Abstract:
A heart-rate detection system can receive heartbeat data generated by a wearable heart-rate sensor worn by a wearer. The system can then execute a noise-reduction process for reducing noise in the heartbeat data. The noise-reduction process can involve applying a lowpass filter to the heartbeat data, generating wavelet coefficients by applying a wavelet transform to the filtered heartbeat data, and generating a reduced set of wavelet coefficients by thresholding the wavelet coefficients. An inverse wavelet signal can then be generated by applying an inverse wavelet transform to the reduced set of wavelet coefficients. R-peaks can be identified by performing peak detection on the instantaneous amplitudes of the data points in the inverse wavelet signal. A heart rate curve can then be generated based on the R-peaks and modified by applying a Hampel filter. Heartbeat data can then be generated based on the modified heart rate curve for output.
Abstract:
Anomalies in a target object can be detected and diagnosed using improved Mahalanobis-Taguchi system (MTS) techniques. For example, an anomaly detection and diagnosis (ADD) system can receive a set of measurements associated with attributes of a target object. A Mahalanobis distance (MD) can be determined using a generalized inverse matrix. An abnormal condition can be detected when the MD is greater than a predetermined threshold value. The ADD system can determine an importance score for each measurement of a corresponding attribute. The attribute whose measurement has the highest importance score can be determined to be responsible for the abnormal condition.
Abstract:
A singular value decomposition (SVD) is computed of a first matrix to define a left matrix, a diagonal matrix, and a right matrix. The left matrix, the diagonal matrix, and the right matrix are updated using an arrowhead matrix structure defined from the diagonal matrix and by adding a next observation vector to a last row of the first matrix. The updated left matrix, the updated diagonal matrix, and the updated right matrix are updated using a diagonal-plus-rank-one (DPR1) matrix structure defined from the updated diagonal matrix and by removing an observation vector from a first row of the first matrix. Eigenpairs of the DPR1 matrix are computed based on whether a value computed from the updated left matrix is positive or negative. The left matrix updated in (C), the diagonal matrix updated in (C), and the right matrix updated in (C) are output.
Abstract:
A computing device determines a bandwidth parameter value for outlier detection or data classification. A mean pairwise distance value is computed between observation vectors. A tolerance value is computed based on a number of observation vectors. A scaling factor value is computed based on a number of observation vectors and the tolerance value. A Gaussian bandwidth parameter value is computed using the mean pairwise distance value and the scaling factor value. An optimal value of an objective function is computed that includes a Gaussian kernel function that uses the computed Gaussian bandwidth parameter value. The objective function defines a support vector data description model using the observation vectors to define a set of support vectors. The Gaussian bandwidth parameter value and the set of support vectors are output for determining if a new observation vector is an outlier or for classifying the new observation vector.
Abstract:
A computing device determines a kernel parameter value for a support vector data description for outlier identification. A first candidate optimal kernel parameter value is computed by computing a first optimal value of a first objective function that includes a kernel function for each of a plurality of kernel parameter values from a starting kernel parameter value to an ending kernel parameter value using an incremental kernel parameter value. The first objective function is defined for a SVDD model using observation vectors to define support vectors. A number of the observation vectors is a predefined sample size. The predefined sample size is incremented by adding a sample size increment. A next candidate optimal kernel parameter value is computed with an incremented number of vectors until a computed difference value is less than or equal to a predefined convergence value.
Abstract:
A computer-readable medium is configured to determine a support vector data description (SVDD). For each of a plurality of values for a kernel parameter, an optimal value of an objective function defined for an SVDD model using a kernel function, a read plurality of data points, and a respective value for the kernel parameter is computed to define a plurality of sets of support vectors. A plurality of first derivative values are computed for the objective function as a difference between the computed optimal values associated with successive values for the kernel parameter. A plurality of second derivative values are computed for the objective function as a difference between the computed plurality of first derivative values associated with successive values for the kernel parameter. A kernel parameter value is selected where the computed plurality of second derivative values first exceeds zero.
Abstract:
Computer-implemented systems and methods are provided for predicting outputs. Global output fractions associated with an object are approximated. Outputs for a group are predicted based upon a cyclical aspect component and a movement prediction. An output prediction is calculated based upon the predicted outputs for a related object group and the approximated global output fraction for a particular object.
Abstract:
Anomalies in a target object can be detected and diagnosed using improved Mahalanobis-Taguchi system (MTS) techniques. For example, an anomaly detection and diagnosis (ADD) system can receive a set of measurements associated with attributes of a target object. A Mahalanobis distance (MD) can be determined using a generalized inverse matrix. An abnormal condition can be detected when the MD is greater than a predetermined threshold value. The ADD system can determine an importance score for each measurement of a corresponding attribute. The attribute whose measurement has the highest importance score can be determined to be responsible for the abnormal condition.
Abstract:
A computer transforms high-dimensional data into low-dimensional data. (A) A distance matrix is computed from observation vectors. (B) A kernel matrix is computed from the distance matrix using a bandwidth value. (C) The kernel matrix is decomposed using an eigen decomposition to define eigenvalues. (D) A predefined number of largest eigenvalues are selected from the eigenvalues. (E) The selected largest eigenvalues are summed. (F) A next bandwidth value is computed based on the summed eigenvalues. (A) through (F) are repeated with the next bandwidth value until a stop criterion is satisfied. Each observation vector of the observation vectors is transformed into a second space using a kernel principal component analysis with the next bandwidth value and the kernel matrix. The second space has a dimension defined by the predefined number of first eigenvalues. Each transformed observation vector is output.
Abstract:
A computing device determines hyperparameter values for outlier detection. An LOF score is computed for observation vectors using a neighborhood size value. Outlier observation vectors are selected from the observation vectors. Outlier mean and outlier variance values are computed of the LOF scores of the outlier observation vectors. Inlier observation vectors are selected from the observation vectors that have highest computed LOF scores of the observation vectors that are not included in the outlier observation vectors. Inlier mean and inlier variance values are computed of the LOF scores of the inlier observation vectors. A difference value is computed using the outlier mean and variance values and the inlier mean and variance values. The process is repeated with each neighborhood size value of a plurality of neighborhood size values. A tuned neighborhood size value is selected as the neighborhood size value associated with an extremum value of the difference value.