In the case of artificial neural networks, deep neural networks are expected to have various layers within architectures for solving complex problems with higher accuracy compared to traditional machine learning. Moreover, high performance automatic results are expected without human intervention." (Ana Gavrovska & Andreja Samčović, "Intelligent Automation Using Machine and Deep Learning in Cybersecurity of Industrial IoT", 2020)

"Is a subset of AI and machine learning that uses multi-layered artificial neural networks to learn from data that is unstructured or unlabeled." (Lejla Banjanović-Mehmedović & Fahrudin Mehmedović, "Intelligent Manufacturing Systems Driven by Artificial Intelligence in Industry 4.0", 2020)

"This method is also called as hierarchical learning or deep structured learning. It is one of the machine learning method that is based on learning methods like supervised, semi-supervised or unsupervised. The only difference between deep learning and other machine learning algorithm is that deep learning method uses big data as input." (Anumeera Balamurali & Balamurali Ananthanarayanan,"Develop a Neural Model to Score Bigram of Words Using Bag-of-Words Model for Sentiment Analysis", 2020)

"A form of machine learning which uses multi-layered architectures to automatically learn complex representations of the input data. Deep models deliver state-of-the-art results across many fields, e.g. computer vision and NLP." (Vincent Karas & Björn W Schuller, "Deep Learning for Sentiment Analysis: An Overview and Perspectives", 2021)

"A sub branch of Artificial intelligence in which we built the DL model and we don’t need to specify any feature to the learning model . In case of DL the model will classify the data based on the input data." (Ajay Sharma, "Smart Agriculture Services Using Deep Learning, Big Data, and IoT", 2021)

"A sub-set of machine learning in artificial intelligence (AI) with network capabilities supporting learning unsupervised from unstructured data." (Mark Schofield, "Gamification Tools to Facilitate Student Learning Engagement in Higher Education: A Burden or Blessing?", 2021)

"A subarea of machine learning, which adopts a deeper and more complex neural structure to reach state-of-the-art accuracy in a given problem. Commonly applied in machine learning areas, such as classification and prediction." (Jinnie Shin et al, "Automated Essay Scoring Using Deep Learning Algorithms", 2021)

"A subset of a broader family of machine learning methods that makes use of multiple layers to extract data from raw input in order to learn its features." (R Karthik et al, "Performance Analysis of GAN Architecture for Effective Facial Expression Synthesis", 2021)

"An artificial intelligence function that imitates the workings of the human brain in processing data and creating patterns for use in decision making." (Wissam Abbass et al, "Internet of Things Application for Intelligent Cities: Security Risk Assessment Challenges", 2021)

"Another term for unsupervised learning that includes reinforcement learning in which the machine responds to reaching goals given input data and constraints. Deep learning deals with multiple layers simulating neural networks with ability to process immense amount of data." (Sujata Ramnarayan, "Marketing and Artificial Intelligence: Personalization at Scale", 2021)

"Application of multi neuron, multi-layer neural networks to perform learning tasks." (Revathi Rajendran et al, "Convergence of AI, ML, and DL for Enabling Smart Intelligence: Artificial Intelligence, Machine Learning, Deep Learning, Internet of Things", 2021)

 "Deep learning approach is a subfield of the machine learning technique. The concepts of deep learning influenced by neuron and brain structure based on ANN (Artificial Neural Network)." (Sayani Ghosal & Amita Jain, "Research Journey of Hate Content Detection From Cyberspace", 2021)

"Deep learning is a compilation of algorithms used in machine learning, and used to model high-level abstractions in data through the use of model architectures." (M Srikanth Yadav & R Kalpana, "A Survey on Network Intrusion Detection Using Deep Generative Networks for Cyber-Physical Systems", 2021)

"Deep learning is a subfield of machine learning that uses artificial neural networks to predict, classify, and generate data." (Usama A Khan & Josephine M Namayanja, "Reevaluating Factor Models: Feature Extraction of the Factor Zoo", 2021)

"Deep leaning is a subset of machine learning to solve complex problems/datasets." (R Suganya et al, "A Literature Review on Thyroid Hormonal Problems in Women Using Data Science and Analytics: Healthcare Applications", 2021)

"Deep learning is a type of machine learning that can process a wider range of data resources, requires less data preprocessing by humans, and can often produce more accurate results than traditional machine-learning approaches. In deep learning, interconnected layers of software-based calculators known as 'neurons' form a neural network. The network can ingest vast amounts of input data and process them through multiple layers that learn increasingly complex features of the data at each layer. The network can then make a determination about the data, learn if its determination is correct, and use what it has learned to make determinations about new data. For example, once it learns what an object looks like, it can recognize the object in a new image." (Bistra K Vassileva, "Artificial Intelligence: Concepts and Notions", 2021)

"Deep learning refers to artificial neural networks that mimic the workings of the human brain in the formation of patterns used in data processing and decision-making. Deep learning is a subset of machine learning. They are artificial intelligence networks capable of learning from unstructured or unlabeled data." (Atakan Gerger, "Technologies for Connected Government Implementation: Success Factors and Best Practices", 2021)

