find scaled+shifted fuzzy copies of a 1-d 'needle' within a 1-d 'haystack'
fuzzy-matching between a 1-d "needle" time series and a "haystack" time series. find scaled+shifted copies of the "needle" within the "haystack".
similar to phase-align but with multiple fuzzy results [and limited to 1-d data].
``sh`
npm i needle-haystack-1d
`javascript
var {getNeedleScaleShift, getMSE, getNeedleHaystackData, removeOverlaps} = require('needle-haystack-1d');
var needle = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
var haystack = [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0,0,0,0,0,0,0,0,0,0,0];
haystack = haystack.map(f=>f*10+5); //scale+shift the haystack
var doRemoveOverlaps = false; //default false
var res = getNeedleHaystackData(needle, haystack, doRemoveOverlaps);
console.log(res);
//doRemoveOverlaps = false
// {
// indicesWithCorrelations: [ // [hitIndex, normalized correlation] sorted by correlation
// [ 21, 2.251800553427485 ],
// [ 20, 2.2069626632689396 ],
// [ 22, 2.1621247731103908 ],
// ...
// }
//doRemoveOverlaps = true
// {
// indicesWithCorrelations: [
// [ 21, 2.251800553427485 ],
// [ 10, -0.5281486364024173 ],
// [ 31, -0.6447271508146415 ]
// ]
// }
//note - correlations are normalized by npm ndarray-normalize to have mean zero and std 1
//extract the top "hit" from the haystack
var futurePeriods = 0; //add extra 'future' periods to the results?
var [topHitIndex, topCorrelation] = res.indicesWithCorrelations[0];
var shifted = getNeedleScaleShift(needle, haystack, topHitIndex, futurePeriods);
console.log(shifted);
// {
// slope: 10,
// yIntercept: -5,
// extractedHaystackSection: [ //original data from haystack
// 5, 15, 25, 35, 45,
// 55, 65, 75, 85, 95
// ],
// extractedHaystackSectionRescaled: [ //data scaled and shifted to resemble needle
// 1, 2, 3, 4, 5,
// 6, 7, 8, 9, 10
// ]
// }
//now we get the mean squared error [MSE] between
// the original needle and the extracted, scaled+shifted needle
var mse = getMSE(needle, shifted.extractedHaystackSectionRescaled);
console.log({mse})
// { mse: 0 }
//remove overlaps in existing results:
//var windowSize = needle.length;
//res = removeOverlaps(res, windowSize);
`
- phase-align
- ndarray-convolve - the correlate` function does most of the work here for us
