System and method for determining distance between signals

A system, comprising:

• a sensor configured to determine and output signal data, wherein elements of a first signal data stored in a memory are selected from the signal data corresponding to a finite alphabet;
• a processor configured to transform the signal data received from the sensor into a mapped signal data using an absolute distance preserving mapping, such that each element of the signal data is mapped to a vector in the mapped signal data, wherein a size of the vector equals to a cardinality of the finite alphabet, wherein a k-norm distance is determined securely in an encrypted domain, wherein the mapped signal data is stored in a database of mapped signal data;
• and
• querying the database of mapped signal data using the k-norm distance with the first mapped signal data to determine at least one nearest neighbor signal data for a k-norm distance metric, wherein a k-norm distance is determined securely in an encrypted domain, and wherein the absolute distance preserving mapping of an element comprises:
• determining a position N of the element in an ordered sequence of symbols of the finite alphabet;
• determining values for each of N elements of the vector as a fractional power 1/k of positive increments in the finite alphabet, wherein k is a positive number;
• and
• determining values for subsequent elements of the vector as zero, wherein the memory stores the mapped signal data.

A computer-implemented method for computing pairwise distance using a processor and signal data stored in a memory connected to the processor, comprising:

• receiving a first signal data representing an output of a sensor, wherein elements of the first signal data are selected from the signal data corresponding to a finite alphabet, wherein the signal data is stored in a database of signal data;
• transforming, using the processor, the first signal data into a first mapped signal data using an absolute distance preserving mapping, such that each element of the first signal data is mapped to a vector in the first mapped signal data, wherein a size of the vector equals to a cardinality of the finite alphabet;
• transforming the signal data in the database using the absolute distance preserving mapping to produce a database of mapped signal data;
• and
• querying the database of mapped signal data using the k-norm distance with the first mapped signal data to determine at least one nearest neighbor signal data for a k-norm distance metric, wherein a k-norm distance is determined securely in an encrypted domain, and wherein the absolute distance preserving mapping of an element comprises:
• determining a position N of the element in an ordered sequence of symbols of the finite alphabet;
• determining values for each of N elements of the vector as a fractional power 1/k of positive increments in the finite alphabet, wherein k is a positive number, and
• determining values for subsequent elements of the vector as zero;
• and
• storing the first mapped signal data in the memory.