Wikibooks contributors, 'Artificial Neural Networks', Wikibooks, The Free Textbook Project, 16 December 2015, 02:03 UTC, &lt;https://en.wikibooks.org/w/index.php?title=Artificial_Neural_Networks&oldid=3029665&gt;

2015 Dec 16, 02:03 UTC [cited 2018 Oct 4].

When using the LaTeX package url (\usepackage{url} somewhere in the preamble) which tends to give much more nicely formatted web addresses, the following may be preferred:

## Artificial Neural Networks/Neural Network Basics

Artificial Neural Networks, also known as “Artificial neural nets”, “neural nets”, or ANN for short, are a computational tool modeled on the interconnection of the neuron in the nervous systems of the human brain and that of other organisms.

Artificial neural networks are very different from biological networks, although many of the concepts and characteristics of biological systems are faithfully reproduced in the artificial systems. Artificial

neural nets are a type of non-linear processing system that is ideally suited for a wide range of tasks, especially tasks where there is no existing algorithm for task completion.

With proper training, ANN are capable of generalization, the ability to recognize similarities among different input patterns, especially patterns that have been corrupted by noise.

The term “Neural Net” refers to both the biological and artificial variants, although typically the term is used to refer to artificial systems only.

Each neuron is a multiple-input, multiple-output (MIMO) system that receives signals from the inputs, produces a resultant signal, and transmits that signal to all outputs.

However, to reproduce the effect of the synapse, the connections between PE are assigned multiplicative weights, which can be calibrated or “trained” to produce the proper system output.

Where ζ is the weighted sum of the inputs (the inner product of the input vector and the tap-weight vector), and σ(ζ) is a function of the weighted sum.

If we recognize that the weight and input elements form vectors w and x, the ζ weighted sum becomes a simple dot product:

The dotted line in the center of the neuron represents the division between the calculation of the input sum using the weight vector, and the calculation of the output value using the activation function.

Neural networks tend to have one input per degree of freedom in the input space, and one output per degree of freedom in the output space.

Expert systems, by contrast, are used in situations where there is insufficient data and theoretical background to create any kind of a reliable problem model.

Expert systems emulate the deduction processes of a human expert, by collecting information and traversing the solution space in a directed manner.

Though such assumptions are not required, it has been found that the addition of such a priori information as the statistical distribution of the input space can help to speed training.

During training, the neural network performs the necessary analytical work, which would require non-trivial effort on the part of the analyst if other methods were to be used.

learning paradigm is supervised, unsupervised or a hybrid of the two, and reflects the method in which training data is presented to the neural network.

A learning rule is a model for the types of methods to be used to train the system, and also a goal for what types of results are to be produced.

During training, care must be taken not to provide too many input examples and different numbers of training examples could produce very different results in the quality and robustness of the network.

Some of the more important parameters in terms of training and network capacity are the number of hidden neurons, the learning rate and the momentum parameter.

These neurons are essentially hidden from view, and their number and organization can typically be treated as a black box to people who are interfacing with the system.

Square root of the sum of squared differences between the network targets and actual outputs divided by number of patterns (only for training by minimum error).

An old version of text is also available on Amazon.com Kindle (also avail for free as a mobi file you can email to your kindle) -- this is not recommended for students taking courses -- see above PDF / bound book options.

See Contributors for information about how to contribute, and who has already, Status for current status and future plans for the text, and Pedagogy for pedagogical info for teachers (and students), including Syllabi from courses using this book.

The content is organized into chapters (below), but also massively hyperlinked, and the content can go very 'deep' while also enabling a very quick and relatively high-level of information that captures the key points, suitable for college undergraduates or even high school curricula.

The authors maintain stringent editorial control over the contents of this book: it is publication-quality material from scientific experts, not anonymous crowd-sourced material as on other wikis (e.g., WikiPedia).

## Social network

A social network is a social structure made up of a set of social actors (such as individuals or organizations), sets of dyadic ties, and other social interactions between actors.

The social network perspective provides a set of methods for analyzing the structure of whole social entities as well as a variety of theories explaining the patterns observed in these structures.&#91;1&#93;

The study of these structures uses social network analysis to identify local and global patterns, locate influential entities, and examine network dynamics.

The social network is a theoretical construct useful in the social sciences to study relationships between individuals, groups, organizations, or even entire societies (social units, see differentiation).

An axiom of the social network approach to understanding social interaction is that social phenomena should be primarily conceived and investigated through the properties of relations between and within units, instead of the properties of these units themselves.

In social science, these fields of study include, but are not limited to anthropology, biology, communication studies, economics, geography, information science, organizational studies, social psychology, sociology, and sociolinguistics.

