INDEXING TIME-SERIES UNDER CONDITIONS OF NOISE - Data Mining in Time Series Databases - page 94

Table 4. Results for ASL data and ASL with added noise.

Distance function Time (sec) Correct clusterings Correct clusterings

(out of 45) (out of 45)

ASL ASL with noise

Euclidean 2.170 15 1

DTW 8.092 20 2

S 1:
s-75%, δ -40% 1.200 15.450 9.933

s-75%, δ -100% 2.297 19.231 10.4667

s-100%, δ -40% 1.345 16.080 12.00

s-100%, δ -100% 2.650 20.00 12.00

Fig. 18. ASL data: Time required to compute the pairwise distances of the 45 combi-
nations (same for ASL and ASL with noise).

6.2.4. Experiment 3 — ASL with Added Noise

We added noise at every sequence of the ASL at a random starting point
and for duration equal to the 15% of the series length. The noise was added
using the function: ,where

randn produces a random number, chosen from a normal distribution with
mean zero and variance one, and rangeValues is the range of values on X or
Y coordinates. In this last experiment we wanted to see how the addition of
noise would affect the performance of the three distance functions. Again,
the running time is the same as with the original ASL data.

x noise ,y noise = x, y + randn ∗ rangeV alues