"It is a machine learning method using multiple layers of nonlinear processing units to extract features from data." (Sercan Demirci et al, "Detection of Diabetic Retinopathy With Mobile Application Using Deep Learning", 2021)

"It is a subarea of machine learning, where the models are built using multiple layers of artificial neural networks for learning useful patterns from raw data." (Gunjan Ansari et al, "Natural Language Processing in Online Reviews", 2021)

"It is an artificial intelligence technology that imitates the role of the human brain in data processing and the development of decision-making patterns." (Mehmet A Cifci, "Optimizing WSNs for CPS Using Machine Learning Techniques", 2021)

"One part of the broader family of machine learning methods based on artificial neural networks with representation learning. Learning can be supervised, semi-supervised or unsupervised." (Jan Bosch et al, "Engineering AI Systems: A Research Agenda", 2021)

"Part of Machine Learning, where methods of higher complexity are used for training data representation." (Andrej Zgank et al, "Embodied Conversation: A Personalized Conversational HCI Interface for Ambient Intelligence", 2021)

"Sub-domain in the field of machine learning that deals with the use of algorithms inspired by human brain cells to solve complex real-world problems." (Shatakshi Singhet al, "A Survey on Intelligence Tools for Data Analytics", 2021)

"This is also a subset of AI where unstructured data is processed using layers of neural networks to identify, predict and detect patterns. Deep learning is used when there is a large amount of unlabeled data and problem is too complex to be solved using machine learning algorithms. Deep learning algorithms are used in computer vision and facial recognition systems." (Vijayaraghavan Varadharajan & Akanksha Rajendra Singh, "Building Intelligent Cities: Concepts, Principles, and Technologies", 2021)

"A rapidly evolving machine learning technique used to build, train, and test neural networks that probabilistically predict outcomes and/or classify unstructured data." (Forrester)

"Deep Learning is a subset of machine learning concerned with large amounts of data with algorithms that have been inspired by the structure and function of the human brain, which is why deep learning models are often referred to as deep neural networks. It is is a part of a broader family of machine learning methods based on learning data representations, as opposed to traditional task-specific algorithms." (Databricks) [source]

"Deep Learning refers to complex multi-layer neural nets.  They are especially suitable for image and voice recognition, and for unsupervised tasks with complex, unstructured data." (Statistics.com)

"is a machine learning methodology where a system learns the patterns in data by automatically learning a hierarchical layer of features. " (Accenture)

🔬Data Science: Classifier (Definitions)

[pattern classifier:] "A neural net to determine whether an input pattern is or is not a member of a particular class. Training data consists of input patterns and the class to which each belongs, but does not require a description of each class; the net forms exemplar vectors for each class as it learns the training patterns." (Laurene V Fausett, "Fundamentals of Neural Networks: Architectures, Algorithms, and Applications", 1994)

[Bayes classifier:] "statistical classification algorithm in which the class borders are determined decision-theoretically, on the basis of class distributions and misclassification costs." (Teuvo Kohonen, "Self-Organizing Maps" 3rd Ed., 2001)

[nonparametric classifier:] "classification method that is not based on any mathematical functional form for the description of class regions, but directly refers to the available exemplary data." (Teuvo Kohonen, "Self-Organizing Maps" 3rd Ed., 2001)

[parametric classifier:] "classification method in which the class regions are defined by specified mathematical functions involving free parameters." (Teuvo Kohonen, "Self-Organizing Maps" 3rd Ed., 2001)

"A set of patterns and rules to assign a class to new examples." (Ching W Wang, "New Ensemble Machine Learning Method for Classification and Prediction on Gene Expression Data", 2008)

"A structured model that maps unlabeled instances to finite set of classes." (Lior Rokach, "Incorporating Fuzzy Logic in Data Mining Tasks", Encyclopedia of Artificial Intelligence, 2009)

"A decision-supporting system that given an unseen (to-be-classified) input object yields a prediction, for instance, it classifies the given object to a certain class." (Ivan Bruha, "Knowledge Combination vs. Meta-Learning", 2009)

"Algorithm that produces class labels as output, from a set of features of an object. A classifier, for example, is used to classify certain features extracted from a face image and provide a label (an identity of the individual)." (Oscar D Suárez & Gloria B García, "Component Analysis in Artificial Vision" Encyclopedia of Artificial Intelligence, 2009)

"An algorithm to assign unknown object samples to their respective classes. The decision is made according to the classification feature vectors describing the object in question." (Michael Haefner, "Pit Pattern Classification Using Multichannel Features and Multiclassification", 2009)

"function that associates a class c to each input pattern x of interest. A classifier can be directly constructed from a set of pattern examples with their respective classes, or indirectly from a statistical model." (Óscar Pérez & Manuel Sánchez-Montañés, Class Prediction in Test Sets with Shifted Distributions, 2009)

