Symbolic Aggregate approXimation
This function converts a numeric times seris into a series of letters with a specific length and alphabet.
SAX(x, alphabet_size, PAA_number, breakpoints = "gaussian", collapse = NULL)
x |
a numeric vector. |
alphabet_size |
a numeric vector of length 1 setting the size of the alphabet. |
PAA_number |
a numeric vector of length 1 setting the number of elements (subsequences) of the Piecewise Aggregate Approximation (PAA). |
breakpoints |
either a character vector ("gaussian", "quantiles")
or a numeric vector specifying the sorted values of the breakpoints
along the distribution of |
collapse |
a character vector of length 1, specifying the way to
collapse the output letters, see |
The SAX method has been developed to reduce the dimensionality of a numerical series into a short chain of characters. SAX follows a two-step process: (1) Piecewise Aggregate Approximation (PAA) and (2) conversion a PAA sequence into a series of letters.
PAA consists in a Z-normalisation, a segmentation of the series of
length n into w segments, and the computation of each segment average.
The conversion of the PAA into a series of letters is achieved by attributing with
equiprobability each value of the PAA to a letter in reference to a
Gaussian distribution. This process therefore assumes that the
distribution of the numeric series x follows a Gaussian
distribution. To relax the constraints of normality we here added the possibility to directly work
on the quantiles of the original data distribution or to specify particular breakpoints along the
distribution of x. See the examples.
A character vector of length (when collapse is
NULL) or number of character (when collapse is
not NULL) corresponding to PAA_number argument.
SAX has been used recently to search similar times series in a soundcape data base (Kasten et al., 2012).
Laurent Lellouch. An improvement added by Pavel Senin.
Kasten, E.P., Gage, S.H., Fox, J. & Joo, W. (2012). The remote environmental assessment laboratory's acoustic library: an archive for studying soundscape ecology. Ecological Informatics, 12, 50 - 67.
Lin, J., Keogh, E., Lonardi, S., Chiu, B., June (2003). A symbolic representation of time series with implications for streaming algorithms. Proceedings of the 8th ACM SIGMOD Workshop on Research Issues in Data Mining and Knowledge Discovery. San Diego, California, USA.
data(tico) spec <- soundscapespec(tico, plot=FALSE)[,2] SAX(spec, alphabet = 5, PAA = 10) # change breakpoints SAX(spec, alphabet = 5, PAA = 10, breakpoints="quantiles") SAX(spec, alphabet = 5, PAA = 10, breakpoints=c(0, 0.5, 0.75, 1)) SAX(spec, alphabet = 5, PAA = 10, breakpoints=c(0, 0.33, 0.66, 1)) # different output formats SAX(spec, alphabet = 5, PAA = 10, collapse="") SAX(spec, alphabet = 5, PAA = 10, collapse="-")
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.