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: Physical-device anomalies and degradation can be mitigated by implementing some aspects described herein. For example, a system can determine a first data window and a second data window by applying a window function to streaming data. The system can determine a first principal eigenvector of the first data window and a first principal eigenvector of the second data window. The system can determine an angle change between the first principal eigenvectors of the two data windows. The system can then detect an anomaly based on determining that the angle change exceeds a predefined angle-change threshold. Additionally or alternatively, the system may compare the first principal eigenvector for the second data window to a baseline value to determine an absolute angle associated with the second data window. The system can then detect a degradation based on determining that the absolute angle exceeds a predefined absolute-angle threshold.

Abstract: Physical-device anomalies and degradation can be mitigated by implementing some aspects described herein. For example, a system can determine a first data window and a second data window by applying a window function to streaming data. The system can determine a first principal eigenvector of the first data window and a first principal eigenvector of the second data window. The system can determine an angle change between the first principal eigenvectors of the two data windows. The system can then detect an anomaly based on determining that the angle change exceeds a predefined angle-change threshold. Additionally or alternatively, the system may compare the first principal eigenvector for the second data window to a baseline value to determine an absolute angle associated with the second data window. The system can then detect a degradation based on determining that the absolute angle exceeds a predefined absolute-angle threshold.

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 employs machine learning and determines a bandwidth parameter value for a support vector data description (SVDD). A mean pairwise distance value is computed between observation vectors. A scaling factor value is computed based on a number of the plurality of observation vectors and a predefined tolerance value. A Gaussian bandwidth parameter value is computed using the computed mean pairwise distance value and the computed 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 SVDD model using the plurality of observation vectors to define a set of support vectors. The computed Gaussian bandwidth parameter value and the defined a set of support vectors are output for determining if a new observation vector is an outlier.

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.