[Naive Bayes classifier:] "A modeling technique where each attribute describes a class independent of any other attributes that also describe that class." (DAMA International, "The DAMA Dictionary of Data Management", 2011)

"An algorithm that implements classification in the field of machine learning and statistical analysis." (Golnoush Abaei & Ali Selamat, "Important Issues in Software Fault Prediction: A Road Map", 2014)

"A computational method that can be trained using known labeled data for predicting the label of unlabeled data. If there's only two labels (also called classes), the method is called 'detector'." (Addisson Salazar et al, "New Perspectives of Pattern Recognition for Automatic Credit Card Fraud Detection", 2018)

[Naive Bayes classifier:] "A way to classify a data item using Bayes' theorem concerning the conditional probabilities P(A|B)=(P(B|A) * P(A))/P(B). It also assumes that variables in the data are independent, which means that no variable affects the probability of the remaining variables attaining a certain value." (David Natingga, "Data Science Algorithms in a Week" 2nd Ed., 2018)

"A type of machine learning program that segments a set of cases into different classes or categorizations." (Shalin Hai-Jew, "Methods for Analyzing and Leveraging Online Learning Data", 2019)

"A supervised Data Mining algorithm used to categorize an instance into one of the two or more classes." (Mu L Wong & S Senthil "Development of Accurate and Timely Students' Performance Prediction Model Utilizing Heart Rate Data", 2020)

"A model that can be used to place objects into discrete categories based on some set of features. Classifiers are trained on datasets." (Laurel Powell et al, "Art Innovative Systems for Value Tagging", 2021)

🔬Data Science: Generalization (Definitions)

"The ability of a neural net to produce reasonable responses to input patterns that are similar, but not identical, to training patterns. A balance between memorization and generalization is usually desired." (Laurene V Fausett, "Fundamentals of Neural Networks: Architectures, Algorithms, and Applications", 1994)

"The ability of an information system to process new, unknown input data in order to obtain the best possible solution, or one close to it." (Nikola K Kasabov, "Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering", 1996)

"The ability of a neural computing system to generalize from the input/output examples it was trained on to produce a sensible output to a previously unseen input. Compromise of the variance-bias dilemma." (Guido J Deboeck and Teuvo Kohonen, "Visual explorations in finance with self-organizing maps", 2000)

"way of responding ill the same way to a class of inputs, some of which do not belong to the training set of the same class." (Teuvo Kohonen, "Self-Organizing Maps 3rd Ed.", 2001)

"The process of creating a model based on specific instances that is an acceptable predictor of other instances." (Robert Nisbet et al, "Handbook of statistical analysis and data mining applications", 2009)

🔬Data Science: Simulation (Definitions)

"A computer model of part of a real-world system." (Jesse Liberty, "Sams Teach Yourself C++ in 24 Hours" 3rd Ed., 2001)

"An interactive environment in which features in the environment behave similarly to real-world events." (Ruth C Clark & Chopeta Lyons, "Graphics for Learning", 2004)

"An attempt to represent a real life system via a model to determine how a change in one or more variable affects the rest of the system. It is also called 'what-if' analysis." (Jae K Shim & Joel G Siegel, "Budgeting Basics and Beyond", 2008)

"An interactive environment that models a real-world system. Simulations may be conceptual, such as a simulation of genetic inheritance, or operational, such as a flight simulator." ( Ruth C Clark, "Building Expertise: Cognitive Methods for Training and Performance Improvement", 2008)

"A simulation uses a project model that translates the uncertainties specified at a detailed level into their potential impact on objectives that are expressed at the level of the total project. Project simulations use computer models and estimates of risk, usually expressed as a probability distribution of possible costs or durations at a detailed work level, and are typically performed using Monte Carlo analysis." (Cynthia Stackpole, "PMP® Certification All-in-One For Dummies®", 2011)

"An interactive environment in which features in the virtual environment behave similarly to real-world events. Simulations may be conceptual, such as a simulation of genetic inheritance, or operational, such as a flight simulator." (Ruth C Clark & Richard E Mayer, "e-Learning and the Science of Instruction", 2011)

"A process by which processes or models are run repeatedly using a variety of inputs. The outputs are normally captured and analyzed to conduct sensitivity analysis, provide insight around likely potential outcomes, and identify bottlenecks and constraints within existing processes or models." (Evan Stubbs, "Delivering Business Analytics: Practical Guidelines for Best Practice", 2013)

"The practice of building models based on experts’ views on how the parts of a complicated system work." (Brenda L Dietrich et al, "Analytics Across the Enterprise", 2014)

"Developing a model of a complex system and experimenting with the model to observe the results" (Nell Dale & John Lewis, "Computer Science Illuminated" 6th Ed., 2015)

"An analytical technique that models the combined effect of uncertainties to evaluate their potential impact on objectives." (Project Management Institute, "A Guide to the Project Management Body of Knowledge (PMBOK® Guide)", 2017)

"The representation of selected behavioral characteristics of one physical or abstract system by another system." (ISO 2382/1)

