Feature-level and decision-level fusion of noncoincidently sampled sensors for land mine detection AbstractÐWe present and compare methods for feature-level (predetection) and decision-level (postdetection) fusion of multisensor data. This study emphasizes fusion techniques that are suitable for noncommensurate data sampled at noncoincident points. Decision-level fusion is most convenient for such data, but it is suboptimal in principle, since targets not detected by all sensors will not obtain the full benefits of fusion. A novel algorithm for feature-level fusion of noncommensurate, noncoincidently sampled data is described, in which a model is fitted to the sensor data and the model parameters are used as features. Formulations for both featurelevel and decision-level fusion are described, along with some practical simplifications. A closed-form expression is available for feature-level fusion of normally distributed data and this expression is used with simulated data to study requirements for sample position accuracy in multisensor data. The performance of feature-level and decision-level fusion algorithms are compared for experimental data acquired by a metal detector, a ground-penetrating radar, and an infrared camera at a challenging test site containing surrogate mines. It is found that fusion of binary decisions does not perform significantly better than the best available sensor. The performance of feature-level fusion is significantly better than the individual sensors, as is decision-level fusion when detection confidence information is also available (ªsoft-decisionº fusion). We have developed a feature-level fusion technique for noncommensurate sensor data sampled at noncoincident locations. The features used for fusion were extracted from spatial signatures of targets by applying nonlinear optimization techniques to data collected in a neighborhood of the location of interest. The maximum a posteriori approximation was used to simplify the exact fusion formulation to a form that was practical to implement. For the special case of normal clutter and normal linear features, fusion can be expressed as the Bayesian linear model for which a compact closed form expression exists. This result was used to demonstrate the importance of accurate sensor position information. We also discussed several decision-level fusion schemes that can be used for these data.. We tested the fusion algorithms on noncommensurate noncoincidently sampled data acquired by EMI, GPR, and IR sensors over a test field containing mine surrogates and both deliberate and unknown clutter. The targets and the clutter present in the test site were both very challenging. Although the number of mine surrogates sampled was small, the results presented here indicate that the performance of feature-level fusion and soft-decision fusion can be significantly better than that of the individual sensors. This performance enhancement is encouraging, especially when we recognize that the IR and EMI sensors were only marginally effective due to both the heavy clutter at the test site and our selection of surrogate targets. As expected, hard-decision fusion showed little improvement over the performance of the best individual sensor since the algorithm most strongly weights the most efffective sensors.. Overall, we have shown that feature-level and softdecision level fusion of noncoincidently sampled EMI, IR, and GPR data can result in significant improvements in mine detection performance. We found a small additional benefit in using feature-level fusion, which provided a 40 percent reduction in the false alarm rate beyond the softdecision fusion case. The feature-level fusion algorithm also provides an explicit method for dealing with position errors, which is not available through the decision-level fusion algorithms. The computational costs of decision-level and feature-level fusion algorithms are approximately equal since the computational expense involved in fusion is dominated by features estimation, and all methods of detection must perform this processing. There is, however, a small penalty for feature-level fusion since the classifier must be somewhat more complex to account for the greater number of inputs.. These results are encouraging but the small sample size of our data set suggests that a larger study be done to confirm these results. A data collection has been done at a larger minefield operated by the US Army at Fort A.P. Hill, Virginia. That study is now complete, and the results will be reported in the future. Brian A. Baertlein received the PhD in electrical engineering from the University of Arizona in 1988. His professional career has included analyses of sensor systems of various types, development of detection and estimation algorithms, and work in sensor fusion, scattering and propagation phenomena, antennas, and electromagnetic compatibility. He is currently a research scientist and adjunct associate professor of electrical engineering at The Ohio State University (OSU) ElectroScience Laboratory (ESL). Before joining OSU, he was a senior scientist with several small businesses doing work for the US Department of Defense and the Department of Energy. He is am member of the IEEE.. F For further information on this or any computing topic, please visit our Digital Library at http://computer.org/publications/dlib.

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Consistent integration of models based on views of meta models Abstract. The complexity of large system models in software engineering nowadays is mastered by using different views. View-based modelling aims at creating small, partial models, each one of them describing some aspect of the system. Existing formal techniques supporting view-based visual modelling are based on typed attributed graphs, where views are related by typed attributed graph morphisms. Such morphisms up to now require a meta model given by a fixed type graph, as well as a fixed data signature and domain. This is in general not adequate for view-oriented modeling where only parts of the complete meta model are known and necessary when modelling a partial view of the system. The aim of this paper is to extend the framework of typed attributed graph morphisms to generalized typed attributed graph morphisms, short GAG-morphisms, which involve changes of the type graph, data signature, and domain. This allows the modeller to formulate type hierarchies and views of visual languages defined by GAG-morphisms between type graphs, short GATG-morphisms. In this paper, we study the interaction and integration of views, and the restriction of views along type hierarchies. In the main result, we present suitable conditions for the integration and decomposition of consistent view models (Theorem 4.1) and extend these conditions to view models defined over meta models with constraints (Theorem 5.1). As a running example, we use a visual domain-specific modelling language to model coarse-grained IT components and their connectors in decentralized IT infrastructures. Using constraints, we formulate connection properties as invariants. In recent years, the complexity of large system models in software engineering is mastered by using different views or viewpoints. View-based modeling rather aims at creating small, partial models, each one of them describing some aspect of the system instead of building complex monolithic specifications. Visual techniques nowadays form an important part of the overall software development methodology. Usually, visual notations like the UML [OMG07] , Petri nets or other kinds of graphs are used in order to specify static or dynamic system aspects. Hence, the syntax definition of visual modeling languages is an important basis for the implementation of tools supporting visual modeling (e.g. visual editor generation) and for model-based system verification.. Two main approaches to visual language (VL) definition can be distinguished: grammar-based approaches or meta-modeling. Using graph grammars and graph transformation [EEPT06] , multidimensional representations are described by graphs. Graph rules are used to manipulate the graph representation of a language element. Meta-modeling (see e.g. [MOF06] ) is also graph-based, but uses constraints instead of a grammar to define a visual language. The advantage of meta-modeling is that UML users, who probably have basic UML knowledge, do not need to learn a new external notation to be able to deal with syntax definitions. Graph grammars are more constructive, i.e. closer to the implementation, and provide a formal basis for visualizing, validating and verifying system properties.. For the application of graph transformation techniques to VL modeling, typed attributed graph transformation systems and grammars [EEPT06] have proven to be an adequate formalism. A VL is modeled by a type graph capturing the definition of the underlying visual alphabet, i.e. the symbols and relations which are available. Sentences or models of the VL are given by graphs typed over (i.e. conforming to) the type graph. Such a VL type graph corresponds closely to a meta model. In order to restrict the set of valid visual models, a syntax graph grammar may be defined, consisting of a set of language-generating graph transformation rules, typed over the abstract syntax part of the VL type graph.. In this paper, we extend the graph transformation framework in order to allow an adequate specification of different views and their relations. In the literature, approaches already exist to model views as morphisms between typed attributed graphs [EEHT97] . Up to now such morphisms require a fixed type graph, as well as a fixed data signature and domain. This is in general not adequate for view-oriented modeling where only parts of the complete type graph and signature are known and necessary when modeling a partial view of the system. Hence, in this paper we develop the notion of generalized attributed graph morphisms (GAG-morphisms) which allows the modeler to change the type graph, data signature and domain. GAG-morphisms are the basis for more flexible, view-oriented modeling since views are independent of each other, now also with respect to the data type definition.. For view-oriented modeling, mechanisms are needed to integrate different views to a full system model. In order to integrate two or more views, their intended correspondences have to be specified. Here, typed graphs and the underlying