The plurality strategy on graphs

The Majority Strategy for finding medians of a set of clients on a graph can be relaxed in the following way: if we are at v, then we move to a neighbor w if there are at least as many clients closer to w than to v (thus ignoring the clients at equal distance from v and w). The graphs on which this Plurality Strategy always finds the set of all medians are precisely those for which the set of medians induces always a connected subgraph

Median computation in graphs using consensus strategies

Following the Majority Strategy in graphs, other consensus strategies, namely Plurality Strategy, Hill Climbing and Steepest Ascent Hill Climbing strategies on graphs are discussed as methods for the computation of median sets of profiles. A review ofalgorithms for median computation on median graphs is discussed and their time complexities are compared. Implementation of the consensus strategies on median computation in arbitrary graphs is discussed.majority strategy;consensus strategy;Hill climbing median computation

Consensus Strategies for Signed Profiles on Graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes.median;consensus function;median graph;majority rule;plurality strategy;Graph theory;Hamming graph;Johnson graph;halfcube;scarcity strategy;Discrete location and assignment;Distance in graphs

Median computation in graphs using consensus strategies

Following the Majority Strategy in graphs, other consensus strategies, namely Plurality Strategy, Hill Climbing and Steepest Ascent Hill Climbing strategies on graphs are discussed as methods for the computation of median sets of profiles. A review of algorithms for median computation on median graphs is discussed and their time complexities are compared. Implementation of the consensus strategies on median computation in arbitrary graphs is discussed

Consensus strategies for signed profiles on graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from (+,-). Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

Consensus Strategies for Signed Profiles on Graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from {+,-}. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a - sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

Heuristic Voting as Ordinal Dominance Strategies

Decision making under uncertainty is a key component of many AI settings, and in particular of voting scenarios where strategic agents are trying to reach a joint decision. The common approach to handle uncertainty is by maximizing expected utility, which requires a cardinal utility function as well as detailed probabilistic information. However, often such probabilities are not easy to estimate or apply. To this end, we present a framework that allows "shades of gray" of likelihood without probabilities. Specifically, we create a hierarchy of sets of world states based on a prospective poll, with inner sets contain more likely outcomes. This hierarchy of likelihoods allows us to define what we term ordinally-dominated strategies. We use this approach to justify various known voting heuristics as bounded-rational strategies.Comment: This is the full version of paper #6080 accepted to AAAI'1

Mining Brain Networks using Multiple Side Views for Neurological Disorder Identification

Mining discriminative subgraph patterns from graph data has attracted great interest in recent years. It has a wide variety of applications in disease diagnosis, neuroimaging, etc. Most research on subgraph mining focuses on the graph representation alone. However, in many real-world applications, the side information is available along with the graph data. For example, for neurological disorder identification, in addition to the brain networks derived from neuroimaging data, hundreds of clinical, immunologic, serologic and cognitive measures may also be documented for each subject. These measures compose multiple side views encoding a tremendous amount of supplemental information for diagnostic purposes, yet are often ignored. In this paper, we study the problem of discriminative subgraph selection using multiple side views and propose a novel solution to find an optimal set of subgraph features for graph classification by exploring a plurality of side views. We derive a feature evaluation criterion, named gSide, to estimate the usefulness of subgraph patterns based upon side views. Then we develop a branch-and-bound algorithm, called gMSV, to efficiently search for optimal subgraph features by integrating the subgraph mining process and the procedure of discriminative feature selection. Empirical studies on graph classification tasks for neurological disorders using brain networks demonstrate that subgraph patterns selected by the multi-side-view guided subgraph selection approach can effectively boost graph classification performances and are relevant to disease diagnosis.Comment: in Proceedings of IEEE International Conference on Data Mining (ICDM) 201

Group Modeling : selecting a sequence of television items to suit a group of viewers

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