Subnetwork state functions define dysregulated subnetworks in cancer Abstract. Emerging research demonstrates the potential of proteinprotein interaction (PPI) networks in uncovering the mechanistic bases of cancers, through identification of interacting proteins that are coordinately dysregulated in tumorigenic and metastatic samples. When used as features for classification, such coordinately dysregulated subnetworks improve diagnosis and prognosis of cancer considerably over single-gene markers. However, existing methods formulate coordination between multiple genes through additive representation of their expression profiles and utilize greedy heuristics to identify dysregulated subnetworks, which may not be well suited to the potentially combinatorial nature of coordinate dysregulation. Here, we propose a combinatorial formulation of coordinate dysregulation and decompose the resulting objective function to cast the problem as one of identifying subnetwork state functions that are indicative of phenotype. Based on this formulation, we show that coordinate dysregulation of larger subnetworks can be bounded using simple statistics on smaller subnetworks. We then use these bounds to devise an efficient algorithm, Crane, that can search the subnetwork space more effectively than simple greedy algorithms. Comprehensive cross-classification experiments show that subnetworks identified by Crane significantly outperform those identified by greedy algorithms in predicting metastasis of colorectal cancer (CRC). Network-based approaches to identification of multiple markers. Highthroughput protein-protein interaction (PPI) data [5] provide an excellent substrate for network-based identification of multiple interacting markers. Networkbased analyses of diverse phenotypes show that products of genes that are implicated in similar phenotypes are clustered together into "hot spots" in PPI networks [6, 7] . This observation is exploited to identify novel genetic markers based on network connectivity [8] [9] [10] . For the identification of differentially expressed subnetworks with respect to GAL80 deletion in yeast, Ideker et al. [11] propose a method that is based on searching for connected subgraphs with high aggregate significance of individual differential expression. Variations of this method are shown to be effective in identifying multiple genetic markers in prostate cancer [12] , melanoma [13] , diabetes [14] , and others [15] [16] [17] .. Coordinate/synergistic dysregulation. Network-based approaches are further elaborated to capture coordinate dysregulation of interacting proteins at a sample-specific resolution [18] . Ulitksy et al. [19] define dysregulated pathways as subnetworks composed of products of genes that are dysregulated in a large fraction of phenotype samples. Chuang et al. [20] define subnetwork activity as the aggregate expression of genes in the subnetwork, quantify the dysregulation of a subnetwork in terms of the mutual information between subnetwork activity and phenotype, and develop greedy algorithms to identify subnetworks that exhibit significant dysregulation. Subnetworks identified by this approach are also used as features for classification of breast cancer metastasis, providing significant improvement over single-gene markers [20] . Nibbe et al. [21, 22] show that this notion of coordinate dysregulation is also effective in integrating protein and mRNA expression data to identify important subnetworks in colon cancer (CRC). Anastassiou [23] introduces the concept of synergy to delineate the complementarity of multiple genes in the manifestation of phenotype. While identification of multiple genes with synergistic dysregulation is intractable [23] , important insights can still be gained through pairwise assessment of synergy [24] .. Contributions of this study. Despite significant advances, existing approaches to the identification of coordinately dysregulated subnetworks have important limitations, including the following: (i) additive formulation of subnetwork activity can only highlight the coordinate dysregulation of interacting proteins that are dysregulated in the same direction, overlooking the effects of inhibitory and other complex forms of interactions; (ii) greedy algorithms may not be able to adequately capture the coordination between multiple genes that provide weak individual signals. In this paper, with a view to addressing these challenges, we develop a novel algorithm, Crane, for the identification of Combinatorially dysRegulAted subNEtworks. The contributions of the proposed computational framework include the following:. -We formulate coordinate dysregulation combinatorially, in terms of the mutual information between subnetwork state functions (specific combinations of quantized mRNA expression levels of proteins in a subnetwork) and phenotype (as opposed to additive subnetwork activity ).. -We decompose combinatorial coordinate dysregulation into individual terms associated with individual state functions, to cast the problem as one of identifying state functions that are informative about the phenotype. -Based on this formulation, we show that the information provided on phenotype by a state function can be bounded from above using statistics of subsets of this subnetwork state. Using this bound, we develop bottom-up enumeration algorithms that can effectively prune out the subnetwork space to identify informative state functions efficiently. -We use subnetworks identified by the proposed algorithms to train neural networks for classification of phenotype, which are better suited to modeling the combinatorial relationship between the expression levels of genes in a subnetwork, as compared to classifiers that require aggregates of the expression profiles of genes as features (e.g., SVMs).. We describe these algorithmic innovations in detail in Section 2.. Results. We implement Crane in Matlab and perform comprehensive crossclassification experiments for prediction of metastasis in CRC. These experiments show that subnetworks identified by the proposed framework significantly outperform subnetworks identified by greedy algorithms in terms of accuracy of classification. We also investigate the highly informative subnetworks in detail to assess their potential in highlighting the mechanisms of metastasis in CRC.. We present these results in Section 3 and conclude our discussion in Section 4. We present a novel framework for network based analysis of coordinate dysregulation in complex phenotypes. Experimental results on metastasis of colorectal cancer show that the proposed framework can achieve almost perfect performance when discovered subnetworks are used as features for classification. These results are highly promising in that the state functions that are found to be informative of metastasis can also be useful in modeling the mechanisms of metastasis in cancer. Detailed investigation of the state functions and the interactions between proteins that together compose state functions might therefore lead to development of novel hypotheses, which in turn may be useful for development of theurapetic intervention strategies for late stages of cancer. In the context of a specific phenotype, a group of genes that exhibit significant differential expression and whose products interact with each other may be useful in understanding the network dynamics of the phenotype. This is because, the patterns of (i) collective differential expression and (ii) connectivity in protein-protein interaction (PPI) network are derived from independent data sources (sample-specific mRNA expression and generic protein-protein interactions, respectively). Thus, they provide corroborating evidence indicating that the corresponding subnetwork of the PPI network may play an important role in the manifestation of phenotype. In this paper, we refer to the collective differential expression of a group of genes as coordinate dysregulation. We call a group of coordinately dysregulated genes that induce a connected subnetwork in a PPI network a coordinately dysregulated subnetwork. Dysregulation of a gene with respect to a phenotype. For a set V of genes and U of samples, let E i ∈ R |U | denote the properly normalized [25] gene expression vector for gene g i ∈ V, where E i (j) denotes the relative expression of g i in sample s j ∈ U. Assume that the phenotype vector C annotates each sample as phenotype or control, such that C j = 1 indicates that sample s j is associated with the phenotype (e.g., taken from metastatic sample) and C j = 0 