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Fig. 2. The support of out-of-phase matching is important. However, the DTW
matches all points (so, the outliers as well), therefore distorting the true distance
between sequences. The LCSS model can support time-shifting and eciently ignore
the noisy parts.
The diculties imposed by DTW include the fact that it is a non-metric
distance function and also that its performance deteriorates in the presence
of large amount of outliers (Figure 2). Although the flexibility provided by
DTW is very important, nonetheless DTW is not the appropriate distance
function for noisy data, since by matching all the points, it also matches
the outliers distorting the true distance between the sequences.
Another technique to describe the similarity is to find the longest com-
mon subsequence (LCSS) of two sequences and then define the distance
using the length of this subsequence [3,7,12,41]. The LCSS shows how
well the two sequences can match one another if we are allowed to stretch
them but we cannot rearrange the sequence of values. Since the values are
real numbers, we typically allow approximate matching, rather than exact
matching. A technique similar to our work is that of Agrawal et al. [3]. In
this chapter the authors propose an algorithm for finding an approxima-
tion of the LCSS between two time-series, allowing local scaling (that is,
different parts of each sequence can be scaled by a different factor before
matching). In [7,12] fast probabilistic algorithms to compute the LCSS of
two time series are presented.
Other techniques to define time series similarity are based on extracting
certain features (Landmarks [32] or signatures [14]) from each time-series
and then use these features to define the similarity. An interesting approach
to represent a time series using the direction of the sequence at regular time
intervals is presented in [35]. Ge and Smyth [18] present an alternative
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