Anomaly detection is a problem with applications for a wide variety of domains; it involves the identification of novel or unexpected observations or sequences within the data being captured. The majority of current anomaly detection methods are highly specific to the individual use case, requiring expert knowledge of the method as well as the situation to which it is being applied. The Internet of Things (IoT) as a rapidly expanding field offers many opportunities for this type of data analysis to be implemented, however, due to the nature of the IoT, this may be difficult. This review provides a background on the challenges which may be encountered when applying anomaly detection techniques to IoT data, with examples of applications for the IoT anomaly detection taken from the literature. We discuss a range of approaches that have been developed across a variety of domains, not limited to IoT due to the relative novelty of this application. Finally, we summarize the current challenges being faced in the anomaly detection domain with a view to identifying potential research opportunities for the future.

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Anomaly Detection for IoT Time-Series Data: A Survey

1 Complex Numbers Sums and Products Basic Algebraic Properties Further Properties Vectors and Moduli Complex Conjugates Exponential Form Products and Powers in Exponential Form Arguments of Products and Quotients Roots of Complex Numbers Examples Regions in the Complex Plane 2 Analytic Functions Functions of a Complex Variable Mappings Mappings by the Exponential Function Limits Theorems on Limits Limits Involving the Point at Infinity Continuity Derivatives Differentiation Formulas Cauchy-Riemann Equations Sufficient Conditions for Differentiability Polar Coordinates Analytic Functions Examples Harmonic Functions Uniquely Determined Analytic Functions Reflection Principle 3 Elementary Functions The Exponential Function The Logarithmic Function Branches and Derivatives of Logarithms Some Identities Involving Logarithms Complex Exponents Trigonometric Functions Hyperbolic Functions Inverse Trigonometric and Hyperbolic Functions 4 Integrals Derivatives of Functions w(t) Definite Integrals of Functions w(t) Contours Contour Integrals Some Examples Examples with Branch Cuts Upper Bounds for Moduli of Contour Integrals Antiderivatives Proof of the Theorem Cauchy-Goursat Theorem Proof of the Theorem Simply Connected Domains Multiply Connected Domains Cauchy Integral Formula An Extension of the Cauchy Integral Formula Some Consequences of the Extension Liouville's Theorem and the Fundamental Theorem of Algebra Maximum Modulus Principle 5 Series Convergence of Sequences Convergence of Series Taylor Series Proof of Taylor's Theorem Examples Laurent Series Proof of Laurent's Theorem Examples Absolute and Uniform Convergence of Power Series Continuity of Sums of Power Series Integration and Differentiation of Power Series Uniqueness of Series Representations Multiplication and Division of Power Series 6 Residues and Poles Isolated Singular Points Residues Cauchy's Residue Theorem Residue at Infinity The Three Types of Isolated Singular Points Residues at Poles Examples Zeros of Analytic Functions Zeros and Poles Behavior of Functions Near Isolated Singular Points 7 Applications of Residues Evaluation of Improper Integrals Example Improper Integrals from Fourier Analysis Jordan's Lemma Indented Paths An Indentation Around a Branch Point Integration Along a Branch Cut Definite Integrals Involving Sines and Cosines Argument Principle Rouche's Theorem Inverse Laplace Transforms Examples 8 Mapping by Elementary Functions Linear Transformations The Transformation w = 1/z Mappings by 1/z Linear Fractional Transformations An Implicit Form Mappings of the Upper Half Plane The Transformation w = sin z Mappings by z2 and Branches of z1/2 Square Roots of Polynomials Riemann Surfaces Surfaces for Related Functions 9 Conformal Mapping Preservation of Angles Scale Factors Local Inverses Harmonic Conjugates Transformations of Harmonic Functions Transformations of Boundary Conditions 10 Applications of Conformal Mapping Steady Temperatures Steady Temperatures in a Half Plane A Related Problem Temperatures in a Quadrant Electrostatic Potential Potential in a Cylindrical Space Two-Dimensional Fluid Flow The Stream Function Flows Around a Corner and Around a Cylinder 11 The Schwarz-Christoffel Transformation Mapping the Real Axis onto a Polygon Schwarz-Christoffel Transformation Triangles and Rectangles Degenerate Polygons Fluid Flow in a Channel Through a Slit Flow in a Channel with an Offset Electrostatic Potential about an Edge of a Conducting Plate 12 Integral Formulas of the Poisson Type Poisson Integral Formula Dirichlet Problem for a Disk Related Boundary Value Problems Schwarz Integral Formula Dirichlet Problem for a Half Plane Neumann Problems Appendixes Bibliography Table of Transformations of Regions Index

