| update to my original post I am coming from a genomics background, so when I read about sliding window on time series data, I think about sliding window approach on regions of genome sequences. The ultimate point of doing this clustering is to find repetitive sub-sequences in the series. This is also something we do commonly in the genomics field (repeatmasker/repeatmodeler software for example). Something we can look at in genomes is a "k-mer coverage". A k-mer is just a k-lengthed sub-sequence (A,T,G,C), analogous to a k-length sub-sequence of a time series. By scanning the genome, we can tally up how many times a k-mer appears in the genome. With this tally, we can determine a k-mer coverage for a region on the genome. This gives us an idea how many times we see this same region on the rest of the genome. Maybe this approach can be adapted somehow? The only problem is that in genomics, we have four discrete classes (A,G,T,C), making finding exact matching relatively easy. In time-series, we have continuous data, making finding matches a lot tougher to do and define. |
The difference I think is that the series in a genome is lexicographic rather than temporal: i.e. which end of a particular strand you read from is irrelevant. On the other hand, a time series has an independent ordering. By analogy, a time series is a directed graph a genome is undirected.
That is the algorithm for finding a subsequence in a time series can be used for finding a subsequence in a genome. But the meaning of a subsequence is different. It's:
versus Time series data contains implication and causality. Any claim about time series data is implicitly a claim about causality: e.g. we might claim a time series appears to be random. We don't really talk about a genome's amino acid sequence being random because the causality (other than the trivial case of analogues) lies outside the sequence - the reason for is assumed to lie outside of T - A - C.[1]: http://plato.stanford.edu/entries/kant-hume-causality/#TimDe...