Abstract: A computing device determines a recommendation. (A) A first parameter matrix is updated using a first direction matrix and a first step-size parameter value that is greater than one. The first parameter matrix includes a row dimension equal to a number of users of a plurality of users included in a ratings matrix and the ratings matrix includes a missing matrix value. (B) A second parameter matrix is updated using a second direction matrix and a second step-size parameter value that is greater than one. The second parameter matrix includes a column dimension equal to a number of items of a plurality of items included in the ratings matrix. (C) An objective function value is updated based on the first parameter matrix and the second parameter matrix. (D) (A) through (C) are repeated until the first parameter matrix and the second parameter matrix satisfy a convergence test.

Abstract: A computing device determines a recommendation. (A) A first parameter matrix is updated using a first direction matrix and a first step-size parameter value that is greater than one. The first parameter matrix includes a row dimension equal to a number of users of a plurality of users included in a ratings matrix and the ratings matrix includes a missing matrix value. (B) A second parameter matrix is updated using a second direction matrix and a second step-size parameter value that is greater than one. The second parameter matrix includes a column dimension equal to a number of items of a plurality of items included in the ratings matrix. (C) An objective function value is updated based on the first parameter matrix and the second parameter matrix. (D) (A) through (C) are repeated until the first parameter matrix and the second parameter matrix satisfy a convergence test.

Abstract: A data streaming environment provides a summary of streaming data. An input interface receives streaming data from a sensor or an input device. The input device includes a user interface. The sensor is an Internet of Things (IOT) device. A processor is communicatively coupled to the input interface for processing the streaming data. A histogram update application is executed with the received data to provide a limited-size summary of the streaming data by fading outdated data by storing distance data and bin data. The processed data includes a plurality of records and variables that describe a characteristic of a physical object. An output interface is communicatively coupled to the processor to provide the processed data to be visually presented in one or more data graphs on a display device.

Abstract: A method of transforming time series data to cluster data is provided. Time series data including a plurality of time series is received. A distance between a first time series of the plurality of time series and each of a remaining set of time series of the plurality of time series is computed pairwise between each of the remaining set of time series of the plurality of time series and the first time series. The computed values of the distance are sorted in increasing value. Gap width values are computed as a difference between successive pairs of the sorted, computed values. Whether a cluster including the received time series data is uniform is determined based on the computed gap width values. Cluster data including the first time series and the remaining set of time series assigned to the cluster is output when the cluster is determined to be uniform.