Biologically inspired computing

The growing complexity of real-world problems has motivated computer scientists to search for efficient problem-solving methods. Evolutionary Computation and Swarm Intelligence metaheuristics are outstanding examples that nature has been an unending source of inspiration. The behavior of bees, bacteria, glowworms, fireflies, slime molds, cockroaches, mosquitoes and other organisms have inspired swarm intelligence researchers to devise new optimization algorithms. This tutorial highlights the most recent nature-based inspirations as metaphors for swarm intelligence metaheuristics. We describe the biological behaviors from which a number of computational algorithms were developed. Also, the most recent and important applications and the main features of such metaheuristics are reported.

Inspired by biological mechanisms and structures in neuroscience, many biologically inspired visual computational models have been presented to provide new solutions for visual recognition task. For example, convolutional neural network (CNN) was proposed according to the hierarchical structure of biological vision, which could achieve superior performance in large-scale image classification. In this paper, we propose a new framework called visual interaction networks (VIN-Net), which is inspired by visual interaction mechanisms. More specifically, self-interaction, mutual-interaction, multi-interaction, and adaptive interaction are proposed in VIN-Net, forming the first interactive completeness of the visual interaction model. To further enhance the representation ability of visual features, the adaptive adjustment mechanism is integrated into the VIN-Net model. Finally, our model is evaluated on three benchmark datasets and two self-built textile defect datasets. The experimental results demonstrate that the proposed model exhibits its efficiency on visual classification tasks. Furthermore, a textile industrial application shows that the proposed architecture outperforms the state-of-the-art approaches in classification performance.

Software systems are becoming ever more complex, as the capabilities of the software upon which they are based increase. To develop software that is manageable, we must look for novel sources of inspiration, rather than requiring an increasingly costly level of human support. Self-organising software suggests benefits in this direction, and this chapter focuses on a particularly relevant area of inspiration, that of natural systems. Indeed many natural systems are themselves self-organising, despite being often very complicated. We consider natural systems both in the context of non-living (mathematical, physical and chemical) and living (cellular, invertebrate and vertebrate, not excluding human beings) examples. We review some of the causal mechanisms and conditions that are fundamental to self-organisation in natural systems, such as: complexity, evolution, ecological interactions, animal behaviour, as well as the complexities of human behaviour, which has given us insights into phenomena such as small-world networks, epidemics, trust and gossip. In each case, we consider the relevance to self-organising software, and we throughout provide a range of references to applications and to other chapters where particular areas will be developed in more detail. We conclude by considering two application areas which arise frequently in the context of self-organising software, in different contexts: trading in markets, and networks when considered from the perspectives of design, management and robustness.

In this paper, we propose a biologically inspired visual integrated model for image classification, called VMVI-CNN. Motivated in part by recent neuroscience progress in revealing integrated functions of human visual system, two bio-inspired visual mechanisms (the visual memory decay mechanism and the visual interaction mechanism) are proposed and built within the VMVI-CNN to (1) control the feature information passing through, and (2) increase the richness of feature information. The proposed method is tested on three benchmark datasets (MNIST, Cifar-10, and Mini-ImageNet) and a real-world industrial dataset. The results demonstrate that the new model can extract distinctive features and exhibit a better recognition performance than the current state-of-the-art approaches.

We present a framework which allows standard stereo reconstruction to be unified with a wide range of classic top-down cues from urban scene understanding. The resulting algorithm is analogous to the human visual system where conflicting interpretations of the scene due to ambiguous data can be resolved based on a higher level understanding of urban environments. The cues which are reformulated within the framework include: recognising common arrangements of surface normals and semantic edges (e.g. concave, convex and occlusion boundaries), recognising connected or coplanar structures such as walls, and recognising collinear edges (which are common on repetitive structures such as windows). Recognition of these common configurations has only recently become feasible, thanks to the emergence of large-scale reconstruction datasets. To demonstrate the importance and generality of scene understanding during stereo-reconstruction, the proposed approach is integrated with 3 different state-of-the-art techniques for bottom-up stereo reconstruction. The use of high-level cues is shown to improve performance by up to 15 % on the Middlebury 2014 and KITTI datasets. We further evaluate the technique using the recently proposed HCI stereo metrics, finding significant improvements in the quality of depth discontinuities, planar surfaces and thin structures. (a) Input data (b) Appearance matching (c) Scene reasoning (d) Output reconstruction Figure 1: An illustration of the different components which are unified within the proposed framework. Specifically including both bottom-up matching (b) and a top-down understanding (c) of an outdoor (top) and indoor (bottom) urban scene.

