Abstract: A method and system for sensor network localization including communicating with a plurality of directly neighboring sensor nodes to determine a patch in a sensor network, localizing the patch, generating a system of equations from computed local coordinates of the patch, incorporating global coordinates of a plurality of sensor nodes into the system of equations, and solving the equations using a distributed equation solver is described. The described methods and systems have utility in the arts of military, radio, police, fire, rescue, business, travel, and other diverse applications.

Abstract: A method and apparatus for measuring and extracting proximity in networks are disclosed. In one embodiment, the present method receives a network from a user for analysis and extraction of a smaller proximity sub-graph. The method computes a candidate sub-graph and determines at least one Cycle Free Escape Conductivity (CFEC) proximity of at least two nodes in accordance with the candidate sub-graph. The method then extracts and presents a proximity sub-graph that best captures the proximity.

Abstract: A system and method for identifying a plurality of nodes for a circular layout, each of the plurality of nodes to be connected via an edge to at least one other of the plurality of nodes, fixing all of the plurality of nodes on a unit circle, except for one of the nodes, moving the unfixed node to a barycenter of the fixed plurality of nodes, projecting the unfixed node to the unit circle of the circular layout and displaying the circular layout.

Abstract: A method and apparatus for measuring and extracting proximity in networks are disclosed. In one embodiment, the present method receives a network from a user for analysis and extraction of a smaller proximity sub-graph. The method computes a candidate sub-graph and determines at least one Cycle Free Escape Conductivity (CFEC) proximity of at least two nodes in accordance with the candidate sub-graph. The method then extracts and presents a proximity sub-graph that best captures the proximity.

Abstract: A system and method for identifying a plurality of nodes for a circular layout, each of the plurality of nodes to be connected via an edge to at least one other of the plurality of nodes, fixing all of the plurality of nodes on a unit circle, except for one of the nodes, moving the unfixed node to a barycenter of the fixed plurality of nodes, projecting the unfixed node to the unit circle of the circular layout and displaying the circular layout.

Abstract: Methods, systems, and products are disclosed for graphing data. A layout is retrieved that comprises locations for vertices. A proximity location is generated for each vertex. Each vertex's location from the layout is merged with each vertex's proximity location. A cost function associated with the layout is minimized.

Abstract: A method and system for drawing directed graphs including receiving data coordinates associated with nodes for graphing, performing a constrained stress minimization, and outputting results of the constrained stress minimization and displaying the results on a visual medium. The described method may take the form of instructions residing on a computer readable medium. The described method and system may be utilized for drawing directed graphs in a very wide range of applications ranging from gene networks, to flowcharts, to display of relational characteristics of breakfast cereal and so on.

Abstract: Example collaborative filtering techniques provide improved recommendation prediction accuracy by capitalizing on the advantages of both neighborhood and latent factor approaches. One example collaborative filtering technique is based on an optimization framework that allows smooth integration of a neighborhood model with latent factor models, and which provides for the inclusion of implicit user feedback. A disclosed example Singular Value Decomposition (SVD)-based latent factor model facilitates the explanation or disclosure of the reasoning behind recommendations. Another example collaborative filtering model integrates neighborhood modeling and SVD-based latent factor modeling into a single modeling framework. These collaborative filtering techniques can be advantageously deployed in, for example, a multimedia content distribution system of a networked service provider.

Abstract: A system and method for identifying a plurality of nodes for a circular layout, each of the plurality of nodes to be connected via an edge to at least one other of the plurality of nodes, fixing all of the plurality of nodes on a unit circle, except for one of the nodes, moving the unfixed node to a barycenter of the fixed plurality of nodes, projecting the unfixed node to the unit circle of the circular layout and displaying the circular layout.

Abstract: A method and system for graph mining direction-aware proximity measurements. A directed graph includes nodes and directed edges connecting the nodes. A direction-aware proximity measurement is calculated from a first node to a second node or from a first group of nodes to a second group of nodes. The direction-aware proximity measurement from a first node to second node is based on an escape probability from the first node to the second node. Disclosed herein are methods for efficiently calculating one or multiple direction-aware proximity measurements. The direction-aware proximity measurements can be used in performing various graph mining applications.

Abstract: Systems and techniques for generating item ratings for a user in order to allow for recommendations of selected items for that user. A set of known ratings of different items for a plurality of users is collected and maintained, and these known ratings are used to estimate rating factors influencing ratings, including user and item factors. Initial user and item factors are estimated and new user and item factors are successively added, with the original rating factors being progressively shrunk so as to reduce their magnitude and their contribution to the rating estimation as successive factors are added. When an appropriate number of user and item factors has been estimated, the rating factors are used to estimate ratings of items for a user, and the estimated ratings are employed to generate recommendations for that user.

Abstract: Systems and techniques for estimation of item ratings for a user. A set of item ratings by multiple users is maintained, and similarity measures for all items are precomputed, as well as values used to generate interpolation weights for ratings neighboring a rating of interest to be estimated. A predetermined number of neighbors are selected for an item whose rating is to be estimated, the neighbors being those with the highest similarity measures. Global effects are removed, and interpolation weights for the neighbors are computed simultaneously. The interpolation weights are used to estimate a rating for the item based on the neighboring ratings, Suitably, ratings are estimated for all items in a predetermined dataset that have not yet been rated by the user, and recommendations are made of the user by selecting a predetermined number of items in the dataset having the highest estimated ratings.

Abstract: Certain exemplary embodiments comprise a method, comprising: in a sensor node network comprising a plurality of sensor nodes, each sensor node from the plurality of sensor nodes having location coordinates that are initially unknown, each sensor node from the plurality of sensor nodes having neighbors, each sensor node from the plurality of sensor nodes capable of determining distances only to that sensor node's neighbors: for each sensor node from the plurality of sensor nodes, communicating with that sensor node's neighbors; and based only on communications between neighbors, in a fully distributed manner, generating a sensor node network layout that indicates the location coordinates of each sensor node.

Abstract: Certain exemplary embodiments comprise a method, comprising: in a sensor node network comprising a plurality of sensor nodes, each sensor node from the plurality of sensor nodes having location coordinates that are initially unknown, each sensor node from the plurality of sensor nodes having neighbors, each sensor node from the plurality of sensor nodes capable of determining distances only to that sensor node's neighbors: for each sensor node from the plurality of sensor nodes, communicating with that sensor node's neighbors; and based only on communications between neighbors, in a fully distributed manner, generating a sensor node network layout that indicates the location coordinates of each sensor node.