On the Size Distribution of Autonomous Systems

This paper explores reasons for the high degree of variability in the sizes of ASes that have recently been observed, and the processes by which this variable distribution develops. AS size distribution is important for a number of reasons. First, when modeling network topologies, an AS size distribution assists in labeling routers with an associated AS. Second, AS size has been found to be positively correlated with the degree of the AS (number of peering links), so understanding the distribution of AS sizes has implications for AS connectivity properties. Our model accounts for AS births, growth, and mergers. We analyze two models: one incorporates only the growth of hosts and ASes, and a second extends that model to include mergers of ASes. We show analytically that, given reasonable assumptions about the nature of mergers, the resulting size distribution exhibits a power law tail with the exponent independent of the details of the merging process. We estimate parameters of the models from measurements obtained from Internet registries and from BGP tables. We then compare the models solutions to empirical AS size distribution taken from Mercator and Skitter datasets, and find that the simple growth-based model yields general agreement with empirical data. Our analysis of the model in which mergers occur in a manner independent of the size of the merging ASes suggests that more detailed analysis of merger processes is needed.

Analysis of OD Flows (Raw Data)

In a recent paper, Structural Analysis of Network Traffic Flows, we analyzed the set of Origin Destination traffic flows from the Sprint-Europe and Abilene backbone networks. This report presents the complete set of results from analyzing data from both networks. The results in this report are specific to the Sprint-1 and Abilene datasets studied in the above paper. The following results are presented here: 1 Rows of Principal Matrix (V) 2 1.1 Sprint-1 Dataset ................................ 2 1.2 Abilene Dataset.................................. 9 2 Set of Eigenflows 14 2.1 Sprint-1 Dataset.................................. 14 2.2 Abilene Dataset................................... 21 3 Classifying Eigenflows 26 3.1 Sprint-1 Dataset.................................. 26 3.2 Abilene Datase.................................... 44

Boosting Nearest Neighbor Classifiers for Multiclass Recognition

This paper introduces an algorithm that uses boosting to learn a distance measure for multiclass k-nearest neighbor classification. Given a family of distance measures as input, AdaBoost is used to learn a weighted distance measure, that is a linear combination of the input measures. The proposed method can be seen both as a novel way to learn a distance measure from data, and as a novel way to apply boosting to multiclass recognition problems, that does not require output codes. In our approach, multiclass recognition of objects is reduced into a single binary recognition task, defined on triples of objects. Preliminary experiments with eight UCI datasets yield no clear winner among our method, boosting using output codes, and k-nn classification using an unoptimized distance measure. Our algorithm did achieve lower error rates in some of the datasets, which indicates that, in some domains, it may lead to better results than existing methods.

On the Geographic Location of Internet Resources

One relatively unexplored question about the Internet's physical structure concerns the geographical location of its components: routers, links and autonomous systems (ASes). We study this question using two large inventories of Internet routers and links, collected by different methods and about two years apart. We first map each router to its geographical location using two different state-of-the-art tools. We then study the relationship between router location and population density; between geographic distance and link density; and between the size and geographic extent of ASes. Our findings are consistent across the two datasets and both mapping methods. First, as expected, router density per person varies widely over different economic regions; however, in economically homogeneous regions, router density shows a strong superlinear relationship to population density. Second, the probability that two routers are directly connected is strongly dependent on distance; our data is consistent with a model in which a majority (up to 75-95%) of link formation is based on geographical distance (as in the Waxman topology generation method). Finally, we find that ASes show high variability in geographic size, which is correlated with other measures of AS size (degree and number of interfaces). Among small to medium ASes, ASes show wide variability in their geographic dispersal; however, all ASes exceeding a certain threshold in size are maximally dispersed geographically. These findings have many implications for the next generation of topology generators, which we envisage as producing router-level graphs annotated with attributes such as link latencies, AS identifiers and geographical locations.

