Synthetic data generation of time series data

One or more tangible non-transitory computer-readable media having computer-executable instructions for performing a method of running a software program on a computing device, the computing device operating under an operating system, the method including issuing instructions from the software program to generate a synthetic variant of a given input for an application, the instructions comprising:

• receiving to and recording on a computer-readable storage device an input time series of K points;
• stochastically resampling the time series of K points into a first set of n points along the series' path, whereby a path distance between the n points is non-uniform;
• extracting and normalizing a direction vector between each consecutive pair of points to a unit length, wherein the direction vector between the each consecutive pair of points is lengthened or shortened as a result of the resampling and normalization;
• concatenating a plurality of normalized direction vectors to create a second set of n points, wherein the origin of the first vector in the series is at the center of a coordinate system, wherein the resulting series forms a shape that can be translated, scaled, skewed and rotated as necessary;
• and
• outputting the synthetic variant based on the formed shape, whereby perturbations are simulated directly on the given input itself

A method of training a gesture recognizer by generating a plurality of synthetic variants of a given input gesture, comprising the steps of:

• receiving to and recording on a computer-readable storage device an input time series of K points;
• extracting a predetermined set of statistical features from the input time series of K points, wherein the predetermined set of features of the input time series include density and closedness of the K points within the input time series;
• stochastically resampling the time series of K points into a first set of n points along the series' path, whereby a path distance between the n points is non-uniform, wherein a cardinality of the first set of n points is established based on statistical features of the input time series of K points;
• randomly selecting a subset of n points from the first set of n points along a trajectory defined by the time series;
• removing the randomly selected subset of n points from the first set of n points;
• extracting and normalizing a direction vector between each consecutive pair of remaining unremoved n points to a unit length, wherein the direction vector between the each consecutive pair of points is lengthened or shortened as a result of the resampling and normalization;
• concatenating a plurality of normalized direction vectors to create a second set of n points, wherein the origin of the first vector in the series is at the center of a coordinate system, wherein the resulting series forms a shape that can be translated, scaled, skewed and rotated as necessary;
• outputting a synthetic variant based on the formed shape, whereby perturbations are simulated directly on the given input itself;
• repeating the foregoing steps to generate the plurality of synthetic variants;
• generating a synthetic samples distribution based on the plurality of synthetic variants;
• measuring the plurality of synthetic variants against the given input;
• generating a synthetic in-class measurements probability distribution from the measurements, wherein the synthetic in-class measurements probability distribution is based on input samples;
• generating an out-of-class measurements probability distribution from out-of-class measurements, wherein the out-of-class measurements probability distribution is based on synthetic non-input samples;
• establishing a rejection threshold based on the synthetic in-class measurements probability distribution and the out-of-class measurements probability distribution, wherein the rejection threshold minimizes the probability of false negative errors and false positive errors,
• wherein the step of establishing the rejection threshold is performed by:
• selecting an objective function to be maximized,
• estimating a value of the objective function using the synthetic in-class measurements probability distribution and the out-of-class measurements probability distribution, wherein the estimate is made at each point along a range of measurement values of the combined synthetic in-class and out-of-class measurements probability distributions, and
• determining a measurement value that maximizes the objective function based on the estimated value of the objective function, wherein the determined measurement value is the rejection threshold;
• and
• training the gesture recognizer with the synthetic samples distribution including the rejection threshold.