🔬Data Science: Mathematical Modeling (Definitions)

"[mathematical] modeling is an activity, a cognitive activity in which we think about and make models to describe how devices or objects of interest behave." (Clive L Dym & Elizabeth S Ivey, "Principles of Mathematical Modeling", 2004)

"A representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form and expressed using a Mathematical language. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models." (Ignacio Blanquer & Vicente Hernandez, "Grid Technologies in Epidemiology", 2009)

[conventional *]: "The applied science of creating computerized models. That is a theoretical construct that represents a system composed by set of region of interest, with a set of parameters, both variables together with logical and quantitative relationships between them, by means of mathematical language to describe the behavior of the system." (Gloria Bueno García et al, "Energy Minimizing Active Models in Artificial Vision", Encyclopedia of Artificial Intelligence, 2009) 

"Description of a system using mathematical concepts and language." (Oscar Tamburis et al, "A Mathematical Model to Plan the Adoption of EHR Systems", 2014)

"Mathematical modeling is the application of mathematics to describe real-world problems and investigating important questions that arise from it." (Sandip Banerjee, "Mathematical Modeling: Models, Analysis and Applications", 2014)

"A process that gives a result to a representation of a physical phenomenon using mathematics." (Luis R S González & Avenilde Romo Vázquez, "Didactic Sequences Teaching Mathematics for Engineers With Focus on Differential Equations", 2017)

"Converting real life situations into mathematical concepts and symbols and thereby converting real life problems into mathematical problems." (G Udhaya Sankar & C Ganesa Moorthy, "Network Modelling on Tropical Diseases vs. Climate Change", 2020)

🔬Data Science: Mathematical Model (Definitions)

"A mathematical model is any complete and consistent set of mathematical equations which are designed to correspond to some other entity, its prototype. The prototype may be a physical, biological, social, psychological or conceptual entity, perhaps even another mathematical model."  (Rutherford Aris, "Mathematical Modelling", 1978)

"The identification and selection of important descriptor variables to be used within an equation or process that can generate useful predictions." (Glenn J Myatt, "Making Sense of Data: A Practical Guide to Exploratory Data Analysis and Data Mining", 2006)

"Mathematical model is an abstract model that describes a problem, environment, or system using a mathematical language." (Giusseppi Forgionne & Stephen Russell, "Unambiguous Goal Seeking Through Mathematical Modeling", 2008)

"A set of equations, usually ordinary differential equations, the solution of which gives the time course behaviour of a dynamical system." (Peter Wellstead et al, "Systems and Control Theory for Medical Systems Biology", 2009)

"An abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science). It can be defined as the representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form." (Roberta Alfieri & Luciano Milanesi, "Multi-Level Data Integration and Data Mining in Systems Biology", Handbook of Research on Systems Biology Applications in Medicine, 2009)

"Mathematical description of a physical system. In the framework of this work mathematical models pursue the descriptions of mechanisms underlying stuttering, putting emphasis in the dynamics of neuronal regions involved in the disorder." (Manuel Prado-Velasco & Carlos Fernández-Peruchena "An Advanced Concept of Altered Auditory Feedback as a Prosthesis-Therapy for Stuttering Founded on a Non-Speech Etiologic Paradigm", 2011)

"Simplified description of a real world system in mathematical terms, e. g., by means of differential equations or other suitable mathematical structures." (Benedetto Piccoli, Andrea Tosin, "Vehicular Traffic: A Review of Continuum Mathematical Models" [Mathematics of Complexity and Dynamical Systems, 2012])

"Stated loosely, models are simplified, idealized and approximate representations of the structure, mechanism and behavior of real-world systems. From the standpoint of set-theoretic model theory, a mathematical model of a target system is specified by a nonempty set - called the model’s domain, endowed with some operations and relations, delineated by suitable axioms and intended empirical interpretation." (Zoltan Domotor, "Mathematical Models in Philosophy of Science" [Mathematics of Complexity and Dynamical Systems, 2012])

"The standard view among most theoretical physicists, engineers and economists is that mathematical models are syntactic (linguistic) items, identified with particular systems of equations or relational statements. From this perspective, the process of solving a designated system of (algebraic, difference, differential, stochastic, etc.) equations of the target system, and interpreting the particular solutions directly in the context of predictions and explanations are primary, while the mathematical structures of associated state and orbit spaces, and quantity algebras – although conceptually important, are secondary." (Zoltan Domotor, "Mathematical Models in Philosophy of Science" [Mathematics of Complexity and Dynamical Systems, 2012])

"They are a set of mathematical equations that explain the behaviour of the system under various operating conditions, and determine the dominant factors that govern the rules of the process. Mathematical modeling is also associated with data collection, data interpretation, parameter estimation, optimization, and provide tools for identifying possible approaches to control and for assessing the potential impact of different intervention measures." (Eldon R Rene et al, "ANNs for Identifying Shock Loads in Continuously Operated Biofilters", 2012)

