## What (idea)? #

Suppose that we need to compare 2 time series (quite *look-alike*),

*An example of 2 time series to be compared using DTW. Source of the idea.*

- They're quite look-alike but if we compare point-to-point, they're clearly very different!
- With
**DTW**, we compare:- hollows of series 1 with ones of series 2.
- cambers of series 1 with ones of series 2.

**Dynamic Time Warping**is used to compare the similarity or calculate the distance between two arrays or time series with different length.

*Difference between DTW and Euclidian distance. Source.*

## How (idea)? #

*By using a distance matrix, we can find a good distance between 2 timeseries using DTW. Here, $8=3^2-1^2$ and we choose the smallest distance in the nearest position. Source.*

*More detailed of calculating the distance matrix using DTW. Ai: element ith of A; D[i-1, j-1]: The DTW between element i-1th and j-1th. Source.*

## When to use? #

**An example**: Voice of a man. He can speak fast. He can speak slowly. However, the both voices are his. If we don't use DTW but Euclidian distance, the distance is very large $\Rightarrow$ there are 2 voices $\Rightarrow$ wrong prediction!**Sound Pattern Recognition**: detect the same kind of sound pattern (like the above example).**Stock Market**:

## Algorithm #

- Divide 2 time series into equal points.
- Calculate distance between 1st point in TS1 with all points in TS2 and then
*store the min*. - Move to 2nd point.
- Repeat step 2 & 3 but with 2nd point as a reference point.
- Add up all stored distances. This is a true measure between 2 time series.

ðŸ‘‰ Check this video fore a more explanation.

## Code #

ðŸ‘‰ dtaidistance

`pip install dtaidistance`

`from dtaidistance import dtw`

s1 = [0, 0, 1, 2, 1, 0, 1, 0, 0]

s2 = [0, 1, 2, 0, 0, 0, 0, 0, 0]

distance = dtw.distance(s1, s2)

# plot

from dtaidistance import dtw_visualisation as dtwvis

import numpy as np

path = dtw.warping_path(s1, s2)

dtwvis.plot_warping(s1, s2, path, filename="warp.png")

ðŸ‘‰ Another option: dtw-python

ðŸ‘‰ fastdtw (an approximate Dynamic Time Warping (DTW) algorithm that provides optimal or near-optimal alignments with an O(N) time and memory complexity)

`pip install fastdtw`

`import numpy as np`

from scipy.spatial.distance import euclidean

from fastdtw import fastdtw

x = np.array([[1,1], [2,2], [3,3], [4,4], [5,5]])

y = np.array([[2,2], [3,3], [4,4]])

distance, path = fastdtw(x, y, dist=euclidean)

print(distance)

^{â€¢}Notes with this notation aren't good enough. They are being updated.