Package 'FARM'

Description

    farm identifies and compensates time warping between query and reference time series by sample and hold for an insertion
                 and a deletion for a remove. Subsequent, the algorithm calculates two relevance values: (1) the correlation of the query
                 to the reference time series for each point locally in the given time window for local relevance and (2) the l2 norm of
                 the mean of a proportion with highest local relevance values and the mean of all local relevance values. In case, the
                 variation of any local sequence (i.e. local query or reference sequence) equals 0 (var(xts) == 0), it adds a small white
                 noise with a std. variation of 0.000001 to normalized (mean = 0) sequences. This avoids NA in using local correlation of
                 constant series.

Usage

farm(
  refTS,
  qryTS,
  lcwin = 5,
  rel.th = 15,
  ff.align = TRUE,
  reshape.fnc = function(x) x,
  fuzzyc = c(2, 6, 10, 6, 2)/10,
  metric.space = TRUE,
  reshape.mode = "uni"
)

Arguments

Value

         list(path, rts.decomp, qts.decomp, qts.shaped, rel.local, rel.local.fuzz, rel.global, qmeas.mean.p, qmeas.slm.f)
                 path            warping path
                 rts.decomp      time warping decomposed reference time series
                 qts.decomp      time warping decomposed query time series
                 qts.shaped      shaped dewarped (if ff.align = T) query time series according to the reshape function reshape.fnc. The reshaping relies on the fuzzified rel.local.fuzz.
                 rel.local       local relevance values (length(rel.local) = length(qryTS)) compliant with metric requirements (triang. ineq.)
                 rel.local.end   local relevance values (not fuzzyfied) with correlation coefficient spot to the end of the lcwin.
                 rel.local.fuzz  local relevance values fuzzyfied according to fuzzyc factors applied on rel.local. Set fuzzyc = 1 to turn off fuzzification.
                 rel.global      global relevance value (scalar) based on local relevance values rel.local (being compliant with metric space). The global relevance relies on the fuzzified rel.local.fuzz.
                 qmeas.mean.p    mean absolute product quality measure for alignment of query with respect to reference time series. **higher** values indicate **better** alignment results.
                 qmeas.slm.f     slope-mean-factorial slm_f quality measure (mean product of slopes) for alignment of query with respect to reference time series. **higher** values indicate **better** alignment results.

Note

date: 11-17-2022 farm

Author(s)

rch

Examples

farm(c(1,2,2,1,3), c(1,1,2,1,4), lcwin = 3, rel.th = 10)

Description

The returned distance is the sine of the absolute angle between vectors if both have a positive or both have a negative argument. For contrasting vectors (v1: +-x,+y and v2: +-x,-y) the resulting distance is: 1-exp(-phi*5), for non-metric space and: . The vector argument 0 is treated as positive argument.

Usage

farm.dist(dyr, dyq = NA, metric.space = FALSE)

Arguments

Value

 double: distance value

Note

date: 11-17-2022 farm.dist

Author(s)

rch

Examples

farm.dist(0.23, -2.85)

Description

An absolute values based quality measure for feature alignment of two independent time series with the same length. The measure returns the mean of the absolute product of two time series according the formula:

$\left |{1 \over n} \sum_{i=0}^{n} {ref_i \cdot qry_i} \right|$

Resulting from the product, the higher the values, the better the result.

Usage

farm.mean.p(rts, qts)

Arguments

Value

double: quality measure *larger means better*

Examples

farm.mean.p(c(1,2,1.5,2.1,5,2.32,1,0.2), c(0.2,0.4,0.4,0.5,1,0.92,0.5,0.2))

Description

The slope-mean-factorial slm_f returns a quality measure for feature alignment of two independent time series with the same length. The measure relies on the mean product of the slopes (i.e. differences) of subsequent data values in two time series, according the formula:

${1 \over n} \sum_{i=2}^{n} {\Delta ref_{[i-1, i]} \cdot \Delta qry_{[i-1, i]}} \over {1 + { \left | \#smp_{orig} - \#smp_{method} \over \#smp_{orig} \right | }}$

Resulting from the inner product of the slopes, the higher the values, the better the result. For penalizing the number of changes in time series for feature matching, the original and modified series length can be set by the parameters l.orig and l.adj respectively.

Usage

farm.slm.f(rts, qts, l.orig = 1, l.adj = 1)

Arguments

Value

double: quality measure *larger means better*

Examples

farm.slm.f(c(1,2,1.5,2.1,5,2.32,1,0.2), c(0.2,0.4,0.4,0.5,1,0.92,0.5,0.2))

Description

Two time series present a warping scheme to each other. For comparison and advanced analysis of warped time series, it requires de-warping time series according a given scheme. This function expands the reference and query time series for resulting in a 1 to 1 data point alignment. The series are expanded according to the farm warping solution by interpolation. There are no data points removed.

Usage

tw.decomp(rts, qts, twp, mode = "uni", abs = FALSE)

Arguments

Value

list(rts=c(rts1, rts2, ..), qts=c(qts1, qts2, ..)): de-warped reference (rts) and query (qts) time series.

Note

date: 11-17-2022 tw.decomp

Author(s)

rch

Examples

tw.decomp(c(0,1,0,0,0), c(0,0.5,0.5,0,0), data.frame(x=c(1,2,2,3,4), y=c(1,2,3,4,4)))