categorical constructions support an integration concept which goes much further than an integration merely based on the use of common names. In this paper, we define type hierarchies and views based on GAG-morphisms, and study the interaction and integration of views, as well as the restriction of views along type hierarchies, the notion of view consistency, and the integration and decomposition of models based on consistent views.. As a running example we use a visual domain-specific modeling language to model coarse-grained IT components and their connectors in decentralized IT infrastructures. An infrastructure model has to provide the basis to handle structural security issues, like firewall placements, of such distributed IT components. In order to provide support to model, build, administrate, monitor and control such a local IT landscape, we present a formal, visual domain-specific language family based on attributed type graph hierarchies and views. A simplified visual language for this purpose using typed graphs without attributes was first introduced in [BBE07] , serving as a basis to transform domain-specific IT infrastructure models to a Reo coordination model [Arb04] for further analysis.. The paper is structured as follows: Sect. 2 defines the category GAGraphs of typed attributed graphs and GAG-morphisms, and introduces the sample VL for IT infrastructures. On this basis, views are defined in Sect. 3, and the view relations interaction and integration are given by categorical constructions. Moreover, the interplay of type hierarchies of VLs and views is considered. Section 4 studies models of visual languages and models of views (view-models) and states as main result conditions for the consistency, integration and decomposition of view-models. Type hierarchies and views with constraints are studied in Sect. 5, an extension which is not included in our conference version [EEEP08] . In Sect. 6, related work is presented and compared to our approach. We conclude and discuss future work in Sect. 7. In this paper we have studied the interaction and integration of views and the restriction of views along type hierarchies. The main result shows under which condition models of these views can be composed to a unique integrated model. The condition is called consistency of view models which means roughly that the models agree on the interaction type of the views. Vice versa, each model can be decomposed up to isomorphism into consistent models of given views. The paper is based on an extended version of typed attributed graph morphisms which allow changes of the type graph including those of data signatures and domains. In Theorem 1 we have considered visual languages based on meta-models given by attributed type graphs without constraints. In Theorem 2 we have shown that the main result can be extended to visual languages including constraints. Full proofs of all technical lemmas used in this paper and some extended results are given in our technical report [EEEP09] .. An important consequence of our work is that we provide the ability to rapidly compose "small" visual languages both at the view (type graph) level and at the view-model level, thus laying the formal basis for multi-view modeling environments. Hence, rather than a "one modeling language does all" approach, we favor a confederation of small, relatively orthogonal visual languages for different system aspects. Future work is planned to investigate the interplay of views and models with behaviour, which is related to the field of merging behavioural models [BCE06, UC04] .. The concept of type hierarchies should allow a language designer to adapt language definitions by performing model transformations at an abstract hierarchy level and "inheriting" the transformation results at the more concrete levels of the hierarchy. Work is in progress to analyze model transformations for hierarchically structured visual languages.. Future work is planned to implement our formal approach by extending our graph transformation engine AGG [AGG09] , a tool supporting visual modeling and analysis of typed, attributed graph transformation systems. Type graphs with inheritance model the underlying structure of the visual language used. The extension will offer means for structuring type graphs by hierarchies to enable language designers to compose/decompose visual languages at different abstraction levels. We will extend the underlying notion of typed attributed graph morphisms in AGG to the more general notion of GAG-morphisms and provide algorithms for checking the consistency conditions for integration and decomposition of view models. From a theoretical point of view, the concepts and results in this paper are closely related to the abstract framework of institutions, introduced by Goguen and Burstall [GB84] as general framework for data type specifications. An institution INST (SIG, Mod, Sen, | ) consists of a category SIG of signatures, a contravariant functor Mod : SIG op → CAT assigning to each signature SIG a category Mod(SIG) of models, a functor Sen : SIG → Sets defining a set Sen(SIG) of sentences over SIG, and a satisfaction relation | , where (M , ϕ) ∈| , written M | ϕ, means that model M satisfies sentence ϕ. The most prominent classical example is the institution EQSIG (SIG, Alg, Eqns, | ) of equational signatures, where SIG is the category of algebraic signatures, Alg(SIG) the category of SIG-algebras and SIG-homomorphisms, Eqns(SIG) the set of equations over SIG, and A | e means that algebra A satisfies equation e. In our paper, the concepts are defining an institution ATG (ATGraphs, Mod, Constr, | ) of attributed type graphs, where ATGraphs is the category GAGraphs restricted to attributed type graphs, Mod(ATG) is the category GAGraphs ATG of attributed graphs AG typed over ATG, Constr(ATG) is the set of graph constraints of ATG-typed graphs, and AG | c means that attributed graph AG satisfies constraint c. Fact 5.1 in our paper corresponds to the well-known satisfaction condition for institutions, and our main Theorem 5.1 means that the institution ATG has amalgamation based on pushouts of attributed type graphs with constraints.. Viewpoint-oriented software development is well-known in the literature [GEMT00, GMT99, EEHT97], however identifying, expressing, and reasoning about meaningful relationships between view models is hard [NFK03] . Up to now existing formal techniques for visual modeling of views and distributed systems by graph transformation support the definition of non-hierarchical views which require a common fixed data signature [EEPT06, GDdL05] . This is in general not adequate for view-oriented modeling where only parts of the complete type graph and signature are known and necessary when modeling a view of the system. Moreover, hierarchical relations between views could not be defined on the typing and data type level resulting in a lack of composition and decomposition techniques for view integration, verification, and analysis.. In [AdLG07] domain specific languages are defined using graphical and textual views based on the metamodeling approach used in the AToM 3 tool. In this approach the language designer starts with the common (integrated) meta-model and selects parts of the meta-model as different diagram views. So a common abstract meta-model is missing allowing to define hierarchical relations between the models.. In [RGH08] abstract graph views are defined, abstracting from specification details allowing a convenient usage of modules. To fulfill this purpose, reference relations have been introduced for the definition of mapping between view elements and abstract model elements (e.g. the database). Given this relations, there are different semantics for modifying view objects which are not studied yet in full detail. In comparison with the presented approach, generalized attributed graph morphisms have a unique formal semantics on the one hand and they provide the flexibility to define hierarchical relations on the other hand.. As a related approach xlinkit [NCEF07] provides rule-based link generation in web content management systems. In this approach semantics are defined using first order logic allowing automatic link generation to manage large document repositories. According to its purpose, this approach is limited to XML documents using XPath and XLink and thus requires an XML based storage format for models.. For related work concerning (nested) graph constraints we refer to [EEPT06, EEHP06, HP05] . Recently, the Query/View/Transformation Specification (QVT), Version 1.0 has been released by the OMG [QVT08] . Here, views are perceived as complex queries to select model parts. Despite its name, the main application area for QVT is model-to-model transformation. Queries and views are seen as special transformations. Transforming views at different meta-model levels, and ensuring consistency of views and view models for such transformations is not yet an issue of the QVT standard and tools.. QVT transformations are based on MOF meta-models and OCL [OCL03] , a textual specification language providing constraint and object query expressions on meta-models that cannot be otherwise be expressed by diagrammatic notation. The combination of meta-models and OCL is closely related to our approach based on type graphs and graph constraints. In fact, the relationship has been discussed in our previous paper [WTEK06] , where we identified a set of OCL constraints which can be translated to graph constraints. The combination of graph transformation rules for VL definition and graph constraints is as expressive as a meta-model with OCL constraints. This was shown e.g. in [BKPPT00] , where a graph-based semantics for OCL is proposed by translating OCL constraints into expressions over graph rules. Vice versa, Cabot et al. present an approach to analyze graph transformation rules based on an intermediate OCL representation [CCGdL08] . Here, rules are translated to OCL with the purpose of verifying their correctness and allowing for interoperability with standards-based model-driven development tools.