lect21

lect21 - Time-series data analysis Why deal with sequential...

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Time-series data analysis
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Why deal with sequential data? Because all data is sequential All data items arrive in the data store in some order Examples transaction data documents and words In some (or many) cases the order does not matter In many cases the order is of interest
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Time-series data Financial time series, process monitoring…
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Questions What is the structure of sequential data? Can we represent this structure compactly and accurately ?
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Sequence segmentation Gives an accurate representation of the structure of sequential data How? By trying to find homogeneous segments Segmentation question:
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Dynamic-programming algorithm Sequence T , length n , k segments, cost function E() , table M For i=1 to n Set M[1,i]=E(T[1…i]) //Everything in one cluster For j=1 to k Set M[j,j] = 0 //each point in its own cluster For j=2 to k For i=j+1 to n Set M[j,i] = min i’<i {M[j-1,i]+E(T[i’+1…i])} To recover the actual segmentation (not just the optimal cost) store also the minimizing values i’ Takes time O(n 2 k) , space O(kn)
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Example t R t R
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Basic definitions Sequence T = {t ,t ,…,t } : an ordered set of n d -dimensional real points t Є R p S s s t p s p t S E 1 | | ) ( - = ∑∑ ∈ ∈ μ
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lect21 - Time-series data analysis Why deal with sequential...

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