indicates that s j is a control sample (e.g., taken from a non-metastatic tumor sample). Then, the mutual information I(E i ; C) = H(C) − H(C|E i ) of E i and C is a measure of the reduction of uncertainty about phenotype C due to the knowledge of the expression level of gene g i . Here, H(X) = − x∈X p(x) log p(x) denotes the Shannon entropy of discrete random variable X with support X . The entropy H(E i ) of the expression profile of gene g i is computed by quantizing E i properly. Clearly, I(E i ; C) provides a reasonable measure of the dysregulation of g i , since it quantifies the power of the expression level of g i in distinguishing phenotype and control samples. Additive coordinate dysregulation. Now let G = (V, E) denote a PPI network where the product of each gene g i ∈ V is represented by a node and each edge g i g j ∈ E represents an interaction between the products of g i and g j . For a subnetwork of G with set of nodes S ⊆ V, Chuang et al. [20] define the subnetwork activity of S as E S = gi∈S E i / |S|, i.e., the aggregate expression profile of the genes in S. Then, the dysregulation of S is given by I(E S ; C), which is a measure of the reduction in uncertainty on phenotype C, due to knowledge of the aggregate expression level of all genes in S. In the following discussion, we refer to I(E S ; C) as the additive coordinate dysregulation of S. Combinatorial coordinate dysregulation. Additive coordinate dysregulation is useful for identifying subnetworks that are composed of genes dysregulated in the same direction (either up-or down-regulated). However, interactions among genes and proteins can also be inhibitory (or more complex), and the dysregulation of genes in opposite directions can also be coordinated, as illustrated in Figure 1 . Combinatorial formulation of coordinate dysregulation may be able to better capture such complex coordination patterns. To define combinatorial coordinate dysregulation, we consider binary representation of gene expression data. Binary representation of gene expression is commonly utilized for several reasons, including removal of noise, algorithmic considerations, and tractable biological interpretation of identified patterns. Such approaches are shown to be effective in the context various problems, ranging from genetic network inference [26] to clustering [27] and classification [28] . Ulitsky et al. [19] also use binary representation of differential expression to identify dysregulated pathways with respect to a phenotype. There are also many algorithms for effective binarization of gene expression data [29] . For our purposes, letÊ i denote the binarized expression profile of gene g i . We say that gene g i has high expression in sample s j ifÊ i (j) = H and low expression ifÊ i (j) = L. Then, the combinatorial coordinate dysregulation of subnetwork S is defined as. where. H} m is the random variable that represents the combination of binary expression states of the genes in S and m = |S|.. The difference between additive and combinatorial coordinate dysregulation is illustrated in Figure 1 . Anastassiou [23] also incorporates this combinatorial formulation to define the synergy between a pair of genes as ψ(g 1 , g 2 ) = I(Ê 1 ,Ê 2 ; C)−(I(Ê 1 ; C)+I(Ê 2 ; C)). Generalizing this formulation to the synergy between multiple genes, it can be shown that identification of multiple genes with synergistic dysregulation is an intractable computational problem [23] . Here, we define combinatorial coordinate dysregulation as a more general notion than synergistic dysregulation, in that coordinate dysregulation is defined based solely on collective differential expression, whereas synergy explicitly looks for genes that cannot individually distinguish phenotype and control samples.. Subnetworks that exhibit combinatorial coordinate dysregulation with respect to a phenotype may shed light into the mechanistic bases of that phenotype. However, identification of such subnetworks is intractable, and due to the combinatorial nature of the associated objective function (I(F S ; C)), greedy algorithms may not suit well to this problem. This is because, as also demonstrated by the example in Figure 1 , it is not straightforward to bound the combinatorial coordinate dysregulation of a subnetwork in terms of the individual dysregulation of its constituent genes or coordinate dysregulation of its smaller subnetworks. Motivated by these considerations, we propose to decompose the combinatorial coordinate dysregulation of a subnetwork into individual subnetwork state functions and show that information provided by state functions of larger subnetworks can be bounded using statistics of their smaller subnetworks. Subnetwork state functions informative of phenotype. Let f S ∈ {H, L} m denote an observation of the random variable F S , i.e., a specific combination of the expression states of the genes in S. By definition of mutual information, we can write the combinatorial coordinate dysregulation of S as. where. Here, p(x) denotes P (X = x), that is the probability that random variable X is equal to x (similarly, p(x|y) denotes P (X = x|Y = y)). In biological terms, J(f S ; C) can be considered a measure of the information provided by subnetwork state function f S on phenotype C. Therefore, we say a state function f S is informative of phenotype if it satisfies the following conditions:. Here, f R f S denotes that f R is a substate of state function f S , that is R ⊆ S and f R maps each gene in R to an expression level that is identical to the mapping provided by f S . Here, the first condition ensures that the information provided by the state function is considered high enough with respect to a user-defined threshold. It can be shown that for any [30] , where p(c) denotes the fraction of phenotype samples among all available samples. Therefore, in practice, we allow the user to specify a threshold j * * in the range [0, 1] and adjust it as j * = j * * j max (p(c)), to make the scoring criterion interpretable and uniform across all datasets. The second condition ensures that informative state functions are non-redundant, that is, a state function is considered informative only if it provides more information on the phenotype than any of its substates can. This restriction ensures that the expression of each gene in the subnetwork provides additional information on the phenotype, capturing the synergy between multiple genes to a certain extent. For a given set of phenotype and control samples and a reference PPI network, the objective of our framework is to identify all informative state functions. Algorithms for the identification of informative state functions. Since the space of state functions is very large, the problem of discovering all informative state functions is intractable. Here, we address this challenge by utilizing a bound on the value of J to effectively prune the search space. Our approach is inspired by a similar result by Smyth and Goodman [31] on information-theoretic identification of association rules in databases. In the following theorem, we show that the information that can be provided by all superstates of a given state function can be bounded based on the statistics of that state function, without any information about the superstate. Theorem 1. Consider a subnetwork S ⊆ V and associated state function f S . For any f R f S , the following bound holds:. The proof of this theorem is provided in the supplementary materials [30] . Note that this theorem does not state that the J-value of a state function is bounded by the J-value of its smaller parts, it rather provides a bound on the J-value of the larger state function based on simpler statistics of its smaller parts. Using this bound, we develop an algorithm, Crane, to efficiently search for informative state functions. Crane enumerates state functions in a bottom-up fashion, by pruning out the search space effectively based on the following principles: Crane enumerates all candidate state functions that qualify according to these principles, for given j * , b, and d. At the end of the search process, the candidate state functions that are not superceded by another candidate state function (the leaves of the enumeration tree) are identified as informative state functions, if their J-value exceeds j * . A detailed pseudo-code for this procedure is given in the supplementary materials [30] . Using state functions to predict metastasis in cancer. An important application of informative state functions is that they can serve as features for classification of