In this article we present an advanced version of Dual-PECCS, a cognitively-inspired knowledge representation and reasoning system aimed at extending the capabilities of artificial systems in conceptual categorization tasks. It combines different sorts of common-sense cat-egorization (prototypical and exemplars-based categorization) with standard monotonic cate-gorization procedures. These different types of inferential procedures are reconciled according to the tenets coming from the dual process theory of reasoning. On the other hand, from a representational perspective, the system relies on the hypothesis of conceptual structures represented as heterogeneous proxytypes. Dual-PECCS has been experimentally assessed in a task of conceptual categorization where a target concept illustrated by a simple common-sense linguistic description had to be identified by resorting to a mix of categorization strategies, and its output has been compared to human responses. The obtained results suggest that our approach can be beneficial to improve the representational and reasoning conceptual capabilities of standard cognitive artificial systems, and –in addition– that it may be plausibly applied to different general computational models of cognition. The current version of the system , in fact, extends our previous work, in that Dual-PECCS is now integrated and tested into two cognitive architectures, ACT-R and CLARION, implementing different assumptions on the underlying invariant structures governing human cognition. Such integration allowed us to extend our previous evaluation.

Many optimization problems in science and engineering are highly nonlinear, and thus require sophisticated optimization techniques to solve. Traditional techniques such as gradient-based algorithms are mostly local search methods, and often struggle to cope with such challenging optimization problems. Recent trends tend to use nature-inspired optimization algorithms. The standard cuckoo search (CS) is an optimization algorithm based on a single cuckoo species and a single host species. This work extends the standard CS by using the successful features of the cuckoo-host co-evolution with multiple interacting species. The proposed multi-species cuckoo search (MSCS) intends to mimic the co-evolution among multiple cuckoo species that compete for the survival of the fittest. The solution vectors are encoded as position vectors. The proposed algorithm is then validated by 15 benchmark functions as well as five nonlinear, multimodal case studies in practical applications. Simulation results suggest that the proposed algorithm can be effective for finding optimal solutions and all optimal solutions are achievable in the tested cases. The results for the test benchmarks are also compared with those obtained by other methods such as the standard cuckoo search and genetic algorithm. The comparison has demonstrated the efficiency of the present algorithm. Based on numerical experiments and case studies, we can conclude that the proposed algorithm can be more efficient in most cases. Therefore, the proposed approach can be a very effective tool for solving nonlinear global optimization problems.

In this work, we investigate the possibility of using inspiration from the self-organizing property of organisms in nature for providing visual representation of an invisible pollutant profile. We present a novel mathematical model of the bacterium and use it to find pollutants in the environment. This model has the capability of exploring the environment to search for sparsely distributed pollutants or food sources and then subsequently exploiting them upon discovery. We also combine the bacterium model in a bacterium–flock algorithm for the purposes of preventing collisions between robots or organisms in addition to providing coverage to a pollutant. By adjusting the velocity of individuals, we show that we are able to control the coverage provided by the population as a whole. Furthermore, we compare the bacterium–flock algorithm with a novel gradient-ascent-flocking algorithm and the well established Voronoi partition algorithm. Results show that bacterium–flock algorithm and the Voronoi partition algorithm are capable of adapting the distribution of the individuals of a population based upon the underlying pollutant profile while the gradient-ascent-flocking algorithm is not. This shows that the bacterium–flock and the Voronoi partition algorithms can potentially be used to track a spatiotemporal function. On the other hand, the gradient-ascent-flock algorithm has a faster convergence time in some cases with the Voronoi partition algorithm having the slowest convergence time overall.

In an attempt to provide a unified account for a vast literature discussing a multiplicity of selves, Shaun Gallagher (2013) has proposed a pattern theory of self. Subsequent discussion on this account has led to a concern that the pattern theory, as originally presented, stands as a mere list of aspects that fails to explain how they are related in real-time. We suggest that one way to address these criticisms and further develop the pattern theory of self is by exploring how it can be used to aid research on self in artificial general intelligence, especially in the context of biologically inspired cognitive architectures. We furthermore propose a conceptual implementation for actualizing such research in regards to the LIDA (Learning Intelligent Decision Agent) cognitive model.

