python implementation of SAX (Symbolic Aggregate Approximation) for time series data

1. Convert time series data into symbolic representation, where the (Euclidean) distance/similarity is lower bound by the distance in the symbolic space
2. The symbolic representation can be viewed as a low-dim (aggregate) representation of time series
3. Symbol based algorithms such as suffix-tree, markov chain can be used to analyze time-series

1. paper
2. website
3. jmotif application
4. tutorial
5. R package
6. Another python implementation
7. GrammarVis
8. GrammarVis github
9. GrammarVis VSM github
10. jMotif github

1. SAX has certain assumptions on time-series data, such as (1) local Gaussian, (2) fixed frequence, (3) real-valued signals. We want to explore more possiblities for other data
2. We want a vector representation of time-series pieces, similiar to the idea of representing words a vectors (Google's word2vec)
3. we need a fast parallel implementation

examples

1. sequitur will be used as the context-free grammar extractor for SAXed data
2. the mined rules will be used for outlier/motif detection
3. we wrap the c++ implementation for python usage - so it is just a quick workaround for now.

1. three papers listed on Grammarviz website
2. sequitur site
3. another python sequitur implementation
4. java implementation can be found in grammarviz2 implementation

1. download c++ code http://sequitur.info/latest/sequitur.tgz
2. put the sequitur code from the uncompressed folder in a convienet place
3. use the pysequitur package and pass the path to sequitur as constructor parameter

1. to make it easier to use with pysax
2. we understand that the c++ implementation treats rule terminals as single characters, whereas in pysax we are dealing with words, so we need to map the words to single characters first - this might change in future based on our understanding of the code.

examples

1. to implement the idea based on Time series anomaly discovery with grammar-based compression - using grammar analysis for time series outlier detection
2. main steps: a. SAX-symbolize the time series b. numerosity reduction c. grammar induction by sequitur d. map rules to subsequences e. mine the patten

examples