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O B I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Intrusion Detection by Ellipsoid Boundary Abstract This paper presents a novel approach to describe the normal behavior of computer networks (as used in IDS) based on Support Vector Data Description (SVDD). In the proposed method we find a minimal hyper-ellipse around the normal objects in the input space. Hyper-ellipse can be expanded in high dimensional space (ESVDD) or to be used as a preprocessing in SVDD method (PESVDD) to obtain better results for IDS. KDD-cup99 has been used as data set for test of the proposed method. The overall experiments show prominence of our work in comparison with similar previous works. Intrusion detection is one major research problem in network security which analyzes the network traffic and looks for potential threats. There are two general approaches to intrusion detection: Misuse Intrusion Detection (MID) and Anomaly Intrusion Detection (AID) [1] [2] [3] . Misuse detection systems, detect known attacks using predefined attack patterns and signatures [4, 5] . Anomaly detection systems detect attacks by observing deviations from the normal behavior of the system [6] .. Both groups of methods have their advantages and disadvantages. Misuse detection methods are fundamentally limited to known attacks. On the other hand, anomaly detection methods are capable to detect known and unknown attacks. However, new legitimate behavior can be falsely identified as an attack, resulting in a false positive. The problem with current state-of-the-art is to reduce false negative and false positive rate, although it is difficult to achieve both simultaneously. The capability of detecting new attacks makes anomaly detection methods an interesting topic of active research.. The one-class classification problem is a kind of anomaly detection systems among machine learning techniques. In this kind of classification, we assume one class of data as target class and the rest classified as outlier. One-class classification is particularly significant in applications where only a single class of data objects is applicable and easy to obtain. Objects from other classes could be too difficult or expensive to be made available. So we would only describe the target class to separate it from outlier.. Three general approaches have been proposed to resolve the one-class classification problems [7] as follows:-(1) The most straightforward method to obtain a one-class classifier is to estimate the density of the training data and to set a threshold on its density. Several distributions can be assumed, such as a Gaussian or a Poisson distribution. The most popular three density models are Gaussian model, mixture of Gaussians and Parzen density [8, 9] . (2) In second method a closed boundary around the target set is optimized.. K-centers, nearest neighborhood method and support vector data description (SVDD) are example of boundary methods [10, 11] . (3) Reconstruction methods are other one-class classification methods which have not been primarily constructed for one-class classification, but rather to model data. By using prior knowledge about data and making assumptions about the generating process, a model is chosen and fitted to data. Some types of reconstruction methods are: the k-means clustering, learning vector quantization, self-organizing maps, PCA, a mixture of PCAs, diabolo networks, and auto-encoder networks.. The SVDD is a kind of one-class classification method based on Support Vector Machine [12] . It tries to construct a boundary around the target data by enclosing the target data within a minimum hyper-sphere. Inspired by the support vector machines (SVMs), SVDD decision boundary is described by a few target objects, known as support vectors (SVs). One more flexible boundary can be obtained with introduction of kernel functions, by which data are mapped into a high-dimensional space. The most commonly used kernel function is Gaussian kernel [13] .. Nowadays, the SVDD method widely uses in outlier detection problems [14] [15] [16] [17] [18] . Intrusion detection is a big and complex outlier detection problem. In this problem normal behaviors are always accessible contrary to intrusion ones. Obtaining the intrusion samples is very costly process. Hence we can use SVDD and other oneclass classification as solution. These methods just focus on normal behaviors and do not need the intrusion patterns to generate decision boundaries.. In this paper we propose a novel one-class classifier based on the SVDD method which is applied in intrusion detection. In this method we try to fit a better boundary around the normal samples. The SVDD method sometimes could not obtain an appropriate decision boundary in the input space and the good result depends on the proper kernel function. Generally, it is been found that by describing the target class with more precision in the input space; the better results will be obtained. Hence, we define a hyper-ellipse around the target class to get a tighter boundary. Indisputably hyper-ellipse constructs a better decision boundary from hyper-sphere in the input space. The experiments confirm the prominence of our proposed method against the standard SVDD in both input and high-dimensional space. Furthermore we use this hyper-ellipse to define a mapping function as a preprocessing for the SVDD method for intrusion detection.. The paper is organized as follows. In the next section intrusion detection methods are reviewed. In Sect. 3 the SVDD method is described. The proposed methods are explained in Sect. 4, and eventually, experimental results are presented. In this paper, we propose a new approach to make the SVDD boundary closely fit the contour of the target data. The SVDD method uses a hyper-sphere which cannot be a good decision boundary for the target data, in the input space. So we define a hyper-ellipse instead of a hyper-sphere and resolve the equations by applying this alteration. Experiments show that using a hyper-ellipse leads to better results in the high-dimensional space beside the input space.. Furthermore we can use the achieved minimal hyper-ellipse as a preprocessing step for the SVDD method to get better decision boundary. As an important benefit, it is less influenced by changing the user defined parameters and we even obtained acceptable results with the inappropriate parameters. Experiments demonstrate the prominence of these methods to detect intrusions in KDD-cup 1999 dataset. Contrary to the other classification methods, the proposed methods are just focused on normal behaviors. Due to this advantage new attacks can be easily recognized. We compare the performances of the SVDD and new proposed methods with a synthetic dataset and some of datasets taken from UCI Machine Learning Dataset Repository [25] . In the last of this section we apply this method for intrusion detection problem. Table 1 provides details about the datasets that are used here.. In Iris and balance-scale datasets three classes with four features are existed. Since, to use them for outlier detection, two of the classes are used as the target class while the remainder class is considered as outlier. Haberman's Survival dataset has two classes and uses three features. In this dataset we have 225 samples in one class and 81 samples in the other one. So we can use it easily for a one class classification problem. In this situation, the class with more samples supposed as the target class.. In the first step we should create some U functions for mapping the various input space into a high dimension high-dimensional space.. Here we deal with datasets by 2, 3 or 4 dimensions. The related mapping function characteristics are presented in Table 2 . For example U 1 is a mapping function which transforms a sample with 2 dimensions into a new position in a 100 dimensions space. We repeat all of the experiments with some of the selected dimensions of U functions (U 0 ). According to the previous section we claim that reducing the dimensions in the high-dimensional space has not any critical effects in the classification. Even in some cases fewer dimensions lead to better results. performance of SVDD and ESVDD methods with Iris, balance-scale and haberman datasets in 10 Iterations. The prominence of our proposed methods will be so clear when we use an elliptical synthetic dataset. In these experiments, we use the same user defined parameters. Thus ESVDD generates better decision boundary than SVDD in the non-spherical datasets specially.. The KDD-cup 1999 data was created based on the 1998 MIT-DARPA, it is available to download from the Information and Computer Science website, at the University of California at Irvine. Similar to the 1998 MIT-DARPA data, the full KDD-cup 1999 dataset, includes 7 weeks of TCP dump network traffic training data that was processed into approximately five million connection records, and 2 weeks of testing data, comprised of 38 different attack types that can be grouped into 5 categories which are shown in Table 4 . The attacks types are grouped into four groups:. 1. Probing: is a class of attacks where an attacker scans a network to gather information or find known vulnerabilities; surveillance and other probing, e.g., port scanning. 2. DOS: Denial of Service; is a class of attacks where an attacker makes some computing or memory resource too busy or too full to handle legitimate requests, thus denying legitimate users access to a machine, e.g., Syn-flood. 3. U2R: User to root exploits are a class of attacks where an attacker starts out with access to a normal user account on the system and is able to exploit vulnerability to gain root access to the system; unauthorized access to local super user (root) privileges, e.g., various ''buffer overflow'' attacks. 4. R2L: A remote to user (R2L) attack is a class of attacks where an attacker sends packets to a machine over a network, then exploits machine's vulnerability to illegally gain local access as a user; unauthorized access from a remote machine, e.g., guessing password.. The training data is made up of 22 different attacks out of the 39 present in the test data. Table 7 in the Appendix shows the different attack types for both training (known) and the additional attack types included for testing (novel) for the four categories. The known attack types are those present in the training dataset while the novel attacks are the additional attacks in the test datasets not available in the training datasets. The testing data does not have the same probability distribution as the training data, and includes additional specific attack types. The KDD-cup 1999 data includes 41 variables that extended from the 11 variables of the raw 1998 MIT-DARPA data. These variables can be found in the Appendix (See Table 8 ).