Foraging theory has been the inspiration for several decision-making algorithms for task-processing agents facing random environments. As nature selects for foraging behaviors that maximize lifetime calorie gain or minimize starvation probability, engineering designs are favored that maximize returned value (e.g. profit) or minimize the probability of not reaching performance targets. Prior foraging-inspired designs are direct applications of classical optimal foraging theory (OFT). Here, we describe a generalized optimization framework that encompasses the classical OFT model, a popular competitor, and several new models introduced here that are better suited for some task-processing applications in engineering. These new models merge features of rate maximization, efficiency maximization, and risk-sensitive foraging while not sacrificing the intuitive character of classical OFT. However, the central contributions of this paper are analytical and graphical methods for designing decision-making algorithms guaranteed to be optimal within the framework. Thus, we provide a general modeling framework for solitary agent behavior, several new and classic examples that apply to it, and generic methods for design and analysis of optimal task-processing behaviors that fit within the framework. Our results extend the key mathematical features of optimal foraging theory to a wide range of other optimization objectives in biological, anthropological, and technological contexts.

This paper reports the hybridization of the artificial bee colony (ABC) and a genetic algorithm (GA), ina hierarchical topology, a step ahead of a previous work. We used this parallel approach for solving theprotein structure prediction problem using the three-dimensional hydrophobic-polar model with side-chains(3DHP-SC). The proposed method was run in a parallel processing environment (Beowulf cluster), andseveral aspects of the modeling and implementation are presented and discussed. The performance of thehybrid-hierarchical ABC-GA approach was compared with a hybrid-hierarchical ABC-only approach forfour benchmark instances. Results show that the hybridization of the ABC with the GA improves the qualityof solutions caused by the coevolution effect between them and their search behavior. Copyright © 2011John Wiley & Sons, Ltd.

In this paper a possible general framework for the representation of concepts in cognitive artificial systems and cognitive architectures is proposed. The framework is inspired by the so called proxytype theory of concepts and combines it with the heterogeneity approach to concept representations, according to which concepts do not constitute a unitary phenomenon. The contribution of the paper is twofold: on one hand, it aims at providing a novel theoretical hypothesis for the debate about concepts in cognitive sciences by providing unexplored connections between different theories; on the other hand it is aimed at sketching a computational characterization of the problem of concept representation in cognitively inspired artificial systems and in cognitive architectures.

In this paper we propose a Lossless data compressor in high level throughput using re programable FPGA technology.Real time data compression is expected to play a crucial role in high rate data communication applications. Most available approaches have largely overlooked the impact of mixed pixels and subpixel targets, which can be accurately modeled and uncovered by resorting to the wealth of spectral information provided by hyperspectral image data. In this paper, we proposed an FPGA-based data compressor on the concept of CAM and Dictionary based compression technique has been proposed in this paper . It has been implemented on a Xilinx Spartan3 -II FPGA formed by several millions of gates, and with high computational power and compact size, which make this reconfigurable device very appealing for onboard, real-time data processing.

This paper describes a study in the evolution of distributed cooperative behavior, specifically leader election, through digital evolution and group selection. In digital evolution, a population of self-replicating computer programs exists in a user-defined computational environment and is subject to instruction-level mutations and natural selection. Group selection is the theory that the survival of the individual is linked to the survival of the group, thus encouraging cooperation. The results of experiments using the AVIDA digital evolution platform demonstrate that group selection can produce populations capable of electing a leader and, when that leader is terminated, electing a new leader. This result serves as an existence proof that group selection and digital evolution can produce complex cooperative behaviors, and therefore have promise in the design of robust distributed computing systems.

We consider the optimal control design of an abstract autonomous vehicle (AAV). The AAV searches an area for tasks that are detected with a probability that depends on vehicle speed, and each detected task can be processed or ignored. Both searching and processing are costly, but processing also returns rewards that quantify designer preferences. We generalize results from the analysis of animal foraging behavior to model the AAV. Then, using a performance metric common in behavioral ecology, we explicitly find the optimal speed and task processing choice policy for a version of the AAV problem. Finally, in simulation, we show how parameter estimation can be used to determine the optimal controller online when density of task types is unknown.