phenotype. Since the genes that compose an informative state function are by definition highly discriminative of phenotype and control when considered together, they are expected to perform better than single-gene features [20] . Note here that Crane discovers specific state functions that are informative of phenotype, as opposed to subnetworks that can discriminate phenotype or control. However, by Equation 2, we expect that a high J(f S , C) for a specific state function f S is associated with a potentially high I(F S , C) for the corresponding subnetwork S. Therefore, for the application of Crane in classification, we sort the subnetworks that are associated with discovered state functions based on their combinatorial coordinate dysregulation I(F S , C) and use the top K disjoint (non-overlapping in terms of their gene content) subnetworks with maximum I(F S , C) as features for classification. In the next section, we report results of classification experiments for different values of K.. Deriving representative features for subnetworks is a challenging task. Using simple aggregates of individual expression levels of genes along with traditional classifiers (e.g., regression or SVMs) might not be adequate, since such representations may not capture the combinatorial relationship between the genes in the subnetwork. For this reason, we use neural networks that incorporate subnetwork states (F S ) directly as features. The proposed neural network model is illustrated in Figure 2 . In the example of this figure, two subnetworks are used to build the classifier. Each input is the expression level of a gene and the inputs that correspond to a particular subnetwork are connected together to an input layer neuron. All input layer neurons, each representing a subnetwork, are connected to a single output layer neuron, which produces the output. Each layer's weights and biases are initialized with the Nguyen-Widrow layer initialization method (provided by Matlab's initnw parameter). Then for a given gene expression dataset for a range of control and phenotype samples (which, in our experiments, is identical to that used for identification of informative state functions), the network is trained with Levenberg-Marquardt backpropagation (using Matlab's trainlm parameter), so that, given expression profiles in the training dataset, the output of the second layer matches the associated phenotype vector within minimal mean squared error. This learned model is then used to perform classification tests on a different gene expression dataset for the same phenotype. Since Neural Networks show stochastic behavior, we train 30 independent NNs with the same training data and take a voting amongst them to determine the final class label of a particular sample.

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An assistive robotic agent for pedestrian mobility The goal of this project is to develop a pedestrian mobility aid for the elderly. In order for this type of assistive technology to be useful and accepted by its intended user community, it must enhance the abilities of users, not replace them. This leads to an agent architecture in which the agent must operate without hindering the user's ability to take direct action when they choose. In other words, the agent cannot simply be a proxy for the user's actions. The agent must select its own goals based on observations of its user's actions. This is crucial not only because users may have diminished capacity to explain their actions to an agent, but because the ability of the agent to correctly interpret the user's goals is tied to its ability to act while still allowing the user to "feel in control". We present a mobility aid, i.e. a wheeled walker, which varies its goals and level of activity based on an estimation of its user's intentions. The assistive agent often takes no action, allowing the user to be fully in control. When the ease or safety of the user's travel is threatened, the agent attempts to influence the user's motion based on its belief in the user's goal. By varying the degree of autonomy, the walker can adjust to the user as their abilities change from day to day, or hour to hour. This prevents the walker from "trying to do too much", allowing the user to feel as if they are in control and not being "lead". The world's elderly population is increasing dramatically. In the US, there are more than 34.8 million people over the age of 65. Furthermore, in only 30 years, this number will more than double to 70 million [11] . In Japan, the nation with the highest percentage of seniors on earth, it is estimated that 1 in 5 people will be seniors within 10 years [18] . At the same time the costs of health care, including caring for the elderly, could rise from its current $1.3 trillion to over $4.0 trillion [4] . If robotic technology could be used to enable the elderly to remain independent, significant costs would be saved and the quality of life improved for these people. The attainable cost savings are significant: for every single month that we delay the transition of the elderly population into nursing homes, the US economy saves over $2 billion [2] .. Many seniors have mobility impairments that cause a downward trend in their quality of life. Lack of independence and exercise can have dramatic results. Walkers are used more than any mobility aid except the cane [16] . This paper describes our work in designing an assistive robotic agent based on a wheeled walkers, or rollator, to aid in pedestrian mobility of the elderly [20] . We describe a shared control strategy that enables an elderly user and their walker to collaborate on movement, increasing the ease and safety of the user's travels. Assistive robotic agents can provide invaluable assistance to their users. The connection between the agent and the user is the key to this. In the case of our walker, this connection is made through the walker frame itself. We argue that this interface meets the goals of assistive technology interfaces in that it does not place any additional cognitive burden on the user during use or training. No additional controls are added to the frame so that any user that can operate a traditional walker can operate the assistive robotic walker. Of particular interest is how users express their satisfaction with the agent's control decisions and how that expression influences the actions of the agent. This feedback is crucial for user approval of the walker.. In our system, the user expresses their lack of approval with the agent by resisting its steering decisions. The assistive agent guesses the user's intent and tries to move the walker appropriately. This guess, act, then check for approval paradigm prevents the user from having to explicitly confirm every action of the agent, but inevitably leads to situations where the user's desire does not mesh with the agent's actions. The agent's model of the human must be based on not only its observations of the human's actions, but also on their resistance to any control commands it has attempted. This leads to the question of trust. Is the user resisting the agent's actions because the agent has misinterpreted their goals or because they simply do not agree with the action the agent is taking to accomplish those goals? The more trust the user has in the agent, the more they may be willing to allow the agent to steer because they believe that the agent has correctly divined their goal. But, the user can never develop so much trust in the agent that stop acting, since the agent requires user interaction with the world to continually refine its notion of user goals. Achieving the right level of trust is a focus of this project.. Ultimately, the success of an assistive robotic agent can be measured by the satisfaction of its user. This, in turn, will be a function of how well the device helps the user accomplish their goals and how it "feels" doing it. We believe that our agent is most successful when the user is least aware of its presence. When the user has to resist motions of the walker, they are reminded that there is another agent in the control system. The more that the agent is able to correctly model the user's intent and thus modify their actions appropriately, the more useful it will be. The actual movement of the walker frame can differ only so much from the user's expectations; otherwise their balance will be compromised. The agent can go unnoticed by making minimal changes to user actions. Since elderly users may have difficulty translating their goals into correct