Hubness-Aware Classification, Instance Selection and Feature Construction: Survey and Extensions to Time-Series - Feature Selection for Data and Pattern Recognition - page 230

Fig. 11.3 Limiting the size of the warping window: only the cells around the main diagonal of the
matrix ( marked cells ) are calculated

The cost of transformation (matching), denoted as c DTW

tr , depends on what value is
replaced by what: if the numerical value v A is replaced by v B , the cost of this step is:

c DT W
tr

( v A , v B ) =| v A − v B | . (11.5)

We set the warping window size to w DTW

= 5%. For more details and further recent

results on DTW, we refer to [ 8 ].

11.4 Hubs in Time-Series Data

The presence of hubs, i.e., some few instances that tend to occur surprisingly
frequently as nearest neighbors while other instances (almost) never occur as near-
est neighbors, has been observed for various natural and artificial networks, such as
protein-protein-interaction networks or the internet [ 3 , 22 ]. The presence of hubs
has been confirmed in various contexts, including text mining, music retrieval and
recommendation, image data and time series [ 43 , 46 , 49 ]. In this chapter, we focus
on time series classification, therefore, we describe hubness from the point of view
of time-series classification.
For classification, the property of hubness was explored in [ 40 - 43 ]. The prop-
erty of hubness states that for data with high (intrinsic) dimensionality, like most of
the time series data, 3 some instances tend to become nearest neighbors much more

3 In case of time series, consecutive values are strongly interdependent, thus instead of the length
of time series, we have to consider the intrinsic dimensionality [ 43 ].