This paper presents an incremental clustering algorithm based on DGC, a density-based algorithm we developed earlier [1]. We experimented with real-life datasets and both methods perform satisfactorily. The methods have been compared with some well-known clustering algorithms and they perform well in terms of z-score cluster validity measure.

A method increasingly used to uniquely identify objects (be they pieces of luggage, transported goods or inventory items in shops and warehouses), is Radio Frequency IDentification (RFID). One of the most important components of RFID systems is the antenna and its design is critical to the utility of such tracking systems. Design engineers have traditionally constructed small antennas using their knowledge and intuition, as there is no simple analytical solution relating antenna structure to performance. This, however, does not guarantee optimal results, particularly for larger, more complex antennas. The problem is ideally suited to automated methods of optimisation. This chapter presents an overview of the automatic design of antennas using the meta-heuristic known as Ant Colony Optimisation (ACO). Apart from a description of the necessary mechanics ACO needs to effectively solve this problem, a novel local search refinement operator and a multi-objective version of the problem are also described. The latter is used to optimise both antenna efficiency and resonant frequency. Computational results for a range of antenna sizes show that ACO is a very effective design tool for RFID antennas.

This paper describes a study in the evolution of cooperative behavior, specifically the construction of communication networks, through digital evolution and multilevel selection. In digital evolution, a population of self-replicating computer programs exists in a user-defined computational environment and is subject to instruction-level mutations and natural selection. Multilevel selection links the survival of the individual to the survival of its group, thus encouraging cooperation. The results of experiments using the Avida digital evolution platform demonstrate that populations of digital organisms are capable of constructing communication networks, and that these networks can exhibit desired properties depending on the selective pressures used. We also show that the use of a digital germline can significantly improve evolvability of cooperation.

There are many successful applications of Backpropagation (BP) for training multilayer neural networks. However, they have many shortcomings. Learning often takes insupportable time to converge, and it may fall into local minima at all. One of the possible remedies to escape from local minima is using a very small learning rate, but this will slow the learning process. The proposed algorithm is presented for the training of multilayer neural networks with very small learning rate, especially when using large training set size. It can apply in a generic manner for any network size that uses a backpropgation algorithm through optical time. This paper studies the performance of the Optical Backpropagation algorithm OBP on training a neural network for online handwritten character recognition in comparison with backpropagation BP.

Many-cores are on the cusp of becoming state-of-the-art processor technology for the next decade. To guarantee efficient communication between multiple cores, a Network-on-a-Chip (NoC) is considered as an alternative to overcome the limitations of the ubiquitous bus technology.

A photomosaic is an image assembled from smaller images called tiles. When a photomosaic is viewed from a distance, it resembles a desired target image. The process of photomosaic generation can be viewed as an optimization problem, where a set of tiles needs to be arranged to resemble a target image. We impose a constraint on the number of times a tile image can be repeated in a photomosaic. A randomized iterative improvement algorithm is used to generate photomosaics and the intermediate results are used to produce interesting animations. We show that the proposed technique is more efficient than genetic algorithm.

The task of radar pulse compression is formulated as a multi-objective optimization problem and has been effectively solved using radial basis function (RBF) network and multiobjective genetic algorithm (NSGA-II). The pulse compression performance of three different codes in terms of signal to peak side-lobe ratio (SSR) under noisy environment, range resolution and Doppler shift are evaluated through exhaustive simulation study and are compared with those obtained by radial basis function (RBF) and auto correlation (ACF) based methods. The results demonstrate excellent performance of the proposed multiobjective method compared to its counterparts. As the number of center increases, the performance compressor also progressively increases but its complexity correspondingly increases. The proposed multi-objective method helps to select appropriate structure that makes a judicious compromise between the complexity and performance.

We present a learning-based method for model completion and adaptation, which is based on the combination of two approaches: 1) R2D2C, a technique for mechanically transforming system requirements via provably equivalent models to running code, and 2) automata learning-based model extrapolation. The intended impact of this new combination is to make model completion and adaptation accessible to experts of the field, like biologists or engineers. The principle is briefly illustrated by generating models of biological procedures concerning gene activities in the production of proteins, although the main application is going to concern autonomic systems for space exploration.