O O O B I O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Singular fractional linear systems and electrical circuits A new class of singular fractional linear systems and electrical circuits is introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transformation, the solution to the state equation of singular fractional linear systems is derived. It is shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches only with an ideal supercapacitor and voltage sources or at least one node with branches with supercoils. Singular (descriptor) linear systems were addressed in many papers and books (Dodig and Stosic, 2009; Dai, 1989; Fahmy and O'Reill, 1989; Kaczorek, 1992; 2004; 2007a; 2007b; Kucera and Zagalak, 1988; Van Dooren, 1979) . The eigenvalues and invariants assignment by state and output feedbacks were investigated by Dodig and Stosic (2009) , Dai (1989) , Fahmy and O'Reill (1989) , or Kaczorek (1992; 2004) , and the realization problem for singular positive continuous-time systems with delays by Kaczorek (2007b) . The computation of Kronecker's canonical form of a singular pencil was analyzed by Van Dooren (1979) .. Fractional positive continuous-time linear systems were addressed by Kaczorek (2008) along with positive linear systems with different fractional orders (Kaczorek, 2010 ). An analysis of fractional linear electrical circuits was presented in another work of Kaczorek (2011) and some selected problems in theory of fractional linear systems in a monograph by the same author (Kaczorek, 2009) .. In this paper a new class of singular fractional linear systems and electrical circuits will be introduced and their solution of state equations will be derived. The paper is organized as follows. In Section 2 the Caputo definition of the fractional derivative and the solution to the state equation of the fractional linear system are recalled. The solution of the state equation of a singular fractional linear system is derived in Section 3 using the Weirstrass pencil decomposition and the Laplace transform. Singular fractional linear electrical circuits are introduced in Section 4. Concluding remarks are given in Section 5.. To the best of the author's knowledge, singular fractional linear systems and electrical circuits have not been considered yet.. The following notation will be used in the paper. The set of n × m real matrices will be denoted by R n×m and R n := R n×1 . The set of m × n real matrices with nonnegative entries will be denoted by R m×n + and R. The set of nonnegative integers will be denoted by Z + and the n × n identity matrix by I n . Singular fractional linear systems and electrical circuits have been introduced. Using the Caputo definition of the fractional derivative, the Weierstrass regular pencil decomposition and the Laplace transform, the solution to the state equation of singular fractional linear system was derived (Theorem 2). Singular fractional linear electrical circuits were analyzed. It was shown that every electrical circuit is a singular fractional system if it contains at least one mesh consisting of branches with only ideal supercapacitors and voltage sources or at least one node with branches with supercoils (Theorem 3). The discussion was illustrated by singular linear electrical circuits. It can be extended to singular fractional linear systems with singular pencils.. An open problem is extension of the results to positive singular fractional linear systems and singular positive linear systems with different fractional orders. Linear systems with different fractional orders are described by (Kaczorek, 2010 ). where x 1 ∈ R n1 , x 2 ∈ R n2 are the state vectors and A ij ∈ R ni×nj , B i ∈ R ni×m , i, j = 1,2, and u ∈ R m is the input vector. The initial conditions for (38) have the form x 1 (0) = x 10 and x 2 (0) = x 20 .

