Abstract: A method and apparatus for tracking communications in a network are disclosed. For example, the method receives a subscription from a customer for a service to track at least one variable associated with a plurality of communicants of the customer. The method identifies a plurality of members of a social network of the customer, and gathers communication data associated with the plurality of members for tracking the at least one variable. The method then displays at least one result derived from the communication data to the customer.

Abstract: Described is a system and method for receiving a signal for transmission and encoding the signal into a plurality of linear projections representing the signal. The encoding includes defining a transform matrix. The transform matrix being defined by processing the signal using a macroseparation matrix, processing the signal using a microseparation matrix and processing the signal using an estimation vector.

Abstract: The first fast solution to the problem of tracking wavelet representations of one-dimensional and multi-dimensional data streams based on a stream synopsis, the Group-Count Sketch (GCS) is provided. By imposing a hierarchical structure of groups over the data and applying the GCS, our algorithms can quickly recover the most important wavelet coefficients with guaranteed accuracy. A tradeoff between query time and update time is established, by varying the hierarchical structure of groups, allowing the right balance to be found for specific data streams. Experimental analysis confirmed this tradeoff, and showed that all the methods significantly outperformed previously known methods in terms of both update time and query time, while maintaining a high level of accuracy.

Abstract: A method of distributed approximate query tracking relies on tracking general-purpose randomized sketch summaries of local streams at remote sites along with concise prediction models of local site behavior in order to produce highly communication-efficient and space/time-efficient solutions. A powerful approximate query tracking framework readily incorporates several complex analysis queries, including distributed join and multi-join aggregates and approximate wavelet representations, thus giving the first known low-overhead tracking solution for such queries in the distributed-streams model.

Abstract: The invention comprises a method and apparatus for determining a rank of a query value. Specifically, the method comprises receiving a rank query request, determining, for each of the at least one remote monitor, a predicted lower-bound rank value and upper-bound rank value, wherein the predicted lower-bound rank value and upper-bound rank value are determined according to at least one respective prediction model used by each of the at least one remote monitor to compute the at least one local quantile summary, computing a predicted average rank value for each of the at least one remote monitor using the at least one predicted lower-bound rank value and the at least one predicted upper-bound rank value associated with the respective at least one remote monitor, and computing the rank of the query value using the at least one predicted average rank value associated with the respective at least one remote monitor.

Abstract: A method and apparatus for computing biased or targeted quantiles are disclosed. For example, the present invention reads a plurality of items from a data stream and inserts each of the plurality of items that was read from the data stream into a data structure. Periodically, the data structure is compressed to reduce the number of stored items in the data structure. In turn, the compressed data structure can be used to output a biased or targeted quantile.

Abstract: A method, apparatus, and computer readable medium for processing a data stream is described. In one example, a set of elements of a data stream are received. The set of elements are stored in a memory as a hierarchy of nodes. Each of the nodes includes frequency data associated with either an element in the set of elements or a prefix of an element in the set of elements. A set of hierarchical heavy hitters is then identified among the nodes in the hierarchy. The frequency data of each of the hierarchical heavy hitter nodes, after discounting any portion thereof attributed to a descendent hierarchical heavy hitter node in said set of hierarchical heavy hitter nodes, being greater than or equal to a fraction of the number of elements in the set of elements.