moment-to-moment actions, it is hoped that small modifications to the user's actions will not only allow the agent to remain invisible, but will make the user feel more empowered. This is because the walker frame will be doing what they meant it to do, even if that is not what their motor commands told it to do. The PAM-AID project [12] [14] developed an assistive walker for the elderly blind. This device allowed its users to receive exercise when their abilities might otherwise allow. Their walker takes a more active role in guiding its user than our assistive robotic agent because the user's visual acuity is typically very limited. The work also focuses on corridor following since exercise is the prime motivation. This project is investigating what can be done with passive devices in home environments. The PAMM project [6] also seeks to create an assistive walker. While development of the actual walker is ongoing, a "smart cane" has been developed. This is also an active device that guides its user based on directional forces placed on the cane. They use an admittance controller [1] to provide obstacle avoidance while letting forces placed on the cane determine which obstacle-free path to take. However, this control system proved difficult to operate in cluttered environments. Our path weighting scheme should allow the walker to determine the user's intentions using a natural interface, the walker frame itself. It is hoped that the fact that the walker is passive, steered as any other rollator, and only acts in certain situations will make the user feel comfortable and in control. It is possible that the agent's corrective actions will not even be noticed if they are along the user's intended path, since this is what the user "meant to do".. The passive steer-only joint of the walker that relies on the user for propulsion is similar to other passive robots, e.g. Cobots [5] and PADyC [17] . These systems use the same concept to allow a human operator to provide coarse motions and timing, while the joints of a robotic apparatus provide the fine-grained motion. Passive robotic systems have been used for automobile assembly and surgery, but are only beginning to be looked at in the assistive technology field. We believe passive systems will have a large impact.. Various other mobility aids have been developed, mostly for powered wheelchairs [8] [9][13] [21] (an exception being the GuideCane [3] ). While all these devices face similar issues as our walker, wheelchairs are essentially mobile robots ridden by their user. Their users do not rely on them for balance in the same manner that a walker user relies on their walker's frame and so different control algorithms can be used. They also provide a form of hierarchical control in which the mobility aid performs detailed actions based on higher-level user specification. This is different than our agent in which the user must always be involved in the actions of the mobility aid.. The agent/user interaction models discussed here are not new [7] . We have applied them to the domains of assistive technology and robotics and have found that these domains lead to interesting issues in terms of user ability and user satisfaction.

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


Optimal location area design to minimize registration signaling traffic in wireless systems Abstract-In this paper, a new scheme is developed for optimal location area design in wireless systems. New algorithms based on intercell traffic prediction and traffic-based cell grouping are used to select the optimal set of cells for location areas (LAs). The expected intercell movement patterns of mobiles are determined by using the new intercell traffic prediction algorithm. Further, the cells are partitioned into LAs by applying the new traffic-based cell grouping algorithm where the cell pairs with higher intercell mobile traffic are grouped into the same LA. Hence, the inter-LA mobile traffic is decreased by increasing the intra-LA mobile traffic. Experimental results show that this cell grouping algorithm reduces the number of location updates by 27 percent to 36 percent on average compared to proximity-based cell grouping schemes. I N cellular wireless networks, the location information about a mobile is maintained by registration [1] , [13] where mobiles update their location area (LA) information in the home location register (HLR). An LA is a set of cells and may be static or dynamic. A static LA is comprised of a group of cells that are permanently assigned to the LA and is fixed for all mobiles. On the other hand, dynamic LAs are created for each mobile during a registration process. Although signaling traffic can be reduced by using dynamic LAs [3] , [4] , [6] , [10] , [11] , they impose higher computation and separate data storage of LAs for each mobile. As a result, most of the current cellular systems use static LAs.. Both in static and dynamic LA designs, determining the optimal number of cells in each LA is important and challenging. The number of cells in an LA plays a substantial role in the signaling traffic, which is composed of paging and registration traffic in location management. With a trade off, when the number of cells in an LA is high, the registration traffic decreases, but the paging traffic [2] , [12] , [15] increases. On the other hand, for smaller LAs, the registration traffic increases, but the paging traffic decreases. Overall, an optimal number of cells in an LA reduces the location management signaling traffic significantly. Therefore, most of the recent references related to the location area design are focused on how to determine an optimal number of cells for an LA. Models that capture the trade off between the traffic created by paging and registration are proposed in [5] , [7] , and [14] . Another formulation to find the optimal number of cells in an LA and to design global LAs for one-dimensional cellular networks is proposed in [9] .. The number of cells in an LA is not the sole factor affecting the location management signaling traffic. If the cells are partitioned into LAs without considering the expected intercell mobile traffic, increasing the number of cells in an LA may also increase the registration traffic, as well as the paging traffic. Hence, the cell-partitioning technique is also very important. If the LAs are designed such that the inter-LA mobile traffic is reduced, the registration traffic decreases for the same LA size.. In this paper, instead of determining the optimal number of cells in an LA as in [5] , [7] , [9] , [14] , we focus on selecting the optimal set of cells for each static LA. We use the intercell traffic prediction and traffic-based cell grouping schemes consecutively to partition the cells into LAs. The intercell traffic prediction scheme is applied to determine the expected intercell movement patterns of mobiles. The total number of intercell movements of mobiles can be predicted by examining the roads (highways, carriageways, footpaths, etc.) between neighbor cells. These predictions are used by the traffic-based cell grouping scheme to group cells into LAs. The neighbor cells with higher intercell traffic are assigned to the same LAs. Hence, the inter-LA movements of mobiles are decreased by increasing the intra-LA movements. The inter-LA movements of mobiles create registration traffic. Therefore, we can reduce signaling traffic by increasing the intra-LA movements of mobiles.. The remainder of the paper is organized as follows: In Section 2, we describe the static location area design (LAD) without considering the intercell mobility patterns, namely, the proximity-based LAD. In Section 3, we introduce our new scheme for static location area design where LAs are created based on the expected intercell mobile traffic. Further, we introduce an intercell traffic prediction scheme, an optimal traffic-based LAD model, and an approximation algorithm for optimal traffic-based LAD. We give experimental results in Section 4. Finally, we conclude the paper in Section 5. In static LAD, the cells of a cellular wireless network are partitioned into LAs where an LA is comprised of a group of cells that are permanently assigned to the LA and fixed for all mobiles. A mobile crossing an LA border registers its new LA. When there is an incoming call for the mobile, the cells in the last registered LA are paged. The number of cells in an LA is the major factor that constitutes the number of registrations and paged cells. Therefore, most of the recent references [5] , [7] , [9] , [14] related