The search for biologically plausible ideas, models and computational paradigms always drew the interest of computer scientists, particularly those from the natural computing area. Also, the concept of optimisation can be abstracted from several natural processes, for instance, in the evolution of species, in the behaviour of social groups, in the dynamics of the immune system, in the food search strategies and in the ecological relationships of different animal populations. Hence, this work highlights the main properties of ecosystems that can be important for building computational tools to solve complex problems. Also, we introduce computational descriptions for such biologically plausible functionalities (e.g., habitats, ecological relationships, ecological succession, and another). The main differential of the discussion presented in this paper is the cooperative use of different populations (candidate solutions) that co-evolve in an ecological context. In addition to the use of different search strategies cooperatively, this work opens the possibility of inserting ecological concepts in the optimisation process allowing the development of new bio-plausible hybrid systems. The potentiality of some ecological concepts is also presented in a simplified ecology-inspired algorithm for optimisation. Finally, concluding remarks and ideas for future research are presented.

Biologically inspired behaviour-based approaches to agent design have been particularly successful in mobile robotics. In this approach, rather than decomposing intelligent agents by function, the systems is segmented into independent components  of end-to-end functionality, which mirror behaviours such as wall-following and obstacle avoidance. To-date, although vision has been a vital part of robotic systems, it has tended to be treated as a monolithic peripheral, even in behaviour based agents. This research explores architectures for systems that extend decomposition by behaviour to vision. In such platforms a number of camera agents, each monitoring some simple vision characteristic (eg movement or boundaries) learn to collaborate in real-time on the interpretation of a scene. Visual learning unifies methods that are developed under the major dichotomy between supervision and adaptation in machine learning. Two monochrome non-stereoscopic look-forward cameras are used to test the strength of agent-based vision for mobile robots.

Biological systems are self-organizing, tolerant of manufacturing defects and they adapt, rather than being programmed, to their environments. The problems they solve involve the interaction of an organism/system with the real world. Bio-inspired computation is the use of computers to model nature, and simultaneously the study of natural biological systems to improve the usage of computers. It is a major subset of natural computation. Recently, bio-inspired computation, such as evolutionary computation, swarm intelligence bacterial foraging, cultural algorithms, neural networks, fuzzy systems, rough sets, molecular computing and other bionics, is becoming increasingly important in face of the complexity of today's demanding applications.

Digital Instrumentation and Control (I&C) systems in safety-related applications of next generation industrial automation systems require high levels of resilience against different fault classes. One of the more essential concepts for achieving this goal is the notion of resilient and survivable digital I&C systems. In recent years, self-healing concepts based on biological physiology have received attention for the design of robust digital systems. However, many of these approaches have not been architected from the outset with safety in mind, nor have they been targeted for the automation community where a significant need exists. This dissertation presents a new self-healing digital I&C architecture called BioSymPLe, inspired from the way nature responds, defends and heals: the stem cells in the immune system of living organisms, the life cycle of the living cell, and the pathway from Deoxyribonucleic acid (DNA) to protein. The BioSymPLe architecture is integrating biological concepts, fault tolerance techniques, and operational schematics for the international standard IEC 61131-3 to facilitate adoption in the automation industry. BioSymPLe is organized into three hierarchical levels: the local function migration layer from the top side, the critical service layer in the middle, and the global function migration layer from the bottom side. The local layer is used to monitor the correct execution of functions at the cellular level and to activate healing mechanisms at the critical service level. The critical layer is allocating a group of functional B cells which represent the building block that executes the intended functionality of critical application based on the expression for DNA genetic codes stored inside each cell. The global layer uses a concept of embryonic stem cells by differentiating these type of cells to repair the faulty T cells and supervising all repair mechanisms. Finally, two industrial applications have been mapped on the proposed architecture, which are capable of tolerating a significant number of faults (transient, permanent, and hardware common cause failures CCFs) that can stem from environmental disturbances and we believe the nexus of its concepts can positively impact the next generation of critical systems in the automation industry.

It is well known that, in nature, populations are dynamic in space and time. This means that the size of populations oscillate across their habitats over time. This work uses the concepts of habitats, ecological relationships, ecological successions and population dynamics to build a cooperative search algorithm, named ECO. This work aims to explore the population sizing not as a parameter but as a dynamic process. The Artificial Bee Colony (ABC) was used in the experiments where benchmark mathematical functions were optimized. Results were compared with ABC running alone, with and without the use of population dynamics. The ECO algorithm with population dynamics performed better than the other approaches, possibly thanks to the ecological interactions (intra and inter-habitats) that enabled the co-evolution of populations and to a more natural survival selection mechanism by the use of population dynamics.

