The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

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Statistical mechanics of complex networks

Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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The Structure and Function of Complex Networks

A number of recent studies have focused on the statistical properties of networked systems such as social networks and the Worldwide Web. Researchers have concentrated particularly on a few properties that seem to be common to many networks: the small-world property, power-law degree distributions, and network transitivity. In this article, we highlight another property that is found in many networks, the property of community structure, in which network nodes are joined together in tightly knit groups, between which there are only looser connections. We propose a method for detecting such communities, built around the idea of using centrality indices to find community boundaries. We test our method on computer-generated and real-world graphs whose community structure is already known and find that the method detects this known structure with high sensitivity and reliability. We also apply the method to two networks whose community structure is not well known—a collaboration network and a food web—and find that it detects significant and informative community divisions in both cases.

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Community structure in social and biological networks

Machine Learning is the study of methods for programming computers to learn. Computers are applied to a wide range of tasks, and for most of these it is relatively easy for programmers to design and implement the necessary software. However, there are many tasks for which this is difficult or impossible. These can be divided into four general categories. First, there are problems for which there exist no human experts. For example, in modern automated manufacturing facilities, there is a need to predict machine failures before they occur by analyzing sensor readings. Because the machines are new, there are no human experts who can be interviewed by a programmer to provide the knowledge necessary to build a computer system. A machine learning system can study recorded data and subsequent machine failures and learn prediction rules. Second, there are problems where human experts exist, but where they are unable to explain their expertise. This is the case in many perceptual tasks, such as speech recognition, hand-writing recognition, and natural language understanding. Virtually all humans exhibit expert-level abilities on these tasks, but none of them can describe the detailed steps that they follow as they perform them. Fortunately, humans can provide machines with examples of the inputs and correct outputs for these tasks, so machine learning algorithms can learn to map the inputs to the outputs. Third, there are problems where phenomena are changing rapidly. In finance, for example, people would like to predict the future behavior of the stock market, of consumer purchases, or of exchange rates. These behaviors change frequently, so that even if a programmer could construct a good predictive computer program, it would need to be rewritten frequently. A learning program can relieve the programmer of this burden by constantly modifying and tuning a set of learned prediction rules. Fourth, there are applications that need to be customized for each computer user separately. Consider, for example, a program to filter unwanted electronic mail messages. Different users will need different filters. It is unreasonable to expect each user to program his or her own rules, and it is infeasible to provide every user with a software engineer to keep the rules up-to-date. A machine learning system can learn which mail messages the user rejects and maintain the filtering rules automatically. Machine learning addresses many of the same research questions as the fields of statistics, data mining, and psychology, but with differences of emphasis. Statistics focuses on understanding the phenomena that have generated the data, often with the goal of testing different hypotheses about those phenomena. Data mining seeks to find patterns in the data that are understandable by people. Psychological studies of human learning aspire to understand the mechanisms underlying the various learning behaviors exhibited by people (concept learning, skill acquisition, strategy change, etc.).

Machine learning

We propose and study a set of algorithms for discovering community structure in networks-natural divisions of network nodes into densely connected subgroups. Our algorithms all share two definitive features: first, they involve iterative removal of edges from the network to split it into communities, the edges removed being identified using any one of a number of possible "betweenness" measures, and second, these measures are, crucially, recalculated after each removal. We also propose a measure for the strength of the community structure found by our algorithms, which gives us an objective metric for choosing the number of communities into which a network should be divided. We demonstrate that our algorithms are highly effective at discovering community structure in both computer-generated and real-world network data, and show how they can be used to shed light on the sometimes dauntingly complex structure of networked systems.

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Finding and evaluating community structure in networks.

Disclosed is a system architecture, components and a searching technique for an Unstructured Information Management System (UIMS). The UIMS may be provided as middleware for the effective management and interchange of unstructured information over a wide array of information sources. The architecture generally includes a search engine, data storage, analysis engines containing pipelined document annotators and various adapters. The searching technique makes use of a two-level searching technique.

System, method and computer program product for performing unstructured information management and automatic text analysis

A system and method for finding one or more target biometric samples that are similar to or match a query biometric sample. A query feature vector is generated from a query biometric vector. The query biometric vector represents the query biometric sample as a set of characteristics. The characteristics are either invariable or variable. The query feature vector comprises a plurality of features which are derived from the query biometric vector using a process that includes canonicalization of the characters in the biometric vector. The query feature vector is compared to a plurality of similarly created target feature vectors, each target feature vector representing a respective target biometric sample. A target biometric sample is a potential match to the query biometric sample when a threshold number of features in the corresponding target feature vector are identical to features in the query biometric vector.

System and method for determining likely identity in a biometric database

A method includes describing the thread configurations of a volume of well-ordered electronic message transmissions (EMT) and utilizing the thread configuration data to conduct selective searches of the EMT volume. An apparatus includes a thread processor and a query manager. The thread processor analyzes the EMT threads and records the thread configuration data. The query manager utilizes the thread configuration data to conduct selective searches of the EMT volume.

Indexing and searching of electronic message transmission thread sets

Computational advertising is an emerging scientific discipline, at the intersection of large scale search and text analysis, information retrieval, statistical modeling, machine learning, optimization, and microeconomics. The central challenge of computational advertising is to find the "best match" between a given user in a given context and a suitable advertisement. The context could be a user entering a query in a search engine ("sponsored search"), a user reading a web page ("content match" and "display ads"), a user conversing on a cell phone ("mobile advertising"), and so on. The information about the user can vary from scarily detailed to practically nil. The number of potential advertisements might be in the billions. Thus, depending on the definition of "best match" this challenge leads to a variety of massive optimization and search problems, with complicated constraints.The main part of this talk will give an introduction to computational advertising and present some illustrative research. In the second part we will discuss connections to recommender systems and present a couple of open problems of potential interest to both communities.

Computational advertising and recommender systems

A system and method to facilitate real-time matching of content to advertising information in a network are described. A request for advertising information is received over a network, the advertising information to be displayed for a user entity in association with content information within a web page requested by the user entity, the request containing the content information, a web page identifier, and additional data associated with the web page. The content information is further analyzed in real-time to construct a page summary of the web page. The web page identifier and the additional data are further analyzed in real-time to extract at least one keyword relevant to the content information. Finally, the advertising information is determined in real-time based on the page summary and the extracted keywords.

Andrei Z. Broder

Papers

System, method and computer program product for performing unstructured information management and automatic text analysis

System and method for determining likely identity in a biometric database

Indexing and searching of electronic message transmission thread sets

Computational advertising and recommender systems

Just-In-Time Contextual Advertising Techniques