Projektgruppe Visual Analytics - Medieninformatik und Multimedia ...

Derivative Dynamic Time Warping
Eamonn J. Keogh † and Michael J. Pazzani ‡
58 Kapitel 3 Multitouch
1 Introduction
hauptsächlich darum, zweidimensionale Sequenzen miteinander zu vergleichen. Dies
wird hauptsächlich bei der Spracherkennung verwendet, lässt sich aber auch für die
Erkennung Time von series Gesten are a auf ubiquitous Multitouch-Eingabegeräten form of data occurring verwenden. in virtually every scientific
discipline. A common task with time series data is comparing one sequence with another.
Um eine In some Geste domains mit einer a very anderen simple distance vergleichen measure, zu such können, as Euclidean müssendistance die Bewegungen will suffice. jeder
Geste However, zunächst it is auf often einthe zweidimensionales case that two sequences Muster have the heruntergerechnet approximately the und same gespeichert overall
werden. component Trenntshapes, man die but Daten these shapes der horizontalen do not line up und in X-axis. vertikalen Figure Bewegung 1 shows this auf, with soakann
mansimple zwei Diagramme example. In erstellen. order to find Hierthe befindet similarity sichbetween dann auf such dersequences, X-Achse die or as Zeit a und
auf der preprocessing Y-Achsestep jeweils before die averaging horizontale them, oder we must vertikale "warp" Bewegung. the time axis of Imone ersten (or both) Prozess
werden sequences die X-Achse to achieve dera gespeicherten better alignment. Geste Dynamic und die time X-Achse warping (DTW), der soeben is a technique ausgeführten
for efficiently achieving this warping. In addition to data mining (Keogh & Pazzani 2000,
Bewegung angeglichen (s. Abb. 3.16). Dies erfolgt über eine Matrix, welche die
Yi et. al. 1998, Berndt & Clifford 1994), DTW has been used in gesture recognition
Distanzen der Y-Werte enthält. Durch Linearisierung (Abb. 3.17) der Distanzen werden
(Gavrila & Davis 1995), robotics (Schmill et. al 1999), speech processing (Rabiner &
die Werte angeglichen.
Juang 1993), manufacturing (Gollmer & Posten 1995) and medicine (Caiani et. al 1998).
A)
0 10 20 30 40 50 60 70 0 10 20 30 40 50 60 70
Abbildung Figure 1: An 3.16: example Angleichung of the utility of der dynamic X-Achse time warping. beim Dynamic A) Two sequences Time-Warping that represent [Keo01] the Y-
axis position of an individual’s hand while signing the word "pen" in Sign Language. The sequences were
recorded on two separate days. Note that while the sequences have an overall similar shape, they are not
aligned in the time axis. A distance measure that assumes the i th point on one sequence is aligned with i th
point on the other will produce a pessimistic dissimilarity. B) DTW can efficiently find an alignment
between the two sequences that allows a more sophisticated distance measure to be calculated.
B)
4
† Department of Information and Computer Science University of California, Irvine,
California 92697 USA eamonn@ics.uci.edu
‡ pazzani@ics.uci.edu
0 5 10 15 20 25 30
1
m
0 5 10 15 20 25 30
j
1 w1
1
w3
w2
…
Figure 3: An example warping path.
Abbildung 3.17: Die Abbildung zeigt die Abstände
2.1 Constraining zwischen den the classic beidendynamic Sequenzen, time warping welchealgorithm
anschließend
The problem
linearisiert
of singularities
werden [Keo01]
was noted at least as early as 1978 (Sakoe, & Chiba
1978)). Various methods have been proposed to alleviate the problem. We briefly review
them here.
1) Windowing: (Berndt & Clifford 1994) Allowable elements of the matrix can be
restricted to those that fall into a warping window, |i-(n/(m/j))| < R, where R is a
positive integer window width. This effectively means that the corners of the
matrix are pruned from consideration, as shown by the dashed lines in Figure 3.
Others have experimented with various other shaped warping windows (Rabiner et
al 1978, Tappert & Das 1978, Myers et. al. 1980). This approach constrains the
maximum size of a singularity, but does not prevent them from occurring.
2) Slope Weighting: (Kruskall & Liberman 1983,Sakoe, & Chiba 1978) If equation
i
wK
n