Sampling Biases in IP Topology Measurements

Considerable attention has been focused on the properties of graphs derived from Internet measurements. Router-level topologies collected via traceroute studies have led some authors to conclude that the router graph of the Internet is a scale-free graph, or more generally a power-law random graph. In such a graph, the degree distribution of nodes follows a distribution with a power-law tail. In this paper we argue that the evidence to date for this conclusion is at best insufficient. We show that graphs appearing to have power-law degree distributions can arise surprisingly easily, when sampling graphs whose true degree distribution is not at all like a power-law. For example, given a classical Erdös-Rényi sparse, random graph, the subgraph formed by a collection of shortest paths from a small set of random sources to a larger set of random destinations can easily appear to show a degree distribution remarkably like a power-law. We explore the reasons for how this effect arises, and show that in such a setting, edges are sampled in a highly biased manner. This insight allows us to distinguish measurements taken from the Erdös-Rényi graphs from those taken from power-law random graphs. When we apply this distinction to a number of well-known datasets, we find that the evidence for sampling bias in these datasets is strong.

Collocation Games and Their Application to Distributed Resource Management

We introduce Collocation Games as the basis of a general framework for modeling, analyzing, and facilitating the interactions between the various stakeholders in distributed systems in general, and in cloud computing environments in particular. Cloud computing enables fixed-capacity (processing, communication, and storage) resources to be offered by infrastructure providers as commodities for sale at a fixed cost in an open marketplace to independent, rational parties (players) interested in setting up their own applications over the Internet. Virtualization technologies enable the partitioning of such fixed-capacity resources so as to allow each player to dynamically acquire appropriate fractions of the resources for unencumbered use. In such a paradigm, the resource management problem reduces to that of partitioning the entire set of applications (players) into subsets, each of which is assigned to fixed-capacity cloud resources. If the infrastructure and the various applications are under a single administrative domain, this partitioning reduces to an optimization problem whose objective is to minimize the overall deployment cost. In a marketplace, in which the infrastructure provider is interested in maximizing its own profit, and in which each player is interested in minimizing its own cost, it should be evident that a global optimization is precisely the wrong framework. Rather, in this paper we use a game-theoretic framework in which the assignment of players to fixed-capacity resources is the outcome of a strategic "Collocation Game". Although we show that determining the existence of an equilibrium for collocation games in general is NP-hard, we present a number of simplified, practically-motivated variants of the collocation game for which we establish convergence to a Nash Equilibrium, and for which we derive convergence and price of anarchy bounds. In addition to these analytical results, we present an experimental evaluation of implementations of some of these variants for cloud infrastructures consisting of a collection of multidimensional resources of homogeneous or heterogeneous capacities. Experimental results using trace-driven simulations and synthetically generated datasets corroborate our analytical results and also illustrate how collocation games offer a feasible distributed resource management alternative for autonomic/self-organizing systems, in which the adoption of a global optimization approach (centralized or distributed) would be neither practical nor justifiable.

Changes in Web Client Access Patterns: Characteristics and Caching Implications

Understanding the nature of the workloads and system demands created by users of the World Wide Web is crucial to properly designing and provisioning Web services. Previous measurements of Web client workloads have been shown to exhibit a number of characteristic features; however, it is not clear how those features may be changing with time. In this study we compare two measurements of Web client workloads separated in time by three years, both captured from the same computing facility at Boston University. The older dataset, obtained in 1995, is well-known in the research literature and has been the basis for a wide variety of studies. The newer dataset was captured in 1998 and is comparable in size to the older dataset. The new dataset has the drawback that the collection of users measured may no longer be representative of general Web users; however using it has the advantage that many comparisons can be drawn more clearly than would be possible using a new, different source of measurement. Our results fall into two categories. First we compare the statistical and distributional properties of Web requests across the two datasets. This serves to reinforce and deepen our understanding of the characteristic statistical properties of Web client requests. We find that the kinds of distributions that best describe document sizes have not changed between 1995 and 1998, although specific values of the distributional parameters are different. Second, we explore the question of how the observed differences in the properties of Web client requests, particularly the popularity and temporal locality properties, affect the potential for Web file caching in the network. We find that for the computing facility represented by our traces between 1995 and 1998, (1) the benefits of using size-based caching policies have diminished; and (2) the potential for caching requested files in the network has declined.

