Sas Institute Inc.

Saba Emrani

Jorge Manuel Gomes Da Silva

Wei Xiao

Ilknur Kaynar Kabul

Arin Chaudhuri

Xin Jiang Hunt

A computing device computes a weight matrix to compute a predicted value. For each of a plurality of related tasks, an augmented observation matrix, a plug-in autocovariance matrix, and a plug-in covariance vector are computed. A weight matrix used to predict the characteristic for each of a plurality of variables and each of a plurality of related tasks is computed. (a) and (b) are repeated with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied: (a) a gradient descent matrix is computed using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, and (b) an updated weight matrix is computed using the computed gradient descent matrix.

Analytic system based on multiple task learning with incomplete data

A computing device computes a weight matrix to predict a value for a characteristic in a scoring dataset. For each of a plurality of related tasks, an augmented observation matrix, a plug-in autocovariance matrix, and a plug-in covariance vector are computed. A weight matrix used to predict the characteristic for each of a plurality of variables and each of a plurality of related tasks is computed. (a) and (b) are repeated with the computed updated weight matrix as the computed weight matrix until a convergence criterion is satisfied: (a) a gradient descent matrix is computed using the computed plug-in autocovariance matrix, the computed plug-in covariance vector, the computed weight matrix, and a predefined relationship matrix, wherein the predefined relationship matrix defines a relationship between the plurality of related tasks, and (b) an updated weight matrix is computed using the computed gradient descent matrix.

A computing device updates an estimate of one or more principal components for a next observation vector. An initial observation matrix is defined with first observation vectors. A number of the first observation vectors is a predefined window length. Each observation vector of the first observation vectors includes a plurality of values. A principal components decomposition is computed using the initial observation matrix. The principal components decomposition includes a sparse noise vector s, a first singular value decomposition vector U, and a second singular value decomposition vector v for each observation vector of the first observation vectors. A rank r is determined based on the principal components decomposition. A next principal components decomposition is computed for a next observation vector using the determined rank r. The next principal components decomposition is output for the next observation vector and monitored to determine a status of a physical object.

Monitoring, detection, and surveillance system using principal component analysis with machine and sensor data

A computing device detects an abnormal observation vector using a principal components decomposition. The principal components decomposition includes a sparse noise vector scomputed for the observation vector that includes a plurality of values, wherein each value is associated with a variable to define a plurality of variables. The sparse noise vector shas a dimension equal to m a number of the plurality of variables. A zero counter time series value &#x109;is computed using &#x109;=&#x3a3;s[i]. A probability value for &#x109;is computed using p=&#x3a3;H[i]/&#x3a3;H[i], where H[i] includes a count of a number of times each value of &#x109;occurred for previous observation vectors. The probability value is compared with a predefined abnormal observation probability value. An abnormal observation indicator is set when the probability value indicates the observation vector is abnormal. The observation vector is output when the probability value indicates the observation vector is abnormal.

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Saba Emrani