Dynamic time warping is an effective similarity measure for time series data that can be applied in numerous applications. DTW allows signals to be compared one-to-one even when they are out of sync in time.
DTW is widely employed for pattern matching and sequence alignment, particularly in speech recognition and time series clustering applications. This is due to DTW’s unique capacity to map between different sequences – an essential feature in these applications.
Table of Content:
- Dynamic Time Warping in Python
- Similarity Measures
- Warping Path Created from an Alignment
- Weighted Warping
- Derivative Warping
- Consideration
Dynamic Time Warping in Python
Dynamic Time Warping (DTW) is a time series alignment algorithm that has been widely employed in research for applications such as speech recognition, music retrieval, fingerprint verification, and online generator coherency identification.
DTW Algorithm:
The DTW Algorithm utilizes temporal distortions between two-time series sequences to find an optimal alignment path. The best alignment path is one that minimizes the distance between them but does not stray too far away from the main diagonal.
A successful alignment path ensures that it does not attempt to skip different features and get stuck at similar ones. This can be accomplished by applying certain constraints on the warping function.
Boundary Condition:
The boundary of a warping path begins with the start points of both sequences and ends at their endpoints. Monotonicity Condition: Throughout the warping path, either its index i or j stays constant or increases, never decreasing.
Time and Space Complexity:
DTW has a time and space complexity of O(M,N), where M and N are the lengths of respective sequences. Faster implementations such as PrunedDTW, SparseDTW, and FastDTW can be used to achieve greater speed.
Examples of Utilizing DTW:
A business ran a marketing campaign for one year in an ideal market and saw outstanding success, including incremental leads. They had high hopes of replicating this success in other candidate markets but weren’t certain which ones to target. Dynamic Time Warping proved invaluable during this process as it allowed them to adjust their target audiences according to market conditions.
Similarity Measures
Similarity measures are employed in a variety of applications, from video, audio, and graphics data to financial data. Their purpose is to detect similarities within time series sequences and detect anomalies within those datasets.
Convert Sequences Into Vectors
One common approach is to convert sequences into vectors and calculate the distance between points in vector space. This distance, known as the Minkowski distance, can be used to assess the degree of similarity between series.
- However, this method is limited in that it requires all series to have the same length and point-to-point correspondence. Without such conditions, it will not be possible to calculate Minkowski’s distance.
- Dynamic time warping (DTW) is an algorithm used to measure the similarity of two sequences. This technique permits more reliable comparisons between sequences that might have differences in speed or shifts.
Warping Path Created from an Alignment
Dynamic Time Warping (DTW’s) accuracy over Euclidean distance doesn’t depend on whether all data points are of equal length, nor does it take into account whether they have been shifted between each other.
In DTW, a warping path is created from an alignment grid of points called the warping path. This path can be defined by several constraints. The boundary condition guarantees that both signals start at their beginning points and terminate at their ends, while the continuity (step size) constraint restricts transitions to adjacent points in time.
DTW (Dotted Tree Wavelet) is a commonly used technique for sequence alignment, yet it has been demonstrated to be inefficient when dealing with signals with uneven sampling frequencies due to its lengthy search time for an optimal alignment path.
Weighted Warping
Warp-weighted looms are an ancient type of weaving tool that holds warp threads parallel under tension by attaching them to weights made of stone, pottery, or metal. They were widely used throughout Europe and the Near East from ancient times until the Middle Ages as the main weaving tool.
One of the most iconic depictions of this loom on ancient Greek vases depicts two black-figured women weaving upwards from a standing position in front of an enormous loom, its warp threads clearly separated and attached to weights. This same type of loom was also found in Catal Huyuk, an ancient city in Anatolia dating back to 7000 BCE; it continues to be used today in part of Norway.
Dynamic Time Warping (DTW) is a method for time series analysis that utilizes the distance measured to find an optimal alignment between two data series. It has proven especially successful at finding non-linear mappings, outperforming Euclidean distance for MODIS NDVI time series clustering.
Derivative Warping
One of the most influential DTW variants is derivative dynamic time warping (DDTW), which utilizes first-order derivatives to align temporal sequences under a new distance metric. Furthermore, weighted dynamic time warping (DTW) is an incentive-based DTW that takes into account the phase difference between two points when computing their distances.
Classic Dynamic Time Warping (DTW) is an improvement to DTW that uses time series local structure information to restrict the search scope of the warping path.
Consideration:
Dynamic time warping is an effective technique for comparing time series that don’t perfectly line up. It employs distance measures to find the optimal mapping between two sequences and has applications across various fields such as data mining, financial markets, speech recognition, and more.