"An abstract representation of the real-world system using mathematical concepts." (R Sridharan & Vinay V Panicker, "Ant Colony Algorithm for Two Stage Supply Chain", 2014)

"Is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modelling. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour." (M T Benmessaoud et al, "Modeling and Simulation of a Stand-Alone Hydrogen Photovoltaic Fuel Cell Hybrid System", 2014)

"A mathematical model is a model built using the language and tools of mathematics. A mathematical model is often constructed with the aim to provide predictions on the future ‘state’ of a phenomenon or a system." (Crescenzio Gallo, "Artificial Neural Networks Tutorial", 2015)

"A mathematical model consists of an equation or a set of equations belonging to a certain class of mathematical models to describe the dynamic behavior of the corresponding system. The parameters involved in this mathematical model are related to a certain mathematical structure. This mathematical model is characterized by its class, its structure and its parameters." (Houda Salhi & Samira Kamoun, "State and Parametric Estimation of Nonlinear Systems Described by Wiener Sate-Space Mathematical Models", 2015)

"Description of a system using mathematical concepts and language." (Tomaž Kramberger, "A Contribution to Better Organized Winter Road Maintenance by Integrating the Model in a Geographic Information System", 2015)

"A description of a system using mathematical concepts and language." (Corrado Falcolini, "Algorithms for Geometrical Models in Borromini's San Carlino alle Quattro Fontane", 2016)

"A mathematical model is a mathematical description (often by means of a function or an equation) of a real-world phenomenon such as the size of a population, the demand for a product, the speed of a falling object, the concentration of a product in a chemical reaction, the life expectancy of a person at birth, or the cost of emission reductions. The purpose of the model is to understand the phenomenon and perhaps to make predictions about future behavior. [...] A mathematical model is never a completely accurate representation of a physical situation - it is an idealization." (James Stewart, "Calculus: Early Transcedentals" 8th Ed., 2016)

"Mathematical representation of a system to describe the behavior of certain variables for an indeterminate time." (Sergio S Juárez-Gutiérrez et al, "Temperature Modeling of a Greenhouse Environment", 2016)

"A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences (such as physics, biology, earth science, meteorology) and engineering disciplines (e.g., computer science, artificial intelligence), but also in the social sciences (such as economics, psychology, sociology, and political science); physicists, engineers, statisticians, operations research analysts, and economists use mathematical models most extensively. A model may help to explain a system and to study the effects of different components, and to make predictions about behavior." (Addepalli V N Krishna & M Balamurugan, "Security Mechanisms in Cloud Computing-Based Big Data", 2019)

"A description of a system using mathematical symbols." (José I Gomar-Madriz et al, "An Analysis of the Traveling Speed in the Traveling Hoist Scheduling Problem for Electroplating Processes", 2020)

"An abstract mathematical representation of a process, device, or concept; it uses a number of variables to represent inputs, outputs and internal states, and sets of equations and inequalities to describe their interaction." (Alisher F Narynbaev, "Selection of an Information Source and Methodology for Calculating Solar Resources of the Kyrgyz Republic", 2020)

🔬Data Science: Semantic Network [SN] (Definitions)

"We define a semantic network as 'the collection of all the relationships that concepts have to other concepts, to percepts, to procedures, and to motor mechanisms' of the knowledge." (John F Sowa, "Conceptual Structures", 1984)

"A graph for knowledge representation where concepts are represented as nodes in a graph and the binary semantic relations between the concepts are represented by named and directed edges between the nodes. All semantic networks have a declarative graphical representation that can be used either to represent knowledge or to support automated systems for reasoning about knowledge." (László Kovács et al, "Ontology-Based Semantic Models for Databases", 2009)

"A graph structure useful to represent the knowledge of a domain. It is composed of a set of objects, the graph nodes, which represent the concepts of the domain, and relations among such objects, the graph arches, which represent the domain knowledge. The semantic networks are also a reasoning tool as it is possible to find relations among the concepts of a semantic network that do not have a direct relation among them. To this aim, it is enough 'to follow the arrows' of the network arches that exit from the considered nodes and find in which node the paths meet." (Mario Ceresa, "Clinical and Biomolecular Ontologies for E-Health", Handbook of Research on Distributed Medical Informatics and E-Health, 2009)

"A form of visualization consisting of vertices (concepts) and directed or undirected edges (relationships)." (DAMA International, "The DAMA Dictionary of Data Management", 2011)

"A term used in computer language processing and in RF and OWL to refer to concepts linked by relationships. Memory maps are an informal example of a semantic network." (Kate Taylor, "A Common Sense Approach to Interoperability", 2011)

"nodes, encapsulating data and information, are connected by edges which include information about how these nodes are related to one another." (Simon Boese et al, "Semantic Document Networks to Support Concept Retrieval", 2014)

"A knowledge representation technique that represents the relationships among objects" (Nell Dale & John Lewis, "Computer Science Illuminated" 6th Ed., 2015)