B O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B O O O O O O O O O O O O O O B B I O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O B B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O B O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


A space-partitioning-based indexing method for multidimensional non-ordered discrete data spaces There is an increasing demand for similarity searches in a multidimensional non-ordered discrete data space (NDDS) from application areas such as bioinformatics and data mining. The non-ordered and discrete nature of an NDDS raises new challenges for developing efficient indexing methods for similarity searches. In this article, we propose a new indexing technique, called the NSP-tree, to support efficient similarity searches in an NDDS. As we know, overlap causes a performance degradation for indexing methods (e.g., the R-tree) for a continuous data space. In an NDDS, this problem is even worse due to the limited number of elements available on each dimension of an NDDS. The key idea of the NSP-tree is to use a novel discrete space-partitioning (SP) scheme to ensure no overlap at each level in the tree. A number of heuristics and strategies are incorporated into the tree construction algorithms to deal with the challenges for developing an SP-based index tree for an NDDS. Our experiments demonstrate that the NSP-tree is quite promising in supporting efficient similarity searches in NDDSs. We have compared the NSP-tree with the ND-tree, a datapartitioning-based indexing technique for NDDSs that was proposed recently, and the linear scan using different NDDSs. It was found that the search performance of the NSP-tree was better than those of both methods. Domains with non-ordered discrete values such as gender and profession are prevalent in database applications. A nonordered discrete data space (NDDS) is the Cartesian product of a number of such domains. There is an increasing demand for similarity searches on databases in NDDSs from application areas such as bioinformatics and data mining. For example, in a genome sequence database, sequences with alphabet {a, g , t, c} are broken into substrings of some fixed length d (i.e., vectors in a d -dimensional NDDS) for similarity searches [Kent 2002 ]. To support efficient similarity searches for large databases in NDDSs, efficient multidimensional index structures are needed.. If the domains of all dimensions in an NDDS are the same, a vector in such an NDDS can be considered as a character string over the domain (alphabet) . Traditional string indexing techniques such as Tries [Knuth 1973; Clement et al. 2001] , the Prefix B-tree [Bayer and Unterauer 1977] , and the String B-tree [Ferragina and Grossi 1999] can be utilized in such a case. However, most of these techniques were designed for exact matches rather than similarity searches, while others are memory based and not suitable for large databases. Moreover, vectors in an NDDS cannot be considered as strings over a fixed alphabet when the domains for different dimensions are different.. The metric trees [Uhlmann 1991; Bozkaya and Ozsoyoglu 1997; Ciaccia et al. 1997; Traina et al. 2002; Zhou et al. 2003; Skopal et al. 2004] , which only assume the knowledge of relative distances among data objects, can be utilized to support similarity searches in an NDDS. However, most of these index trees are static and require costly reorganizations for dynamic data sets. Besides, these trees were developed for general metric spaces, without taking the special characteristics of an NDDS into consideration. Hence their performance is not optimized when they are used for NDDSs.. There are numerous multidimensional indexing schemes for continuous data spaces (CDSs; i.e., spaces of domains with ordered continuous values). These methods can be divided into two categories: data partitioning (DP) based and space partitioning (SP) based. DP index structures such as the R * -tree [Beckmann et al. 1990 ], the SS-tree [White and Jain 1996] , and the SR-tree [Katayama and Satoh 1997] split an overflow node by grouping its indexed vectors (data) into two sets X 1 and X 2 for two new tree nodes such that the new nodes meet the minimum (disk) space utilization requirement. However the minimum bounding regions for X 1 and X 2 may overlap. On the other hand, SP methods like the K-D-B tree [Robinson 1981 ], the hB-tree [Lomet and Salzberg 1990] , and the LSD h -tree [Henrich 1998 ] split an overflow node by partitioning its corresponding data space into two nonoverlapping subspaces for two new tree nodes. The indexed vectors are then placed in the new nodes based on which subspace they belong to. Although having nonoverlapping subspaces for the nodes at the same level of an SP-based index tree leads to high search performance, the nodes in such a tree usually do not guarantee the minimum space utilization.. Unfortunately, the above DP-based and SP-based indexing techniques cannot be directly applied to an NDDS since some essential geometrical concepts/ properties such as bounding regions and areas are not defined for the NDDS where data elements on each dimension cannot even be labeled on an ordered axis. Note that simply mapping each non-ordered element into an ordered value can only be used for exact matches. It fails for similarity searches since it would make some elements "closer" than others, which is not the original semantics of the elements.. Recently, we proposed an indexing technique for an NDDS, called the ND-tree, in Qian et al. [2003 Qian et al. [ , 2006 . The key idea is to first map the essential geometrical concepts in a CDS into an NDDS and then extend and apply some strategies and heuristics from several popular indexing techniques for CDSs, such as the R * -tree [Beckmann et al. 1990 ] and the X-tree [Berchtold et al. 1996] . It has been shown that the ND-tree outperforms the direct method-linear scan and a popular metric tree-M-tree [Ciaccia et al. 1997] for similarity queries in NDDSs. Based on its tree construction method, the ND-tree can be classified as a DP method for NDDSs.. Research has shown that for a DP method in a CDS, as the dimensionality of the space becomes larger, the amount of overlap among the bounding regions in the index tree increases significantly, resulting in a dramatic degradation of query performance [Berchtold et al. 1996] . As found in Qian et al. [2003 Qian et al. [ , 2006 , overlap also causes a severe performance degradation in an NDDS. In fact, the situation in an NDDS is even worse, since the alphabet size for each dimension is limited, which causes the percentage of overlap to grow very fast as the number of data objects shared by two bounding regions increases. Although the ND-tree employs several strategies to minimize the overlap in the tree, as a DP method, overlap may still occur. For example, it may be forced to allow a large overlap to guarantee the minimum space utilization when dealing with skewed data. The performance of the ND-tree can be poor in such a case.. In this article, we propose an SP-based indexing technique, called the NSPtree, to index vectors in an NDDS. One advantage of an SP method is that it guarantees an overlap-free index tree, leading to efficient query processing. However, the non-ordered and discrete nature of an NDDS raises a number of challenges for developing an efficient SP method for the NDDS.. First, we cannot split an NDDS based on a single split point on a dimension as we do for a CDS. Splitting a CDS is relatively easy since a split point p on a dimension can divide the values on the dimension into two sets, for example, {x|x ≤ p} and {x|x > p}, based on their ordering. However, a single element in a non-ordered discrete domain cannot determine a partition of the domain (dimension). On the other hand, this characteristic of an NDDS gives us a flexibility to group the elements of the domain based on their distribution in the indexed vectors to balance the tree so that the (disk) space utilization and the search performance of the tree can be improved. The NSP-tree fully utilizes this characteristic via its tree building heuristics.. • G. Qian et al. Second, it is difficult to determine the suitable side (splitting group) of a split to place the elements that have not appeared on the split dimension in any indexed vector. For the existing elements, the strategy mentioned previously can be applied to place the corresponding vectors into subspaces based on their distribution to balance the tree. However, no information is available to properly place those absent elements in the subspaces. To deal with this challenge, the NSP-tree only partitions the current space, namely, the space determined by the elements appearing in present indexed vectors, rather than the whole (static) data space. As more vectors are inserted into the tree, the current space and its partition in the tree are dynamically adjusted.. Third, it is unclear how to balance the pruning power and the fanout of a node in an index tree for an NDDS to maximize the search performance. Using the subspaces from a space partition, an SP method can prune a subtree whose subspace is not within the search range of a query. However, the subspace for a subtree often contains large dead spaces (i.e., contains no indexed vectors). To enhance the search performance of an SP method in a CDS, people have suggested to add an auxiliary bounding box/region for each node of an index tree to achieve some additional pruning power (by reducing the dead space) [Henrich 1998; Chakrabarti and Mehrotra 1999] . Note that, although the idea to use a bounding box for a node is similar to that in the DP methods, the bounding boxes here are auxiliary in the sense that they are attached to the corresponding subspaces which are determined first. Hence, such index trees are still considered as the SP methods according to the conventional classification [Henrich 1998; Chakrabarti and Mehrotra 1999] . Since some storage space is needed for the auxiliary bounding boxes, the fanout of the node will be reduced (to fit in a given node space capacity). As we know, query performance can be improved by increasing the pruning power and the fanout of each tree node. However, since increasing both factors is impossible, balancing the two factors is required to achieve the best performance. Unfortunately, the well-known technique that uses grids to control the balance between these two factors for CDSs is not applicable for an NDDS due to its non-ordering nature. To solve the problem, we propose another approach to controlling the balance between the two factors by allowing several (child) tree nodes to share one auxiliary bounding box or letting one (child) node to have several auxiliary bounding boxes. Our empirical study shows that using a proper number (e.g., two) of bounding boxes for each node can significantly improve the performance of an SP index tree in an NDDS. The NSP-tree incorporates this strategy into its tree structure.. In summary, the NSP-tree is an SP-based indexing method specially designed for NDDSs. Although it has some similarity to the SP methods in CDSs, it is adapted to utilize the special properties of the NDDS, which is reflected in its unique tree structure, building heuristics and construction algorithms. Our experimental results demonstrate that the NSP-tree outperforms the NDtree [Qian et al. 2003 [Qian et al. , 2006 , which is the only existing index tree specially developed for NDDSs, in terms of search performance for skewed data sets. The degree of improvement increases dramatically as the skewness of the data set increases (resulting in more overlap in the ND-tree). For a uniform data set, the performance of the NSP-tree is comparable to that of the ND-tree. The space utilization of the NSP-tree is also reasonable although it cannot guarantee the minimum space utilization as the ND-tree can.. The rest of the article is organized as follows. Section 2 describes the relevant concepts and terms. Section 3 presents the structure and construction algorithms of the NSP-tree. Section 4 shows experimental results. Section 5 concludes the article. To support efficient similarity searches for large databases in NDDSs, robust multidimensional indexing techniques are needed. Unfortunately, most existing indexing methods were not designed for NDDSs. They either cannot be directly applied to an NDDS (e.g., the R-tree [Guttman 1984 ] and the K-D-B-tree [Robinson 1981 ]) due to lack of essential geometric concepts or are not optimized for NDDSs (e.g., the M-tree [Ciaccia et al. 1997 ]) due to their generic nature. The only existing indexing technique that was specially designed for NDDSs in the literature is the ND-tree [Qian et al. 2003 [Qian et al. , 2006 . Although the ND-tree can guarantee the minimum space utilization, its performance degrades as the data sets become skewed. We have proposed a new indexing method, called the NSP-tree, to support efficient similarity searches in NDDSs, which is robust for skewed data.. Unlike the ND-tree, which is based on the DP approach, the NSP-tree is based on the SP approach. It is inspired by several popular SP-based indexing techniques for CDSs including the K-D-B tree [Robinson 1981 ], the hB-tree [Lomet and Salzberg 1990] , and the LSD h -tree [Henrich 1998 ]. However, to tackle the new challenges for developing an SP-based index tree for NDDSs, a number of unique strategies have been incorporated into the NSP-tree construction algorithms, such as SP on the current data space instead of the whole space, adding multiple auxiliary DMBRs to each node, employing a linear scheme to determine effective DMBRs, and utilizing a histogram-based technique to generate a balanced split for an overflow leaf. In addition, some useful strategies from existing indexing techniques for CDSs, such as splitting a subspace on the dimension with the largest stretch and re-splitting an overflow leaf with its sibling, are extended and applied to the NSP-tree construction based on an evaluation of their effectiveness in NDDSs.. The experimental results for a variety of data sets have demonstrated the high efficiency of the NSP-tree. The NSP-tree not only outperforms the direct method-linear scan for executing range queries in NDDSs-but also outperforms the ND-tree for executing range queries on skewed data sets. When the data is uniformly distributed, the performance of the NSP-tree is comparable to that of the ND-tree. As the data skewness increases, the performance of the NSP-tree is increasingly better than that of the ND-tree. Our experimental results also show that the NSP-tree scales well with the database size, alphabet size and dimensionality. The (disk) space utilization of the NSP-tree is reasonable compared to that of the ND-tree although the latter always guarentees the minimum space utilization. In summary, our study shows that the NSPtree is a promising indexing method for supporting efficient similarity searches in NDDSs .. In future work, we plan to derive theoretical cost models for the NSP-tree and extend the technique to support more query types such as nearest-neighbor queries.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Visualization and clustering of crowd video content in MPCA subspace This paper presents a novel approach for the visualization and clustering of crowd video contents by using multilinear principal component analysis (MPCA). In contrast to feature-point-based approach and frame-based dimensionality reduction approach, the proposed method maps each short video segment to a point in MPCA subspace to take temporal information into account naturally through tensorial representations. Specifically, MPCA projects each short segment of a video to a low-dimensional tensor first. A few MPCA features are then selected according to the variance captured as the final representation. Thus, a video is visualized as a trajectory in MPCA subspace. The trajectory generated enables visual interpretation of video content in a compact space as well as visual clustering of video events. The proposed method is evaluated on the PETS 2009 datasets through comparison with three existing methods for video visualization. The MPCA visualization shows superior performance in clustering segments of the same event as well as identifying the transitions between events. Analysis of crowd video content is becoming an important topic, where detection and tracking of individual subjects have become extremely difficult due to the large number of subjects in the scene. In this paper, we use MPCA, a recent multilinear statistical method, to analyze crowd activities and events, with no need for object detection and tracking. We consider a video segment as a basic video element and map it to a point in MPCA subspace. The MPCA visualization characterizes the entire video sequence with an abstract description of the events and it provides a valuable tool in analyzing video content for video summarization, anomaly detection, and behavior understanding. In particular, the visualization enables visual clustering of events. Experiments show that the proposed MPCA-based method gives much better visualization of challenging PETS 2009 crowd video sequences and produces more visible clusters of events than three existing methods.

B O B O B O O O B O O O O O O O O O B O B O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O B B O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O


A Semantic-Oriented Approach for Organizing and Developing Annotation for E-Learning Abstract-This paper presents a solution to extend the IEEE LOM standard with ontology-based semantic annotations for efficient use of learning objects outside Learning Management Systems. The data model corresponding to this approach is first presented. The proposed indexing technique for this model development in order to acquire a better annotation of learning resources is further presented. This technique extends and combines two consecrated alternative methods for structure-based indexing of textual resources: the mathematical approach of the latent semantic indexing and the linguistic-oriented WordNet-based text processing. Thus, the reason behind the good results provided by the first method becomes more transparent due to the linguistic controlled choices proposed by the second method. The paper results are important in the context of adopting semantic web technologies in the e-learning field, but also as a progress in the area of ontology-based indexing of textual resources. T HE actual decentralization and interinstitution collaboration that characterize e-learning solutions increase the demand in making learning objects accessible not only across the e-learning platforms, but also across other Web applications. This demand could be solved with the support of semantic technologies, whose main goal is to reveal to the computer applications the resources' semantics, as information automatically processable.. The approach of extending e-learning solutions with semantic Web facilities involves mainly two aspects: e-learning data modeling and the processing technique leading to the established model.. The present paper first proposes a model that extends the IEEE LOM (Learning Object Metadata) standard with ontology-based semantic annotations for efficient use of Learning Objects (LOs) outside Learning Management Systems (LMS). This model is presented in the context of existing approaches that adopt ontologies in order to annotate e-learning resources. Its particularity consists in a simple solution for integrating semantic annotations in the structure of the IEEE LOM description of the e-learning resources, without requiring a special RDF LOM binding. Thus, the ontology considered in annotations is kept independently, while inside the IEEE LOM structure is