to the location area design are focused on how to determine the optimal number of cells for an LA. In these papers, it is assumed that the registration traffic decreases and the paging traffic increases for larger LAs. However, increasing the number of cells does not always decrease the registration cost if the cells are grouped into LAs without considering that the mobility traffic between cells is different for each cell pair. This is clearly observed in our experiments. When we design LAs based on only proximity, we observe that the number of location updates may increase for higher LA sizes. In our experiments, we also observe that designing LAs based on Table 3 . Fig. 18 . m for the multiplication factors in Table 3 . expected intercell mobile movements significantly decreases inter-LA mobile movements.. Being motivated by this, we developed the TB-LAD scheme where we first predict the mobile traffic between the cells based on the characteristics of roads traversing them. Then, using these traffic expectations, the trafficbased cell grouping technique partitions cells into LAs such that the neighbor cells with higher intercell traffic are assigned to the same LAs. Since the number of cells in an LA is not a changing parameter in TB-LAD, it does not increase or decrease the paging traffic. However, better design of an LA, i.e., partitioning cells into LAs based on predicted intercell movements of mobiles, reduces the number of location updates. Therefore, TB-LAD decreases the number of location updates without increasing the number of paged cells during a call delivery.. To evaluate the performance of our new scheme, we performed experiments by using data collected in a metropolitan area. We examine the relation of inter-LA traffic with cell size and number of cells in an LA and compare the performance of our design with the performance of PB-LAD. Experimental results show that our technique TB-LAD reduces inter-LA traffic 27 to 36 percent on the average over PB-LAD. TB-LAD outperforms PB-LAD when the average cell sizes are larger than 2,000 meters and the average number of cells in an LA is larger than nine. For our experiment region, which is an actual metropolitan city, our scheme manages to partition the cells into LAs so successfully that the number of location updates becomes almost zero when the LA size is larger than 13 cells and the cell size is larger than 2,500 meters.

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


Ontology matching using vector space Abstract. Interoperability of heterogeneous systems on the Web will be achieved through an agreement between the underlying ontologies. Ontology matching is an operation that takes two ontologies and determines their semantic mapping. This paper presents a method of ontology matching which is based on modeling ontologies in a vector space and estimating their similarity degree by matching their concept vectors. The proposed method is successfully applied to the test suit of Ontology Alignment Evaluation Initiative 2005 [10] and compared to the results reported by other methods. In terms of precision and recall, the results look promising. The current World Wide Web has over 22.47 billion pages [17] , but the vast majority of them are in human readable format only. In order to allow software agents to understand and process the web information in a more intelligent way, researchers have created the Semantic Web vision [15] , where data has structure. Like the Web, the semantic Web will necessarily be distributed and heterogeneous. Therefore, the integration of resources found on the semantic Web is a key issue. A standard approach to the resulting problem lies in the use of ontologies for data description. Ontologies allow users to organize information into taxonomies of concepts, each with their properties, and describe relationships between concepts [16] . However, the available ontologies could themselves introduce heterogeneity: given two ontologies, the same entity can be given different names in each of them or simply be defined in different ways, whereas both ontologies may express the same knowledge but in different languages. So, one of the key challenges of Semantic Web is to find semantic correspondences between ontologies. The underlying problem, which we call the ontology matching (or alignment), is the operation of taking two distinct ontologies, finding a set of entities with similar relationships which exist in both ontologies and return the similar entities. Shvaiko et al. classifies ontology alignment techniques in two general categories: element-level techniques and structure-level techniques [5] . The former techniques concentrate just on individual elements while in latter approaches the structural arrangement of elements and their relation to each other is more of interest. The structural-level techniques involve Graph-based techniques which consider the input as labeled graph, Taxonomy-based techniques which consider only the specialization relation, Repository of structures which stores schemas/ontologies and their fragments together with pairwise similarities (e.g., coefficients in the [0 1] range) between them and finally Model-based algorithms which handle the input based on its semantic interpretation (e.g., model-theoretic semantics). Furthermore, ontology matchers can be categorized into automatic and semi-automatic techniques. Automatic ontology matchers are those which perform their operation independent of human operator, while semi-automatic techniques are dependent on user preferences. This paper presents an automatic taxonomy-based ontology alignment technique that is based on a vector matching method. Any ontology consists of a set of concepts and each concept is described by a set of properties. These concepts and properties define a space such that each distinct concept and property represents one dimension in that space. Modeling ontologies in multi-dimensional vector spaces will enable us to use vector matching methods for performing ontology alignment. An iterative approach has been employed to achieve convergence, in which vectors representing ontology concepts and properties are matched iteratively and their similarity degree is estimated. In order to model two ontologies in a vector space, RDF [1] and OWL [7] subclass predicates are utilized and concepts are described with respect to their ancestors and successors and properties. Properties are also described with respect to their domain and range concepts. The rest of the paper is organized as follows. In section 2 we discuss state of the art of matching systems from the structured base ontology matching perspective. Our approach is presented in section 3. Experimental results are reported in Section 4. Finally, Section 5 contains some conclusions and future work. We carried out experiments on OAEI (Ontology Alignment Evaluation Initiative) 2005 test suite [10] . The evaluation organizers provide a systematic benchmark test suite with pairs of ontologies to align as well as expected (human-based) results. The ontologies are described in OWL-DL and serialized in the RDF/XML format. The expected alignments are provided in a standard format expressed in RDF/XML.. There are different groups of tests in this benchmark [10] : Simple tests (tests 1xx). such as comparing the reference ontology with itself, with another irrelevant ontology or the same ontology in its generalization or restriction to OWL-Lite .. Systematic tests (tests 2xx) . that are obtained by discarding some features of the reference ontology. (The considered features are names, comments, hierarchy, instances, relations, restrictions, etc.). • Tests 201 to 210: focus on labels and comments of entities. Names of entities can be replaced by random strings, synonyms, names with different conventions, strings in a language other than English.. • Tests 221 to 247: for these tests the structure is changed. In fact hierarchy can be suppressed, expanded or flattened; properties can be suppressed or their imposed restrictions on classes are discarded and classes can be expanded or flattened.. • Tests 248 to 266: for these tests, names of entities are replaced by random strings; hierarchy can be suppressed, expanded or flattened and properties can be suppressed. Four real-life ontologies of bibliographic references (3xx). that were found on the web and left mostly untouched. These real world ontologies are a combination of complications of the previously mentioned tests. We obtained 3 kinds of results in our experiments: 1) Excellent