"A knowledge base that represents semantic relations between concepts. Formally, the underlying representation model is a directed graph consisting of nodes, which represent concepts, and links, which represent semantic relations between concepts, mapping or connecting semantic fields." (Dmitry Korzun et al, "Semantic Methods for Data Mining in Smart Spaces", 2019)

"A knowledge base that represents semantic relations between concepts in a network. The model of knowledge representation is based on a directed or undirected graph consisting of vertices, which represent concepts, and edges, which represent semantic relations between concepts, mapping or connecting semantic fields." (Svetlana E Yalovitsyna et al, "Smart Museum: Semantic Approach to Generation and Presenting Information of Museum Collections", 2020)

🔬Data Science: Bayesian Network (Definitions)

"A mathematic model in graphic form that represents a set of variables and their probabilistic independencies. It can be used, for example, to calculate the probability of a patient having a specific disease." (Attila Benko & Cecília S Lányi, "History of Artificial Intelligence", 2009) 

"A Bayesian network is a set of causally interrelated variables represented graphically in which the input information is generally subjective and can be updated in light of empirical data, by using Bayes’ theorem." (Herbert I Weisberg, "Bias and Causation: Models and Judgment for Valid Comparisons", 2010)

"A type of neural network. The Bayesian network is based on the fundamentals of probability theory." (Meta S Brown, "Data Mining For Dummies", 2014)

"A Bayesian network is a directed acyclical graph (there are no cycles in the graph) that is composed of three basic elements: 
nodes: each feature in a domain is represented by a single node in the graph.
edges: nodes are connected by directed links; the connectivity of the links in a graph encodes the influence and conditional independence relationships between nodes. 
conditional probability tables: each node has a conditional probability table (CPT) associated with it. A CPT lists the probability distribution of the feature represented by the node conditioned on the features represented by the other nodes to which a node is connected by edges." (John D Kelleher et al, "Fundamentals of Machine Learning for Predictive Data Analytics: Algorithms, worked examples, and case studies", 2015) 

"A representation of knowledge in the form of a directed acyclic graph representing random variables as nodes and their conditional dependencies as edges." (Petr Berka, "Machine Learning", 2015)

"They are acyclic graphical models that capture conditional dependence among random variables. Each node is associated with a function that gives the probability of finding the variable in a given state, given particular states of its parent variables." (Hamid R Arabnia et al, "Application of Big Data for National Security", 2015)

"A graph model representing random variables with their conditional dependencies." (David Natingga, "Data Science Algorithms in a Week" 2nd Ed., 2018)

"A particular type of statistical model that represents a set of variables and their conditional dependencies. It is usually used to make previsions in a great variety of events." (Gaetano B Ronsivalle & Arianna Boldi, "Artificial Intelligence Applied: Six Actual Projects in Big Organizations", 2019)

"A model that represents and calculates the probabilistic relationships between a set of random variables and an uncertain domain via a directed acyclic graph." (Accenture)

"Bayesian Neural Networks (BNNs) refers to extending standard networks with posterior inference in order to control over-fitting. From a broader perspective, the Bayesian approach uses the statistical methodology so that everything has a probability distribution attached to it, including model parameters (weights and biases in neural networks). In programming languages, variables that can take a specific value will turn the same result every-time you access that specific variable." (Databricks) [source]

🔬Data Science: Business Analysis (Definitions)

 "(1) The study of business processes, practices and business systems requirements. (2) The application of information to better understand business opportunities and challenges." (DAMA International, "The DAMA Dictionary of Data Management", 2011)

"A set of tools and methods used for execrating business insight making from the available data or system structure. It provide meaningful information with dynamic and sophisticate methods of problem solving such as optimization." (Shokoufeh Mirzaei, Defining a Business-Driven Optimization Problem, 2014)

"Business analytics is the combination of skills, technologies, applications, and processes used by organizations to gain insight into their business-based data and statistics to drive business planning." (K Hariharanath, "BIG Data: An Enabler in Developing Business Models in Cloud Computing Environments", 2019)

"It is the process of working with factual information in organizations, using suitable tools and techniques to identify the nuggets of wisdom (insights) from them that can have direct impact on influencing good decision making." (Tanushri Banerjee & Arindam Banerjee, "Designing a Business Analytics Culture in Organizations in India", 2021)

"Business analysis is the means through which operational problems and issues are systematically identified and investigated, different approaches are evaluated, and optimal solutions are determined." (Qlik) [source]

"The set of tasks, knowledge, tools and techniques required to identify business needs and determine solutions to business problems" (Business Analysis BOK) 

🔬Data Science: Delphi Method (Definitions)

"A qualitative forecasting method that seeks to use the judgment of experts systematically in arriving at a forecast of what future events will be or when they may occur. It brings together a group of experts who have access to each other's opinions in an environment where no majority opinion is disclosed." (Jae K Shim & Joel G Siegel, "Budgeting Basics and Beyond", 2008)