included just information about the concepts and their weights for the current LO.. The paper also introduces a technique for automatic processing of e-learning textual resources leading to the development of the semantic annotation according to the proposed model. Traditionally, three alternative method types are used for structure-based indexing of textual resources: classification methods, linguistic methods, and mathematical methods. Instead of focusing on one such method, the proposed technique extends and combines two consacrated alternative methods: the mathematical approach of the latent semantic indexing (LSI) and the linguistic-oriented WordNet-based text processing. Thus, the reason behind the good results provided by the first method becomes more transparent due to the linguistic controlled choices proposed by the second method.. The ontology-based modeling was adopted in the e-learning field not only for the learning resources, but also for the user profile. In [12] we provided such a solution, where the user profile is focused on the user competencies, which are expressed in terms of the same ontology adopted in LOs' annotation. The ontology-based annotation uniformity of the various types of e-learning resources (such as LOs and users) could be exploited in many ways, in order to provide users with personalized functionalities:. . For selecting the suitable users for being coopted into a certain project, whose topics are also expressed through ontology concepts; . For selecting the materials suitable for a certain user into a certain situation: when accessing a specific course site section, or when solving a certain course homework (as student), or when developing a certain course material (as teacher); . For redirecting the student, in the case he gives a wrong answer to a test, to all the materials which provide explanations (not only to those specified by the test creator as feedback information); . For better providing the student with the appropriate materials which are recommended or published by his collaborators in different projects or interest groups. These facilities could be exported from an e-learning system to another if they are implemented, for example, in the form of web services. Thus, the user mobility across distributed e-learning communities is facilitated not only because the user competencies profile is recognized by other systems, but also because the e-learning materials are uniformly modeled.. We already worked on exploiting the semantic annotations associated with e-learning resources inside an existing tracking system that capture the user current activity, which is developed based on the Contextualized Attention Metadata (CAM) 1 [36] framework. In [7] , we exposed a solution for recommending documents to students according to their current activity that is tracked in terms of semantic annotations associated with the accessed resources.. Aiming to define an ontology-based annotation model for e-learning documents, the present paper starts by presenting the context of e-learning and semantic web standards, discussing how semantic technologies could be integrated into e-learning. Considering IEEE-LOM e-learning standard, a document model solution that semantically extends it will be further presented. The solution considers an ontology-based annotation set for LOs. The document model development considers a manual and an automatic part for the annotation process. The latter concerns textual LOs and combines TFxIDF indexing with latent semantic indexing with WordNet-based processing. Before defining the solution for automatic annotations, a review of techniques for document indexing relevant to our approach is presented. Conclusions and further work directions are finally presented.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Accurate and efficient curve detection in images: the importance sampling Hough transform The Hough transform is a well known technique for detecting parametric curves in images. We place a particular group of Hough transforms, the probabilistic Hough transforms, in the framework of importance sampling. This framework suggests a way in which probabilistic Hough transforms can be improved: by specifying a target distribution and weighting the sampled parameters accordingly to make identiÿcation of curves easier. We investigate the use of clustering techniques to simultaneously identify multiple curves in the image. We also use probabilistic arguments to develop stopping conditions for the algorithm. Results from applying our method and two popular versions of the Hough transform to both simulated and real data are shown. ? The Hough transform is a well known technique for detecting parametric curves in images. We place a particular group of Hough transforms, the probabilistic Hough transforms, in the framework of importance sampling. This framework suggests a way in which probabilistic Hough transforms can be improved: by specifying a target distribution and weighting the sampled parameters accordingly to make identiÿcation of curves easier. We investigate the use of clustering techniques to simultaneously identify multiple curves in an image. We also use probabilistic arguments to develop stopping conditions for the algorithm. The resulting methodology is called the the term pixels to refer to foreground and background pixels. We deÿne N to be the total number of points in the image space.. In order to detect instances of a particular parametric curve in an image, one must decide upon a parameterization of the curve. We will denote the curve parameterization by . The dimension of the curve will be denoted by p. For instance, if a line is parameterized in Cartesian coordinates, p = 2, and = {m; c}, where m and c are the slope and intercept of the line, respectively.. Several of the HTs we discuss use an accumulator array to detect curves. An accumulator array, denoted by A, is a discretization of the parameter space, . Each cell of A is used to store votes for curves whose parameters are contained within the cell. We have found importance sampling to be a natural framework with which to design, view, and understand probabilistic Hough transforms. We feel that the notion of a target distribution, which deÿnes an importance weight associated with every sampled parameter, is fundamental to the successful implementation of a PHT. We investigated the feasibility of detecting multiple curves from a given batch of sampled parameters. We found that simple clustering methods provided good identiÿcation of curve parameters, provided that the sampled parameters not associated with curves present in the image were ÿl-tered out. The removal of these "noise" parameters was achieved via a simple thresholding of the importance weights. Probabilistic arguments can be used to determine reasonable stopping conditions for PHTs.. As with most data processing algorithms, their successful implementation often depends on correctly setting several tuning parameters. We feel that, depending on the given image, the tuning parameters of the ISHT are reasonably intuitive to set. One parameter, the batch size (if one is employing the second stopping condition) can a ect the e ciency and accuracy of the ISHT. If the batch size is too large, the increased e ciency of sampling from a smaller pool of points is lost. Conversely, if the batch size is too small, curves may be detected after only being sampled once, thus increasing the bias in the parameter estimates. One possible way to avoid this problem is to use a small batch size, and employ an algorithm similar to the Dynamic RHT. That is, for each detected curve, select all the points near the curve and perform a reÿned HT on these points. This technique can be thought of as adaptively sampling the parameter space, and it is of course not the only conceivable approach to take.. The importance sampling framework is broad enough to incorporate many of the beneÿcial features of other existing PHTs. For example, we used a very simple sampling distribution, whereas one could use a more sophisticated sampling distribution, e.g. one based on the Connective RHT. In addition, the identiÿcation of curves could be improved by incorporating an adaptive sampling mechanism, such as in the dynamic RHT. The main computational burden of our approach over other PHTs is the evaluation of the target distribution. This should be an O(N ) operation, where N is the total number of points in the image. We feel that the beneÿt of evaluating the quality of a curve far outweighs the cost of its computation. In summary, we feel that importance sampling provides a framework in which di erent PHTs can be understood, and which will be useful in guiding the design of better curve detection methods. c are mutually exclusive (one cannot sample two curves at the same time). Similarly, the probability of the intersection of all events can be written as. Substituting these expressions into the ÿrst equation we ÿnd that the probability of not sampling all curves at least once after t samples have been drawn from g(·) is:. The probability of having sampled all curves after t samples is simply this quantity subtracted from 1. The lines detected by each method are shown in Fig. 2 . Each method detected all 10 lines in the image with no false positives, but the three methods di ered substantially in speed and accuracy. Table 1 shows the run times of each method, and the mean squared errors for and Â.. In terms of accuracy, the ISHT was clearly the best. The MSE for was nearly an order of magnitude bet- ter for the ISHT than for the RHT D, and two orders of magnitude better than for the SHT. The MSE for Â for the ISHT was 4 times lower than for either of the older methods. The SHT was the fastest method, approximately 3 times faster than the ISHT, which was an order of magnitude faster than the RHT D. This is not too surprising given that the parameter space