An amorphous computer is a multitude of tiny computers each with a CPU, memory, and local communication capability. An iSurface is a particular instance of an amorphous computer, an “intelligent” coasting capable of computing, sensing and some limited output. This can be regarded as a massively parallel computing system, albeit one with random structure and unreliable nodes, and, as such, is likely to be extremely difficult to program conventionally. Prior research into amorphous computing suggests that utilising principles of self-organisation is successful in providing some functionality to an amorphous computer. Here we argue there is a definite need for techniques in engineering emergent functionality to match user requirements; the development of systems that utilise self-organisation in a user-directed manner. We present an early version of a methodology to do this and an example of its successful usage.

Based on the workings of visual cortical area V1, a model for an architecture for early computer vision is proposed. We propose to do image processing for computer vision on the basis of a combined map, of edge orientation and ocular-dominance, rather than on the basis of an edge map alone. In particular, the combined representation of edge orientation and ocular dominance is proposed for the computation of stereoscopic disparity.

This paper presents our vision of the futuristic product. Proactive Home Furnishings allows user to realize (useful) information embedded of physical objects and/or on the top of architectural surfaces. Proactive Home Furnishings also display as interactive art form through the used of interactive techniques and computer graphics in an augmented physical object. The goal of Proactive Home Furnishings is to create the combination between both the digital aesthetics and the functional information, as well as seamless with living environment in a soothing way. This paper describes five interactive artworks used biomimetic perspective to develop the interaction feature-MSOrgm, Lbskeletons, Portrait of Dandelion, Artificial Phototropism, River Space. We treat them as pioneers to investigate the ongoing relation between the user and the home furnishings in a future living.

A model of face representation, inspired by the biology of the visual system, is compared to experimental data on the perception of facial similarity. The face representation model uses aggregate primary visual cortex (V1) cell responses topographically linked to a grid covering the face, allowing comparison of shape and texture at corresponding points in two facial images. When a set of relatively similar faces was used as stimuli, this "linked aggregate code" (LAC) predicted human performance in similarity judgment experiments. When faces of perceivable categories were used, dimensions such as apparent 'sex' and 'race' emerged from the LAC model without training. The dimensional structure of the LAC similarity measure for the mixed category task displayed some psychologically plausible features but also highlighted differences between the model and the human similarity judgements. The human judgements exhibited a racial perceptual bias that was not shared by the LAC model. The results suggest that the LAC based similarity measure may offer a fertile starting point for further modelling studies of face representation in higher visual areas, including studies of the development of biases in face perception.

Although inspired by the biological aspect, the concept of autonomic computing is emblematic of the diversity of solutions that propose a self-governance of systems from high-level objectives. From the human point of view, the autonomic nervous system has as a central point the direct intervention of a small region of the brain called the hypothalamus. This article seeks to discuss the concept of computational autonomy from an analysis of the human autonomic system, addressing its internal functioning, in order to propose a correlated computational model that can be applied. Finally, the bio-inspired computational model is mapped to an approach for knowledge-based systems aimed at its applicability.

This paper reports about progress in two areas towards quantum computing architectures with elements inspired from biological controls, as proposed in an earlier paper. The first area is about exploiting mathematical results in coloured algebras, which, combined with the colouring of particle flows, would reduce the decoherence and enhance the decidability in the quantum processing elements; definitions are being recalled, with the required assumptions and results. The second area is to provide experimental results, and a patented biological feedback process in synapse , about light and acoustic excitations in a live animal species to enhance reactivity; the experimental setup is characterized , the measurement results provided, and the implications are explicated for quantum processing elements approximating a synapse. A paragraph on open issues explains how the results in the two areas will be combined and will help in the design a very early compiler version. KEYWORDS Quantum computing architecture; quantum biological computing; coloured algebras; decoherence; synapse control; light and sound excitation of live creatures

Introduction to Algorithms for Data Mining and Machine Learning (book)  introduces the essential ideas behind all key algorithms and techniques for data mining and machine learning, along with optimization techniques. Its strong formal mathematical approach, well selected examples, and practical software recommendations help readers develop confidence in their data modeling skills so they can process and interpret data for classification, clustering, curve-fitting and predictions. Masterfully balancing theory and practice, it is especially useful for those who need relevant, well explained, but not rigorous (proofs based) background theory and clear guidelines for working with big data.