results from ontologies that have similar names (labels) (in tests 1xx, 221 to 247). Because similar names make vectors more similar to each other. In fact the labels are the most important feature to recognize alignments in this approach and if the labels denote an alignment, every thing else can be abandoned. As table 1 shows, both precisions (the number of correct alignments found, divided by the total number of alignments found) and recalls(the number of correct alignments found, divided by the total number of expected alignments) are equal to "1" except for 3 cases; 2) Good results in ontologies are those with similar structures but different naming conventions (in tests 201 to 210 and 249). However the labels are the most important feature in distinction of alignments, the structures of ontologies also play a key role in our approach. We obtained precisions and recalls in the range of 0.78 to 1 and 0.85 to 1 respectively ( Although VBOM only focuses on sub/super class chains and properties in ontologies, our experiments show that it is comparable with hybrid models like foam [8] and ola [14] and omap [18] that use linguistic and structural methods. Even in some cases VBOM worked better than the hybrid methods.. VBOM results show that in ontologies that include the sub/super predicate, it is possible to achieve reasonable results by focusing on this predicate and properties. This method is simple and efficient. The Cupid system [9] implements a generic schema matching algorithm combining linguistic and structural schema matching techniques, and computes normalized similarity coefficients with the assistance of a precompiled thesaurus. The algorithm contains two phases. The first phase, called linguistic matching and the second one is the structural matching of schema elements based on the similarity of their contexts or vicinities. Finally the weighted similarity, a mean of the first and second phases results are calculated. Anchor-PROMPT [2] is another structure base algorithm. It takes as input a set of pairs of related termsanchors-from the source ontologies. Either the user identifies the anchors manually or the system generates them automatically with the help of string-based techniques, or another matcher computing linguistic (dis)similarity between frame names (labels at nodes) [6] . Then it refines them based on the ontology structures and users' feedback. Anchor-PROMPT traverses the paths between the anchors in the corresponding ontologies. As it traverses the two paths, Anchor-PROMPT increases the similarity score for the pairs of terms in the same positions in the paths. It aggregates the similarity score from all the traversals to generate the final similarity score.. The compositional systems like [12] , [4] consist of a set of elementary matchers based on rules, exploiting codified knowledge in ontologies, such as information about super-and sub-concepts, super-and sub-properties, etc. The approach described in [11] is relatively similar to our method. It uses vector characteristics and presents a semantic similarity measure based on a matrix representation of nodes from an RDF labeled directed graph. In this algorithm an entity is described with respect to how it relates to other entities using N-dimensional vectors, N being the number of selected external predicates. Similarities are computed using graph matching algorithm [13] . There are some other methods that benefit from structure of ontologies as well as other techniques such as ola [14] , foam [8] and omap [18] . Vector Based Ontology Matching, which we present here, is another vector based model that providing another suggestions for possible matching terms.

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


A Randomized Exhaustive Propositionalization Approach for Molecule Classification Drug discovery is the process of designing compounds that have desirable properties, such as activity and non-toxicity. Molecule classification techniques are used along this process to predict the properties of the compounds in order to expedite their testing. Ideally, the classification rules found should be accurate and reveal novel chemical properties, but current molecule representation techniques lead to less than adequate accuracy and knowledge discovery. This work extends the propositionalization approach recently proposed for multi-relational data mining in two ways: it generates expressive attributes exhaustively and it uses randomization to sample a limited set of complex ("deep") attributes. Our experimental tests show that the procedure is able to generate meaningful and interpretable attributes from molecular structural data, and that these features are effective for classification purposes. The molecule classification problem is a data mining problem (Jiawei and Kamber 2000) that consists of classifying 2 groups of molecules that exhibit different behavior in order to predict the group to which a new molecule belongs. This problem arises in a variety of situations, especially during the different phases of a drug design process, where it is needed to distinguish toxic from non toxic molecules, active from non active molecules, and so on. For a fairly comprehensive overview of the role played by molecule classification within a drug design process, see Weaver (2004) . Molecule classification may be addressed in two ways: with a traditional classification technique or with a relational learning technique.. Traditional classification techniques, such as decision trees (Rokach and Maimon 2005) and support vector machines (Cristianini and Shawe-Taylor 2000) , operate on data sets represented by a single table -where the rows are molecules and the columns are predefined attributes that describe them. While these methods have enjoyed some success (Svetnik et al. 2003) , they require a molecule representation that preserves as much information about the molecule as possible and such representation may not be immediately obvious even for someone with expert knowledge.. A great variety of numerical representations of chemical structures exist within the field of Cheminformatics (Todeschini and Consonni 2000) , and they can be classified based upon the degree of structural information required to compute them. At the simplest level, 0-Dimensional descriptors consist of counts of atoms or summations of the properties of atoms present within a compound. These include such values as molecular weight, number of atoms and number of bonds. 1-Dimensional descriptors require a certain degree of connectivity information and typically consist of counts of particular types of fragments (e.g., the number of amide groups or the number of carboxylic acids), or counts of single atoms with particular bonding patterns. 2-Dimensional descriptors have access to the complete connectivity graph of each molecule. A great many descriptors can be computed from this topological representation and include values such as walk and path counts, graph theoretic values such as minimum or maximum eigenvalues, topological fragment indicators or frequencies, and topological separation indices (e.g., the presence/frequency of carbon and chlorine atoms separated by N bonds), among many others. 3-Dimensional descriptors require not only the topological connectivity matrix but additionally the geometric arrangement of atoms within 3-D space. This leads to additional matrixbased calculations as well as geometrically centered mass, charge, and other property indices, as well as geometric separation indices. Considering that many compounds can adopt multiple 3-dimensional conformations, 4-dimensional descriptors attempt to capture the details of multiple, equally viable arrangements of a molecule's atoms. Interestingly, it has been shown that on average, 2-dimensional descriptors perform as well or better than higher dimensional representations calling into question the need to expend computational effort to predict low-energy 3-dimensional structures (Matter and Potter 1999, Dixon and Merz 2001) .. One of the most commonly and successfully used molecular representations is the binary fingerprint. Molecular fingerprints consist of a vector of binary digits which represent the presence or absence of a particular molecular fragment within the molecule. A surprisingly diverse collection of fingerprints exist, two of which are used here. The MACCS Keys are a collection of pre-existing molecular substructures (that have presumably been deemed 'interesting' or 'useful'), each on-bit identifies that fragment as existing within the