Complex variables and applications

Open Power System Data: Frictionless data for electricity system modelling

Load forecasting is a vital part of smart grids for predicting the required electrical power using artificial intelligence (AI). Deep learning is broadly used for load forecasting in the smart grid using the artificial neural network (ANN). Generally, computing the deep learning in the smart grid requires massive data aggregation or centralization and significant computational time. This paper presents a survey of deep learning-based load forecasting techniques from 2015 to 2020. This survey discusses the studies based on their deep learning techniques, Distributed Deep Learning (DDL) techniques, Back Propagation (BP) based works, and non-BP based works in the load forecasting process. Consequent to the survey, it was determined that data aggregation dependency would be beneficial for reducing computational time in load forecasting. Therefore, a conceptual model of DDL for smart grids has been presented, where the HSIC (Hilbert-Schmidt Independence Criterion) Bottleneck technique has been incorporated to provide higher accuracy.

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HSIC Bottleneck Based Distributed Deep Learning Model for Load Forecasting in Smart Grid With a Comprehensive Survey

Human behaviour modelling for welfare technology using hidden Markov models

Using the Hierarchical Temporal Memory Spatial Pooler for short-term forecasting of electrical load time series

In this paper, we present an open-source software tool 'ABC-PLOSS', which is developed for use in optimisation processes. Path-loss optimisation deals with searching for the best set of operator-specific parameters in telecommunication that gives the least cost of operation. It is a primary issue that challenges mobile communication operators, particularly the global system mobile (GSM) operators in tuning mobile-base station networks for efficient and reliable operation. The tool uses a sequential processor architecture based on a swarm intelligence algorithm called artificial bee colony (ABC) and the cost-231 Hata path-loss model as cost function for path-loss minimisation (PLM). Using the ABC-PLOSS framework, the ABC algorithm is compared with two other existing and popular artificial intelligent (AI) algorithms called the genetic algorithm (GA) and particle swarm optimisation (PSO). Results of simulation studies show that this tool is indeed useful as it gives a competitive or lower path-loss estimate when compared with conventional techniques. It also shows that it is possible for the ABC to attain an estimated seven-fold and two-fold path-loss improvement over the GA and the PSO techniques respectively.

ABC-PLOSS: a software tool for path-loss minimisation in GSM telecom networks using artificial bee colony algorithm

HTM-MAT is a MATLAB based toolbox for implementing cortical learning algorithms (CLA) including related cortical-like algorithms that possesses spatiotemporal properties. CLA is a suite of predictive machine learning algorithms developed by Numenta Inc. and is based on the hierarchical temporal memory (HTM). This paper presents an implementation of HTM-MAT with several illustrative examples including several toy datasets and compared with two sequence learning applications employing state-of-the-art algorithms - the recurrentjs based on the Long Short-Term Memory (LSTM) algorithm and OS-ELM which is based on an online sequential version of the Extreme Learning Machine. The performance of HTM-MAT using two historical benchmark datasets and one real world dataset is also compared with one of the existing sequence learning applications, the OS-ELM. The results indicate that HTM-MAT predictions are indeed competitive and can outperform OS-ELM in sequential prediction tasks.

HTM-MAT: An online prediction software toolbox based on cortical machine learning algorithm.

Paper presented at the iSTEAMS SMART-MIINDs Conference at Yabatech on the 26th–28th June, 2018.

pCWoT-MOBILE: a collaborative web based platform for real time control in the smart space

Predictive coding (PDC) has recently attracted attention in the neuroscience and computing community as a candidate unifying paradigm for neuronal studies and artificial neural network implementations particularly targeted at unsupervised learning systems. The Mismatch Negativity (MMN) has also recently been studied in relation to PC and found to be a useful ingredient in neural predictive coding systems. Backed by the behavior of living organisms, such networks are particularly useful in forming spatio-temporal transitions and invariant representations of the input world. However, most neural systems still do not account for large number of synapses even though this has been shown by a few machine learning researchers as an effective and very important component of any neural system if such a system is to behave properly. Our major point here is that PDC systems with the MMN effect in addition to a large number of synapses can greatly improve any neural learning system's performance and ability to make decisions in the machine world. In this paper, we propose a novel bio-mimetic computational intelligence algorithm – the Deviant Learning Algorithm, inspired by these key ideas and functional properties of recent brain-cognitive discoveries and theories. We also show by numerical experiments guided by theoretical insights, how our invented bio-mimetic algorithm can achieve competitive predictions even with very small problem specific data.

Emmanuel N. Osegi

Papers

Using the Hierarchical Temporal Memory Spatial Pooler for short-term forecasting of electrical load time series

ABC-PLOSS: a software tool for path-loss minimisation in GSM telecom networks using artificial bee colony algorithm

HTM-MAT: An online prediction software toolbox based on cortical machine learning algorithm.

pCWoT-MOBILE: a collaborative web based platform for real time control in the smart space

Deviant Learning Algorithm: Learning Sparse Mismatch Representations through Time and Space