Learning Embeddings for Indexing, Retrieval, and Classification, with Applications to Object and Shape Recognition in Image Databases

Nearest neighbor retrieval is the task of identifying, given a database of objects and a query object, the objects in the database that are the most similar to the query. Retrieving nearest neighbors is a necessary component of many practical applications, in fields as diverse as computer vision, pattern recognition, multimedia databases, bioinformatics, and computer networks. At the same time, finding nearest neighbors accurately and efficiently can be challenging, especially when the database contains a large number of objects, and when the underlying distance measure is computationally expensive. This thesis proposes new methods for improving the efficiency and accuracy of nearest neighbor retrieval and classification in spaces with computationally expensive distance measures. The proposed methods are domain-independent, and can be applied in arbitrary spaces, including non-Euclidean and non-metric spaces. In this thesis particular emphasis is given to computer vision applications related to object and shape recognition, where expensive non-Euclidean distance measures are often needed to achieve high accuracy. The first contribution of this thesis is the BoostMap algorithm for embedding arbitrary spaces into a vector space with a computationally efficient distance measure. Using this approach, an approximate set of nearest neighbors can be retrieved efficiently - often orders of magnitude faster than retrieval using the exact distance measure in the original space. The BoostMap algorithm has two key distinguishing features with respect to existing embedding methods. First, embedding construction explicitly maximizes the amount of nearest neighbor information preserved by the embedding. Second, embedding construction is treated as a machine learning problem, in contrast to existing methods that are based on geometric considerations. The second contribution is a method for constructing query-sensitive distance measures for the purposes of nearest neighbor retrieval and classification. In high-dimensional spaces, query-sensitive distance measures allow for automatic selection of the dimensions that are the most informative for each specific query object. It is shown theoretically and experimentally that query-sensitivity increases the modeling power of embeddings, allowing embeddings to capture a larger amount of the nearest neighbor structure of the original space. The third contribution is a method for speeding up nearest neighbor classification by combining multiple embedding-based nearest neighbor classifiers in a cascade. In a cascade, computationally efficient classifiers are used to quickly classify easy cases, and classifiers that are more computationally expensive and also more accurate are only applied to objects that are harder to classify. An interesting property of the proposed cascade method is that, under certain conditions, classification time actually decreases as the size of the database increases, a behavior that is in stark contrast to the behavior of typical nearest neighbor classification systems. The proposed methods are evaluated experimentally in several different applications: hand shape recognition, off-line character recognition, online character recognition, and efficient retrieval of time series. In all datasets, the proposed methods lead to significant improvements in accuracy and efficiency compared to existing state-of-the-art methods. In some datasets, the general-purpose methods introduced in this thesis even outperform domain-specific methods that have been custom-designed for such datasets.

Spatiotemporal Gesture Segmentation

Spotting patterns of interest in an input signal is a very useful task in many different fields including medicine, bioinformatics, economics, speech recognition and computer vision. Example instances of this problem include spotting an object of interest in an image (e.g., a tumor), a pattern of interest in a time-varying signal (e.g., audio analysis), or an object of interest moving in a specific way (e.g., a human's body gesture). Traditional spotting methods, which are based on Dynamic Time Warping or hidden Markov models, use some variant of dynamic programming to register the pattern and the input while accounting for temporal variation between them. At the same time, those methods often suffer from several shortcomings: they may give meaningless solutions when input observations are unreliable or ambiguous, they require a high complexity search across the whole input signal, and they may give incorrect solutions if some patterns appear as smaller parts within other patterns. In this thesis, we develop a framework that addresses these three problems, and evaluate the framework's performance in spotting and recognizing hand gestures in video. The first contribution is a spatiotemporal matching algorithm that extends the dynamic programming formulation to accommodate multiple candidate hand detections in every video frame. The algorithm finds the best alignment between the gesture model and the input, and simultaneously locates the best candidate hand detection in every frame. This allows for a gesture to be recognized even when the hand location is highly ambiguous. The second contribution is a pruning method that uses model-specific classifiers to reject dynamic programming hypotheses with a poor match between the input and model. Pruning improves the efficiency of the spatiotemporal matching algorithm, and in some cases may improve the recognition accuracy. The pruning classifiers are learned from training data, and cross-validation is used to reduce the chance of overpruning. The third contribution is a subgesture reasoning process that models the fact that some gesture models can falsely match parts of other, longer gestures. By integrating subgesture reasoning the spotting algorithm can avoid the premature detection of a subgesture when the longer gesture is actually being performed. Subgesture relations between pairs of gestures are automatically learned from training data. The performance of the approach is evaluated on two challenging video datasets: hand-signed digits gestured by users wearing short sleeved shirts, in front of a cluttered background, and American Sign Language (ASL) utterances gestured by ASL native signers. The experiments demonstrate that the proposed method is more accurate and efficient than competing approaches. The proposed approach can be generally applied to alignment or search problems with multiple input observations, that use dynamic programming to find a solution.