structure in question (Durant et al. 2002) . While being used very commonly and showing reasonable success across applications, a fundamental drawback of this fingerprint type is that the set of fragments is unchanging and may over time lose its useful or interesting character or may fail to include newly identified fragments emerging from the chemistry space. We also tested an alternative approach, which we call "Daylight", consisting of generating a compendium of molecular fragments from the tested datasets (independently). The simplest method of fragment generation consists of enumeration of unique paths (unique in atom type and connectivity) up to a maximum length within the set of molecules followed by a hash function to assign bits within a fingerprint of desired length 1 . An example of an alternative fingerprint representation is to generate all fragments consisting of atoms and bonds that extend radially from a central atom the same distance up to a defined maximum (Rogers et al. 2005) . However, many variations of molecular fingerprinting exist (Hert at al. 2004) .. All these representation techniques suffer from the same fundamental drawback: they consider only predefined characteristics or methods of computation and ignore others outside a predefined scope. This leads to two major limitations, one on the accuracy and one on the knowledge discovery. First, King et al. (2001) noted that any predefined attribute representation causes some loss of information because "all the information about a particular example is forced into a single row of a table", which reduces the upper bound of the classification accuracy. Second, the classification rules cannot involve characteristics other than the ones included in the chosen representation. In other words, a traditional data mining process is incapable of generating attributes that were not included in the data set, limiting the knowledge discovery to expressing the classification rule in terms of a logical expression that involves the predefined attributes.. Relational learning techniques do not have these shortcomings. Instead of starting from a single table, they consider a database and search for patterns that involve more tables. A compounds database, for example, consists of a table containing the molecules, a table containing the atoms, and a table containing the bonds, connected to each other through foreign key (FK) relationships. The patterns found are represented by queries performed on a subset of tables. In practice, these techniques search for classification patterns in the space of the queries, by finding the ones that yield to the best classification accuracy. In this way, they potentially use all information contained in the database and find new patterns that have not been explicitly considered.. There are two families of relational learning techniques: multi relational decision trees (MRDTs) and propositionalization. In the former, the data set is iteratively split by successively adding refinements, creating a decision tree -as in Atramentov et al. (2003) -where each leaf corresponds to the attribute needed to classify a subset of molecules. In the latter, the database navigation leads to the generation of a set of attributes used to create a tabular data set on which the data mining task is eventually executed. In practice, the goal of propositionalization techniques is only the generation of new features, after which the classification task is executed by a given classifier.. MRDTs tend to find patterns corresponding to local optima because the refinements are built in a greedy fashion, though variations have been recently proposed by Serrurier and Prade (2008) . On the other hand, propositionalization techniques overcome this problem by generating as many attributes as possible without evaluating their utility for the classification, until they have all been generated. The separation between feature generation and classification highlights a practical advantage of propositionalization over MRDTs, namely, it allows for the application of any classification technique. This makes it possible to exploit all the existing work that has been done in this field. Using well studied classifiers accelerates the implementation and increases the classification performance.. On the other hand, MRDTs have an important advantage over propositionalization: the feature space of MRDT techniques is larger. In other words, there are classification rules that can be found by MRDTs and not by propositionalization. The features generated by propositionalization have two limitations compared to MRDTs: they are less "deep" and less "expressive". Both "depth" and "expressivity" of a feature depend on the complexity of the query used to generate the feature. As it will be explained, this complexity can be arbitrarily large, making the feature space infinite. Obviously, the propositionalization approach needs the definition of a limit in order to stop, while MRDT approaches do not, because the tree will continue growing -generating deeper and more expressive features -as long as the growth increases the accuracy. These differences, together with examples, will be explored below.. Our work extends the current approaches for propositionalization in two ways. First, we generate "expressive" attributes that are not generated by existing approaches, making our approach an "exhaustive" propositionalization approach, in the sense that it is capable of generating all the attributes that can be found using a SQL query. Although the attribute search space is exhaustive for obvous practical reasons the approach does not generate all attributes. Second, we randomly choose and generate a few "deep" attributes, which are ignored by existing approaches, making our approach a "randomized" propositionalization approach. The focus is on the feature generation and not on the classification; therefore we use a set of publicly available classifiers and compare the accuracy obtained with different propositionalization approaches. A statistical analysis shows that our extensions significantly improve the performance of the classification. Interestingly, ours is a general purpose method, and can be used to tackle any classification problem, not only molecule classification. We improve the current propositionalization procedures that are typically used in the process of drug discovery by creating a method that generates more expressive and complex (deeper) attributes. Our experimental testing shows that the multi-relational data mining (MRDM) methodology that we employed is competitive with current methods within the field of cheminformatics and quantitative structure activity relationship modeling. MRDM has the advantage that no precalculated molecular representations were required but rather the technique uses the molecular structure itself and derives the necessary descriptors from it during the modeling process. Both datasets utilized are very well characterized and represent two biochemical processes that differ dramatically in their complexity, and in both cases MRDM is competitive with published results and those we have obtained previously using more traditional techniques (not shown). To our knowledge, this represents the first application of the MRDM technology within the field of drug discovery highlighting their potential and opening new avenues of research within this hybrid field. Techniques such as these provide a mechanism to prioritize chemical compounds for purchase or synthesis and increase the probability of bringing a successful drug to market within a shorter time and at reduced costs. Given that current estimates of the cost to bring a single drug to market in the range of $500 million to $2,000 million (DiMasi, Hansen et al. 2003) , efforts to reduce costs are necessary to ensure efficient improvements in healthcare.. Future research opportunities based on our work include improving the accuracy and interpretability of the attributes that the procedure identifies. We have identified that embedding a procedure for selecting attributes (that is not based on sampling) is a challenging problem. An improved representation of the ADs may result in more interpretable attributes. We currently represent them by a SQL query, but a graphical representation -where an attribute is represented as the presence or absence of a particular characteristic -may provide additional insights. Finally, we believe that our propositionalization approach can be applied to other classification problems in fields such as marketing and finance.

