Overview of Dynamic Time Warping
Dynamic Time Warping, or DTW, is a distance measure used in comparing two time series. It seeks to find the optimal match between the two sequences using the dynamic programming technique. DTW is commonly used for temporal sequences in video, audio, and graphics data, and can be used for any data that can be converted into a linear sequence.
DTW has been widely used in various applications, including automatic speech recognition, speaker recognition, and online signature recognition. It is also useful in partial shape matching application, where it compares two shapes with different lengths and sizes but similar patterns. DTW can detect similarities in walking even if one person is walking faster than the other, or if there are changes in speed or direction during the observation.
How DTW Works
DTW works on the principle that similar elements in two time series may not necessarily occur at the same point in time. It finds the optimal warping path between the two sequences by calculating the distance between every corresponding points and selects the least expensive path, the one that minimizes the total distance between the two sequences. The algorithm follows a set of rules and restrictions to ensure that the mapping of the indices from one sequence to the other is monotonically increasing.
DTW compares two sequences by mapping the indices of one sequence to the indices of the other sequence. The algorithm uses a distance metric such as Euclidean distance, Manhattan distance, or Cosine distance to compute the distance between two corresponding elements of the two sequences. It then adds up the distance of the matched elements until it finds the optimal mapping path.
To calculate the similarity between two time-series data, the algorithm follows the following rules:
- Every index from the first sequence must be matched with one or more indices from the other sequence, and vice versa.
- The first index from the first sequence must be matched with the first index from the other sequence (but it does not have to be its only match).
- The last index from the first sequence must be matched with the last index from the other sequence (but it does not have to be its only match).
- The mapping of the indices from the first sequence to indices from the other sequence must be monotonically increasing, and vice versa. If j>i are indices from the first sequence, then there must not be two indices l>k in the other sequence, such that index i is matched with index l and index j is matched with index k, and vice versa.
Applications of DTW
DTW has been used in various applications, including:
- Automatic Speech Recognition: In speech recognition, DTW is used to compare an unknown speech signal to a set of reference patterns. It is especially useful when the speech signals have different speaking speeds or accents. DTW can recognize patterns in speech that may be missed by other techniques.
- Speaker Recognition: DTW can be used to compare two speech signals from the same speaker to confirm their identity. It can also be used to compare speech signals from different speakers to determine their similarity or dissimilarity.
- Online Signature Recognition: DTW can be used to recognize a signature based on the dynamics of the signature. By capturing the trajectory of the signature over time, DTW can identify the person who made the signature.
- Gesture Recognition: DTW can be used to recognize hand gestures for controlling games, robots, or devices. By comparing the trajectory of the hand movements, DTW can identify the intended gesture even if it varies in speed or direction from the expected pattern.
- Instrument Recognition: DTW can be used to recognize musical instruments based on their sound wave patterns. By comparing the sound waves produced by different instruments, DTW can identify the instrument being played.
DTW has many other potential applications in various fields, ranging from medical diagnosis to finance. It is a powerful tool for analyzing time series data and finding patterns that may be missed by other methods.
Dynamic Time Warping is a powerful tool for comparing two time series data. Its ability to account for variations in speed, direction, and scale makes it an ideal solution for various applications such speech recognition, signature recognition, gesture recognition, and instrument recognition. DTW is a highly flexible method that can be adapted to suit many different domains, making it a valuable tool for many industries and researchers.