was of low dimension (high dimension adversely a ects the SHT more than the RHT), and that the image was complex (the complexity of the image a ects the RHT more than the SHT).. The ÿnal classiÿcations for each method are shown in Fig. 6 . We considered 26 of the blood cells in the image to be detectable. The number of cells correctly detected, along with the run times, the number of false positives, and the number of duplicates are shown in Table 2 .. The ISHT detected 21 of the 26 blood cells, detected no false positives and no duplicates, and had by far the shortest run time. The RHT D detected more blood cells (23), but also detected 13 false positives. The SHT detected fewer blood cells (20), and also detected ÿve duplicates. We can see by visually comparing the images in Fig. 6 that the circles detected by the ISHT ÿt the blood cells better. The ISHT did not detect several of the cells that are not fully within the image, as well as the two partially occluded cells that are fully contained within the image. However, with suitable modiÿcations of the target distribution these cells could conceivably be detected. For the ISHT, we chose the sampling distribution corresponding to the sampling mechanism of the RHT with point distance criterion with d min = 1, and dmax = 50, i.e. the two pixels selected must be within 50 pixels of each other. The components of our target distribution were given by. , where W (·) is the Gaussian weighting function with R = 2, and = 2.. This target distribution allows points within 2 pixels of the line to be associated with the curve, but penalizes curves that do not have at least half as many points near the line as pixels on the line. We used a peak detection method with an importance weight threshold of zero. The cell size of the accumulator array (in { ; Â} notation) was 1:8 × 2 =100. The batch size was 50, and the HT was stopped if two consecutive batches failed to detect any curves.. For the RHT D, we set the threshold to be 10 points, and used the same point distance criterion as the ISHT above. We ceased sampling when the number of points remaining in the image was less than 30% of the original total. The cell size of the accumulator array was 1:8 × 2 =100. When removing detected curves from the image we removed all points within a 3 pixel radius of the curves.. For the SHT, the threshold was set at 130 points. The cell size of the accumulator array was 3:6 × =100. After thresholding the accumulator array (all cells below the threshold were set to zero), we ran a connected components algorithm on the non-empty cells. The cell with the most votes inside each connected component was identiÿed as corresponding to a curve present in the image. The parameters of the curve were given by the parameters of the center of the cell. This curve identiÿcation procedure is similar to our ISHT clustering algorithm.. We used the same circle parameterization for each HT, namely = {r; a; b}, where r is radius of the circle, and {a; b} is the row and column position of the circle center (all in pixels). For the ISHT, we chose a batch size of 200 samples. The sampling mechanism and target distribution are the same as in the previous example. Again we clustered the sampled parameters after each batch using our peak detection method. The cell size used was (in {r; a; b} notation) 0:8 × 11 × 11 and the sample was thresholded based on an importance weight of 45. The ISHT was stopped if four consecutive batches detected no curves.. For the RHT D, we set the threshold of the RHT D to be 10 points, and used the same point distance criterion as the ISHT above. The size of a cell in the accumulator array was 0:8 × 5 × 5. As in the previous example, we stopped sampling when the number of points remaining in the image was less than 30% of the original total, and we used a 3 pixel radius when determining which points should be removed after a curve had been detected.. In order to alleviate the severe storage requirements of the SHT once the number of parameters reaches 3, as here with circles, we employed the Gerig-Klein modiÿ-cation to the HT [16] . This modiÿed HT allows only one circle to be detected at each given center. This reduces the accumulator array from a three-dimensional array to two-dimensional arrays. The cost is the inability to de-

O O O O O O O O B I B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Area, Curve Complexity, and Crossing Resolution of Non-planar Graph Drawings Abstract. In this paper we study non-planar drawings of graphs, and study tradeoffs between the crossing resolution (i.e., the minimum angle formed by two crossing segments), the curve complexity (i.e., maximum number of bends per edge), the total number of bends, and the area. Planarity is one of the most desirable properties when drawing a graph because planar drawings are more readable and more aesthetically pleasant than non-planar ones. Unfortunately, very few graphs are planar in practice and edge crossings are unavoidable in the vast majority of the application scenarios where relational data are visualized and analyzed by means of graph drawing techniques.. While a large body of literature has been published about the problem of reducing the number of crossings in a non-planar drawing of a graph, by the well-known crossinglemma this number is quadratic with the number of the edges for dense graphs. This, together with cognitive experiments showing the negative impact of edge crossings on the human understanding of a graph drawing, apparently leads to the conclusion that computing readable node-link visualizations of dense graphs is a hopeless challenge [6, 7, 8] .. However, new cognitive experiments on large drawings of graphs refine the conclusions in [6, 7, 8] by showing that actually the human's understanding of the relations between the nodes of a network is not bothered by those edge crossings that form large angles [3, 4, 5] . These experiments suggest a new and fascinating research scenario in which the problem of maximizing the crossing resolution of a drawing (i.e. the smallest angle formed by two crossing edges) becomes as important for the non-planar graphs as the problem of avoiding edge crossings is for the planar graphs.. With this motivation, we study the trade-offs between crossing resolution, curve complexity, total number of bends, and area of non-planar drawings of graphs. The area is measured as the number of grid points contained in or on a bounding box of the drawing, i.e., the smallest axis-aligned box enclosing the drawing. The curve complexity is the maximum number of bends along each edge of the drawing.. We recall that the special case where the crossing resolution of a drawing is between the edge density and the curve complexity in a RAC drawing. In this paper we extend the study of [1] in two ways: we take into account the area requirement and we relax the crossing resolution constraints to angles smaller than π 2 . Our main results can be listed as follows.. -We study the trade-off between area requirement and curve complexity of RAC drawings. We establish an Ω(n 2 ) lower bound on the area requirement of RAC drawings and show an O(n + m)-time algorithm whose input is a graph G with n vertices and m edges and whose output is a RAC drawing of G having curve complexity 4, total number of bends O(m), and area O(n 3 ). We observe that the previously known algorithm requires area O(n 4 ) and curve complexity 3 [1] . -We relax the constraint on the crossing resolution and introduce the Large Angle. Crossing drawings (LAC drawings, for short). In a LAC drawing the edge crossings are allowed to form angles at least π 2 − ε for any given 0 < ε < π 2 . For any choice of the constant ε, we show an infinite family of graphs such that any LAC drawing of an n-vertex graph in the family requires curve complexity 1, total number of bends Ω(n 2 ), and Ω(n 2 ) area. -We describe an O(n + m)-time algorithm whose input is a graph G with n vertices and m edges and a constant 0 < ε < π 2 and whose output is a LAC drawing of G having crossing resolution

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A method for counting people attending large public events Abstract The algorithm for people counting in crowded scenes, based on the idea of virtual gate which uses optical flow method is presented. The concept and practical application of the developed algorithm under real conditions is depicted. The aim of the work is to estimate the number of people passing through entrances of a large sport hall. The most challenging problem was the unpredicted behavior of people while entering the building. The examined flow of people fluctuated between individual persons and dense crowd. A series of experiments during sport and entertainment events was made. The results of the experiments show a high efficiency of the elaborated algorithm. The concept and practical application results of the algorithm for people counting in a crowd passing through the gates of large sport object were presented in this paper. We described the approach to the analysis of motion data obtained with the dense optical flow estimated with the devised Virtual Gate algorithm. The algorithm efficiency was examined using some real videos recorded at a large sport and entertainment hall (Ergo-Arena in Gdansk). The counting precision achieved of 97.6 % on an average at total 6,649 persons, is satisfactory considering the real people behavior which was far from the organized movement. A further work will focus on extending the system to operate at other entrances to the hall of the ErgoArena object being used less frequently. Moreover, changes of organization of the process of crowd entering the building would be necessary in order to improve the algorithm accuracy. The future work may also focus on a practical application of the system to other large public objects.

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