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


Compiling regular patterns to sequential machines Pattern matching combined with regular expressions has many applications including semistructured data matching and lexical analysis in compilers. Variables in patterns allow one to refer to parts of the matching input. But some regular patterns suffer from inherent ambiguity, yielding more than one valid result. A match policy like shortest or longest match can disambiguate such patterns.In this paper, we show that regular pattern matching corresponds to sequential transduction. We derive straightforward ways to optimally compile regular patterns to sequential machines and to decide when regular patterns are unambiguous. Unambiguous patterns can be matched in a single traversal of the input. Ambiguities in patterns correspond to nondeterminism in sequential machines. Applying the match policy optimally yields two deterministic sequential machines, which produce the shortest match in two consecutive runs. Many programming languages have a pattern matching construct that can be generalized to deal with regular expressions. This is especially useful for decomposing semistructured data in languages like XDUCE [12] and CDUCE [1] . For general-purpose programming, regular pattern matching is used in XTATIC [10, 9] , HARP [4] (an extension of HASKELL) and SCALA [16] . XEN filters [15] and XPATH expressions are related constructs. Regular pattern matching in various forms is also being applied to DNA sequences or TCP network packets, and for lexical analysis in parsers. Language support for regular patterns can be highly desirable in such domains.. Regular patterns are a natural generalization of pattern matching as known from ML and HASKELL. Here is an example on how to Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. We use the convention that is a wildcard pattern and that a binding pattern v@p matches everything p matches, binding the result to the variable v. The pattern should bind everything between "From : " and the first newline character to the variable x. But the iterated wildcard pattern matches arbitrarily many arbitrary characters, so the binding pattern x @ might possibly stretch far beyond the first newline. The pattern is ambiguous; several values for x are possible.. Ambiguity can be removed by imposing a match policy. We are interested in the shortest match here because we want binding to stop at the first newline character. Ambiguities appear also in absence of wildcards, as can be seen from the minimal example (x@'a' , y@'a' ).. In this paper, we give a formal model of shortest match and derive decision procedures and algorithms from it. The essential idea is that binding to a variable can be seen as tagging parts of the input with the variable. Let us agree on writing xa for appending input element a to variable x. Then matching "From : jj@foo.net N L To : . . . " against the email pattern above is conceptually the same as transforming the input string to. The desired substitution {x → "jj@foo.net"} can be read off the output (do not confuse the character @ with the binding operator @). The shortest match and the semantics of pattern matching can be concisely specified by reasoning on such annotated strings. We obtain a natural formulation of pattern matching as lengthpreserving rational transduction.. Contributions. The contributions of this paper are (1) the (apparently first) sequential machine formulation of regular pattern matching, (2) algorithms based on this model that generate code with linear runtime complexity, (3) a decision procedure for unambiguous patterns, (4) an intuitive account on match policies and position automata. The accompanying report [7] discusses various generalizations and applications and should be consulted for details.. The technique discussed in this paper is implemented in the reference SCALA compiler [6] and used in practice. The results should help implement regular pattern matching, relate different approaches and proof techniques, and prevent implementors from reinventing the wheel.. Related work. Ambiguities are first mentioned by Hosoya, Vouillon and Pierce [12] . Disambiguation of patterns is specified rigorously by Tabuchi et al [17] .. Frisch and Cardelli [8] implement disambiguated pattern matching. Their goals and assumptions differ though: (1) They consider "greedy matching", a local approximation of the longest match. We show how the longest match can be obtained without approximation with the same runtime complexity. (2) Their approach is presented in a framework that prohibits the rewriting of regular expressions. In our approach however, we show that rewriting turns out to be indispensable for longest/shortest match. Moreover, the correspondence with sequential machines presented here seems rather more intuitive than the sets of structured values they employ.. Broberg, Farre and Svenningsson [4] add regular patterns to HASKELL. They handle ambiguities with greedy and non-greedy operators, and by returning a list of all matches in other cases. This poses challenges to efficient implementation, however.. Disambiguated operators are also present in PERL and JAVA. We sketch how our approach can be extended to disambiguated operators without sacrificing efficiency.. Organization of the paper The accompanying technical report [7] contains the complete definitions, proofs and a larger example. We introduce patterns and bindings in Section 2. We then recall position automata and put them in correspondence to shortest match in Section 3. In Section 4, we introduce sequential machines. In Section 5, we turn to efficient compilation to these sequential machines, followed by conclusion, acknowledgment and references. We showed how to compile regular patterns with a match policy to sequential machines. Rewriting regular expressions is crucial in our approach. The longest/shortest match of ambiguous patterns is obtained in two runs, which is optimal in the general case.. The accompanying report discusses straightforward generalizations, and sketches changes necessary for longest (left-longest) match, which is derived from the minimal run.. Further research has to be done on whether sequential machines can be used in compiler optimizations.

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


Dual-Bounded Generating Problems: Partial And Multiple Transversals Of A Hypergraph Abstract. We consider two natural generalizations of the notion of transversal to a finite hypergraph, arising in data-mining and machine learning, the so called multiple and partial transversals. We show that for an arbitrary hypergraph the families of multiple and partial transversals are both dual-bounded in the sense that the size of the corresponding dual hypergraph is bounded by a polynomial in the cardinality and the length of description of the input hypergraph. Our bounds are based on new inequalities of extremal set theory and threshold Boolean logic, which may be of independent interest. We also show that the problems of generating all multiple and all partial transversals for a given hypergraph are polynomial-time reducible to the generation of all ordinary transversals for another hypergraph, i.e., to the well-known dualization problem for hypergraphs. As a corollary, we obtain incremental quasi-polynomial-time algorithms for both of the above problems, as well as for the generation of all the minimal binary solutions for an arbitrary monotone system of linear inequalities.Key words. Transversals of hypergraphs, dualization of monotone Boolean functions, incremental polynomial time algorithms, data mining, maximal infrequent sets, minimal frequent sets, AMS subject classifications. 68R05, 68Q25, 68Q321. Introduction. In this paper we consider some problems involving the generation of all subsets of a finite set satisfying certain conditions. The most well-known problem of this type, the generation of all minimal transversals, has applications in combinatorics [31] , graph theory [20, 22, 32, 34]

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