Constraint-based Mining of Frequent Arrangements of Temporal Intervals

The problem of discovering frequent arrangements of temporal intervals is studied. It is assumed that the database consists of sequences of events, where an event occurs during a time-interval. The goal is to mine temporal arrangements of event intervals that appear frequently in the database. The motivation of this work is the observation that in practice most events are not instantaneous but occur over a period of time and different events may occur concurrently. Thus, there are many practical applications that require mining such temporal correlations between intervals including the linguistic analysis of annotated data from American Sign Language as well as network and biological data. Two efficient methods to find frequent arrangements of temporal intervals are described; the first one is tree-based and uses depth first search to mine the set of frequent arrangements, whereas the second one is prefix-based. The above methods apply efficient pruning techniques that include a set of constraints consisting of regular expressions and gap constraints that add user-controlled focus into the mining process. Moreover, based on the extracted patterns a standard method for mining association rules is employed that applies different interestingness measures to evaluate the significance of the discovered patterns and rules. The performance of the proposed algorithms is evaluated and compared with other approaches on real (American Sign Language annotations and network data) and large synthetic datasets.

Large-Scale Neural Systems for Vision and Cognition

— Consideration of how people respond to the question What is this? has suggested new problem frontiers for pattern recognition and information fusion, as well as neural systems that embody the cognitive transformation of declarative information into relational knowledge. In contrast to traditional classification methods, which aim to find the single correct label for each exemplar (This is a car), the new approach discovers rules that embody coherent relationships among labels which would otherwise appear contradictory to a learning system (This is a car, that is a vehicle, over there is a sedan). This talk will describe how an individual who experiences exemplars in real time, with each exemplar trained on at most one category label, can autonomously discover a hierarchy of cognitive rules, thereby converting local information into global knowledge. Computational examples are based on the observation that sensors working at different times, locations, and spatial scales, and experts with different goals, languages, and situations, may produce apparently inconsistent image labels, which are reconciled by implicit underlying relationships that the network’s learning process discovers. The ARTMAP information fusion system can, moreover, integrate multiple separate knowledge hierarchies, by fusing independent domains into a unified structure. In the process, the system discovers cross-domain rules, inferring multilevel relationships among groups of output classes, without any supervised labeling of these relationships. In order to self-organize its expert system, the ARTMAP information fusion network features distributed code representations which exploit the model’s intrinsic capacity for one-to-many learning (This is a car and a vehicle and a sedan) as well as many-to-one learning (Each of those vehicles is a car). Fusion system software, testbed datasets, and articles are available from http://cns.bu.edu/techlab.

Biased ART: A Neural Architecture that Shifts Attention Toward Previously Disregarded Features Following an Incorrect Prediction

Memories in Adaptive Resonance Theory (ART) networks are based on matched patterns that focus attention on those portions of bottom-up inputs that match active top-down expectations. While this learning strategy has proved successful for both brain models and applications, computational examples show that attention to early critical features may later distort memory representations during online fast learning. For supervised learning, biased ARTMAP (bARTMAP) solves the problem of over-emphasis on early critical features by directing attention away from previously attended features after the system makes a predictive error. Small-scale, hand-computed analog and binary examples illustrate key model dynamics. Twodimensional simulation examples demonstrate the evolution of bARTMAP memories as they are learned online. Benchmark simulations show that featural biasing also improves performance on large-scale examples. One example, which predicts movie genres and is based, in part, on the Netflix Prize database, was developed for this project. Both first principles and consistent performance improvements on all simulation studies suggest that featural biasing should be incorporated by default in all ARTMAP systems. Benchmark datasets and bARTMAP code are available from the CNS Technology Lab Website: http://techlab.bu.edu/bART/.