Efficient Kernel-Based Subsequence Search for Enabling Health Monitoring Services in IoT-Based Home Setting
- Designing a kernel learning task aimed at approximating DTW to reduce computational burden of the subsequence search.
- Comparing the proposed kernel-based DTW approximation with traditional DTW-based implementations and other state-of-the-art algorithms.
- Validating the proposed approach on a simple benchmark toy example (https://www.cs.unm.edu/mueen/FastestSimilaritySearch.html) and on a more complex one, namely, the “User Identification From Walking Activity” dataset, freely downloadable from the UCI Repository.
- Validating the results through pattern query experiments on a dataset self-rehabilitation dataset, specifically collected in a real-life project. Self-rehabilitation dataset is available from the corresponding author on reasonable request.
2.1. Dynamic Time Warping
- Boundary conditions and . These conditions enforce the alignment to start and finish at the extremes of the two series, meaning that the first elements of X and Y, as well as the last ones, must be aligned to each other.
- Monotonicity condition: and . This condition simply ensures that if an element in X precedes a second one this should also hold for the corresponding elements in Y, and vice versa.
- Step size condition: for . This condition ensures that no element in X and Y can be omitted and that there are no replications in the alignment, meaning that all the index pairs contained in a warping path are pairwise distinct. Note that the step size condition implies the monotonicity condition.
|Algorithm 1 Optimal warping path algorithm|
|Input Accumulated cost matrix D |
Output optimal warping path
2.2. Dynamic Time Warping for Subsequence Search
|Algorithm 2 DTW-based subsequence search algorithm|
reference pattern , a longer data stream , with , and a threshold |
Output a list of repetitions of X within Y having, individually, a DTW lower than . The list is ranked depending on the individual DTW
3. Learning a Kernel to Approximate DTW
3.1. Time-Series Kernels via Alignments
3.2. Learning a Kernel for Subsequence Search
3.3. Extension to Multiple Reference Patterns
|Algorithm 3 Learning a kernel for approximating DTW in the case of multiple references and multiple data streams|
|Inputn reference patterns , m data streams and parameters .|
Output a matrix containing the kernel values.
4. Experimental Setting
4.1. Organization of the Experiments
4.2. Experiment 1: A Univariate Case
- MASS : a fast similarity search algorithm for subsequences under Euclidean distance and correlation coefficient (experiments refer to MASS under Euclidean distance, only). A strong assumption of MASS is that the identified subsequences have the same length of the reference.
- DTW with fixed window: based on the same assumption of MASS but using DTW instead of Euclidean distance.
- DTW-based subsequence search algorithm described in Algorithm 2.
- DTW-based Kernel constructed to approximate the exact DTW.
4.3. Experiment 2: A Multivariate Case
- Sampling frequency of the accelerometer: DELAY_FASTEST with network connections disabled.
- A separate file for each participant.
- Every row in each file consists of time-step, x acceleration, y acceleration, and z acceleration.
4.4. Experiment 3: A Real-Life Application
- Flexo-extension of the knee (sit-down position)
- Raise and lower the arms (sit-down position)
- Rotate the torso (sit-down position)
- Back extension of the legs (stand-up position)
- Light squat (stand-up position)
4.5. Computational Setting
5.1. Results of Experiment 1
5.2. Results on Experiment 2
5.3. Results of Experiment 3
Conflicts of Interest
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|Exercise||DTW-Based Subsequence Search||Kernel-Based DTW Approximation|
|Flexo-extension of the|
knee, sit-down position.
Five repetitions planned.
Five repetitions planned.
|Back extension of the|
legs, stand-up position.
Five repetitions planned.
|Rotate the torso,|
Five repetitions planned.
|Raise and lower the arms,|
Ten repetitions planned.
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Candelieri, A.; Fedorov, S.; Messina, E. Efficient Kernel-Based Subsequence Search for Enabling Health Monitoring Services in IoT-Based Home Setting. Sensors 2019, 19, 5192. https://doi.org/10.3390/s19235192
Candelieri A, Fedorov S, Messina E. Efficient Kernel-Based Subsequence Search for Enabling Health Monitoring Services in IoT-Based Home Setting. Sensors. 2019; 19(23):5192. https://doi.org/10.3390/s19235192Chicago/Turabian Style
Candelieri, Antonio, Stanislav Fedorov, and Enza Messina. 2019. "Efficient Kernel-Based Subsequence Search for Enabling Health Monitoring Services in IoT-Based Home Setting" Sensors 19, no. 23: 5192. https://doi.org/10.3390/s19235192