Tönnies argued that social groups can exist as personal and direct social ties that either link individuals who share values and belief (Gemeinschaft, German, commonly translated as 'community') or impersonal, formal, and instrumental social links (Gesellschaft, German, commonly translated as 'society').&#91;7&#93;

Durkheim gave a non-individualistic explanation of social facts, arguing that social phenomena arise when interacting individuals constitute a reality that can no longer be accounted for in terms of the properties of individual actors.&#91;8&#93;

Georg Simmel, writing at the turn of the twentieth century, pointed to the nature of networks and the effect of network size on interaction and examined the likelihood of interaction in loosely knit networks rather than groups.&#91;9&#93;

Later, drawing upon Parsons' theory, the work of sociologist Peter Blau provides a strong impetus for analyzing the relational ties of social units with his work on social exchange theory.&#91;22&#93;&#91;23&#93;&#91;24&#93;

Also independently active in the Harvard Social Relations department at the time were Charles Tilly, who focused on networks in political and community sociology and social movements, and Stanley Milgram, who developed the 'six degrees of separation' thesis.&#91;25&#93;

Fowler, and others, developing and applying new models and methods to emerging data available about online social networks, as well as 'digital traces' regarding face-to-face networks.

At the micro-level, social network research typically begins with an individual, snowballing as social relationships are traced, or may begin with a small group of individuals in a particular social context.

This framework has the capacity to represent social-structural effects commonly observed in many human social networks, including general degree-based structural effects commonly observed in many human social networks as well as reciprocity and transitivity, and at the node-level, homophily and attribute-based activity and popularity effects, as derived from explicit hypotheses about dependencies among network ties.

These probability models for networks on a given set of actors allow generalization beyond the restrictive dyadic independence assumption of micro-networks, allowing models to be built from theoretical structural foundations of social behavior.&#91;42&#93;

Complex networks: Most larger social networks display features of social complexity, which involves substantial non-trivial features of network topology, with patterns of complex connections between elements that are neither purely regular nor purely random (see, complexity science, dynamical system and chaos theory), as do biological, and technological networks.

Such complex network features include a heavy tail in the degree distribution, a high clustering coefficient, assortativity or disassortativity among vertices, community structure (see stochastic block model), and hierarchical structure.

The basis of Heterophily Theory was the finding in one study that more numerous weak ties can be important in seeking information and innovation, as cliques have a tendency to have more homogeneous opinions as well as share many common traits.

For example, in business networks, this is beneficial to an individual's career because he is more likely to hear of job openings and opportunities if his network spans a wide range of contacts in different industries/sectors.

Communication Studies are often considered a part of both the social sciences and the humanities, drawing heavily on fields such as sociology, psychology, anthropology, information science, biology, political science, and economics as well as rhetoric, literary studies, and semiotics.

Murders can be seen to diffuse outwards from a single source, because weaker gangs cannot afford to kill members of stronger gangs in retaliation, but must commit other violent acts to maintain their reputation for strength.

This line of research seeks to explain why some become 'early adopters' of ideas and innovations, and links social network structure with facilitating or impeding the spread of an innovation.

In demography, the study of social networks has led to new sampling methods for estimating and reaching populations that are hard to enumerate (for example, homeless people or intravenous drug users.) For example, respondent driven sampling is a network-based sampling technique that relies on respondents to a survey recommending further respondents.

Sociologists, such as Mark Granovetter, have developed core principles about the interactions of social structure, information, ability to punish or reward, and trust that frequently recur in their analyses of political, economic and other institutions.

Granovetter examines how social structures and social networks can affect economic outcomes like hiring, price, productivity and innovation and describes sociologists' contributions to analyzing the impact of social structure and networks on the economy.&#91;51&#93;

Analysis of social networks is increasingly incorporated into health care analytics, not only in epidemiological studies but also in models of patient communication and education, disease prevention, mental health diagnosis and treatment, and in the study of health care organizations and systems.&#91;52&#93;

Studies of language and linguistics, particularly evolutionary linguistics, focus on the development of linguistic forms and transfer of changes, sounds or words, from one language system to another through networks of social interaction.

Social capital is a form of economic and cultural capital in which social networks are central, transactions are marked by reciprocity, trust, and cooperation, and market agents produce goods and services not mainly for themselves, but for a common good.

For example, newly arrived immigrants can make use of their social ties to established migrants to acquire jobs they may otherwise have trouble getting (e.g., because of unfamiliarity with the local language).

In the case of consulting firm Eden McCallum, the founders were able to advance their careers by bridging their connections with former big three consulting firm consultants and mid-size industry firms.&#91;65&#93;

A study of high tech Chinese firms by Zhixing Xiao found that the control benefits of structural holes are 'dissonant to the dominant firm-wide spirit of cooperation and the information benefits cannot materialize due to the communal sharing values' of such organizations.&#91;66&#93;

In a computer mediated communication context, social pairs exchange different kinds of information, including sending a data file or a computer program as well as providing emotional support or arranging a meeting.

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