"A systematic forecasting practice that seeks input or advice from a panel of experts. Each expert provides their forecast input in a successive series of rounds, until consensus is achieved." (Steven Haines, "The Product Manager's Desk Reference", 2008)

"A systematic, interactive forecasting method that relies on a panel of experts. The experts answer questionnaires in two or more rounds. After each round, a facilitator provides an anonymous summary of the experts’ forecasts from the previous round as well as the reasons they provided for their judgments." (Project Management Institute, "Practice Standard for Project Estimating", 2010)

"Data collection method that happens in an anonymous fashion." (Adam Gordon, "Official (ISC)2 Guide to the CISSP CBK" 4th Ed., 2015)

"A structured communication technique used to conduct interactive forecasting. It involves a panel of experts." (IQBBA)

🔬Data Science: Descriptive Statistics (Definitions)

"Numbers that summarize how questionnaire items were answered. Descriptive statistics include frequency, percentage, cumulative frequency, and cumulative percentage." (Teri Lund & Susan Barksdale, "10 Steps to Successful Strategic Planning", 2006)

"Statistics that characterize the central tendency, variability, and shape of a variable." (Glenn J Myatt, "Making Sense of Data: A Practical Guide to Exploratory Data Analysis and Data Mining", 2006)

"Describe the values in a set. For example, if you sum a set of values, that sum is a descriptive statistic. If you find the largest value or the smallest value in a set of numbers, that’s also a descriptive statistic." (E C Nelson & Stephen L Nelson, "Excel Data Analysis For Dummies ", 2015)

"Those statistics or statistical procedures that summarise and/or describe the characteristics of a sample of scores." (K  N Krishnaswamy et al, "Management Research Methodology: Integration of Principles, Methods and Techniques", 2016)

🔬Data Science: Fuzzy Rule (Definitions)

"A conditional of the form IF X IS A, THEN Y IS B where A and B are fuzzy sets. In mathematical terms a rule is a relation between fuzzy sets. Each rule defines a fuzzy patch (the product A x B) in the system 'state space'. The wider the fuzzy sets A and B, the wider and more uncertain the fuzzy patch. Fuzzy rules are the knowledge-building blocks in a fuzzy system. In mathematical terms each fuzzy rule acts as an associative memory that associates the fuzzy response B with the fuzzy stimulus A." (Guido Deboeck & Teuvo Kohonen (Eds), "Visual Explorations in Finance with Self-Organizing Maps" 2nd Ed., 2000)

"In general, in rule-based systems, rules look something like: If A1 and A2 and … An then C1 and C2 and … Cm; where the Ai are the antecedents (conditions) on the left hand side (LHS) of the rule and the Cj are the consequents (conclusions) on the right hand side (RHS) of the rule. In this format, if all of the antecedents on the LHS of the rule are true then the rule will fire and the consequents will be asserted / executed. With Fuzzy rules both antecedents and conclusions can be of fuzzy nature." (Juan R González et al, Nature-Inspired Cooperative Strategies for Optimization, 2008)

"Fuzzy If-Then or fuzzy conditional statements are expressions of the form 'If A Then B', where A and B are labels of fuzzy sets characterised by appropriate membership functions. Due to their concise form, fuzzy If-Then rules are often employed to capture the imprecise modes of reasoning that play an essential role in the human ability to make decision in an environment of uncertainty and imprecision. The set of If-Then rules relate to a fuzzy logic system that are stored together is called a Fuzzy Rule Base." (Masoud Mohammadian, Supervised Learning of Fuzzy Logic Systems, 2009)

🔬Data Science: Hash Function (Definition)

"A function that maps a set of keys onto a set of addresses." (S. Sumathi & S. Esakkirajan, "Fundamentals of Relational Database Management Systems", 2007)

"A function that maps a string of arbitrary length to a fixed size value in a deterministic manner. Such a function may or may not have cryptographic applications." (Mark S Merkow & Lakshmikanth Raghavan, "Secure and Resilient Software Development", 2010)

[cryptographic hash function:] "A function that takes an input string of arbitrary length and produces a fixed-size output for which it is unfeasible to find two inputs that map to the same output, and it is unfeasible to learn anything about the input from the output." (Mark S Merkow & Lakshmikanth Raghavan, "Secure and Resilient Software Development", 2010)

[one-way hash function:] "A hash function for which it is computationally unfeasible to determine anything about the input from the output." (Mark S Merkow & Lakshmikanth Raghavan, "Secure and Resilient Software Development", 2010)

"A function that operates on an arbitrary-length input value and returns a fixed-length hash value." (Oracle, "Database SQL Tuning Guide Glossary", 2013)

[one-way hash:] "A one-way hash is an algorithm that transforms one string into another string (a fixed-length sequence of seemingly random characters) in such a way that the original string cannot be calculated by operations on the one-way hash value (i.e., the calculation is one way only). One-way hash values can be calculated for any string, including a person’s name, a document, or an image. For any input string, the resultant one-way hash will always be the same. If a single byte of the input string is modified, the resulting one-way hash will be changed and will have a totally different sequence than the one-way hash sequence calculated for the unmodified string. One-way hash values can be made sufficiently long (e.g., 256 bits) that a hash string collision (i.e., the occurrence of two different input strings with the same one-way hash output value) is negligible." (Jules H Berman, "Principles of Big Data: Preparing, Sharing, and Analyzing Complex Information", 2013)

"A hash function is an algorithm that maps from an input, for example, a string of characters, to an output string. The size of the input can vary, but the size of the output is always the same." (Dan Sullivan, "NoSQL for Mere Mortals®", 2015)

[one-way hash:] "Cryptographic process that takes an arbitrary amount of data and generates a fixed-length value. Used for integrity protection." (Adam Gordon, "Official (ISC)2 Guide to the CISSP CBK" 4th Ed., 2015)

"A function that takes as input the key of an element and produces an integer as output" (Nell Dale et al, "Object-Oriented Data Structures Using Java" 4th Ed., 2016)

"encryption methods that use no keys." (Manish Agrawal, "Information Security and IT Risk Management", 2014)

"A function that operates on an arbitrary-length input value and returns a fixed-length hash value." (Oracle, "Oracle Database Concepts")

🔬Data Science: Inference (Definitions)

"Drawing some form of conclusion about a measurable functional response based on representative or sample experimental data. Sample size, uncertainty, and the laws of probability play a major role in making inferences." (Clyde M Creveling, "Six Sigma for Technical Processes: An Overview for R Executives, Technical Leaders, and Engineering Managers", 2006)

"Reasoning from known propositions." (DAMA International, "The DAMA Dictionary of Data Management", 2011)

"In general, inference is the act or process of deriving new facts from facts known or assumed to be true. In Artificial Intelligence, researchers develop automated inference engines to automate human inference." (Michael Fellmann et al, "Supporting Semantic Verification of Process Models", 2012)

[statistical inference:] "A method that uses sample data to draw conclusions about a population." (Geoff Cumming, "Understanding The New Statistics", 2013)

"Any conclusion drawn on the basis of some set of information. In research, we draw inferences on the basis of empirical data we collect and ideas we construct." (K  N Krishnaswamy et al, "Management Research Methodology: Integration of Principles, Methods and Techniques", 2016)

[causal inference:] "Conclusion that changes in the independent variable resulted in a change in the dependent variable. It may be drawn only if all potential confounding variables are properly controlled." (K  N Krishnaswamy et al, "Management Research Methodology: Integration of Principles, Methods and Techniques", 2016)

"The process of using a probabilistic model to answer a query, given evidence." (Avi Pfeffer, "Practical Probabilistic Programming", 2016)

[inductive inference] "A machine learning method for learning the rules that produced the actual data." (David Natingga, "Data Science Algorithms in a Week" 2nd Ed., 2018)

"The ability to derive information not explicitly available." (Shon Harris & Fernando Maymi, "CISSP All-in-One Exam Guide" 8th Ed., 2018)

🔬Data Science: Data Modeling (Definitions)

"The task of developing a data model that represents the persistent data of some enterprise." (Keith Gordon, "Principles of Data Management", 2007)

"An analysis and design method, building data models to 

a) define and analyze data requirements,

b) design logical and physical data structures that support these requirements, and

c) define business and technical meta-data." (DAMA International, "The DAMA Dictionary of Data Management", 2011)

"The process of creating a data model by applying formal data model descriptions using data modeling techniques." (Christian Galinski & Helmut Beckmann, "Concepts for Enhancing Content Quality and eAccessibility: In General and in the Field of eProcurement", 2012)

"The process of creating the abstract representation of a subject so that it can be studied more cheaply (a scale model of an airplane in a wind tunnel), at a particular moment in time (weather forecasting), or manipulated, modified, and altered without disrupting the original (economic model)." (George Tillmann, "Usage-Driven Database Design: From Logical Data Modeling through Physical Schmea Definition", 2017)

"A method used to define and analyze the data requirements needed to support an entity’s business processes, defining the relationship between data elements and structures." (Solutions Review)

"A method used to define and analyze data requirements needed to support the business functions of an enterprise. These data requirements are recorded as a conceptual data model with associated data definitions. Data modeling defines the relationships between data elements and data structures. (Microstrategy)

"A method used to define and analyze data requirements needed to support the business functions of an enterprise. These data requirements are recorded as a conceptual data model with associated data definitions. Data modeling defines the relationships between data elements and structures." (Information Management)

"Refers to the process of defining, analyzing, and structuring data within data models." (Insight Software)

"Data modeling is a way of mapping out and visualizing all the different places that a software or application stores information, and how these sources of data will fit together and flow into one another." (Sisense) [source]

"Data modeling is the process of documenting a complex software system design as an easily understood diagram, using text and symbols to represent the way data needs to flow. The diagram can be used to ensure efficient use of data, as a blueprint for the construction of new software or for re-engineering a legacy application." (Techtarget) [source]