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..., where | ‚ ~€ $ is the length of warping path. See Fig. 5 for more details. The warping path is subjected to several constraints such as, boundary conditions, continuity, monotonicity, and windowing =-=[8]-=-. n 387 787 3 ~ 387 78793 „ƒ and wK $ H M UTWV =YXZV [ \^] and (1) i wk JG <SM H M JG <SM \^] where, is Curvature _a`b4cèd f Threshold, , and gihkj l mSh is \^] operator. is the threshold for retainin...

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... We empirically evaluate the effectiveness of our method in trajectory classification by comparing to a well-known trajectory matching algorithm. We consider the Derivative Direct Time Warping (DDTW) =-=[7]-=- method, because of its robustness in higher dimensional signals. For a fair comparison, we do not consider anomalous events. Table. 2 enumerates the average accuracy and precision of all classes usin...

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...hat finds a spatio-temporal warping between two instances of motion captured data. In the context of data mining there have been several extensions of DTW [14] to align time series. Keogh and Pazzani =-=[15]-=- used derivatives of the original signal to improve alignment with DTW. Listgarten et al. [16] proposed continuous profile models, a probabilistic method for simultaneously aligning and normalizing se...

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...tween sequences of signal strength measurements for speed estimation, we apply two sequences of signal strength measurements, one called the training and the other called the testing, to the Dynamic Time Warping (DTW) Algorithm. Dynamic Time Warping is a classic dynamic programming algorithm which has been widely used for optimal alignment of two time series datasets and was particularly popular for applications like speech processing[15], [19], data mining[16], [14], and gesture recognition[8]. In particular, we use a variant of the DTW algorithm called Derivative Dynamic Time Warping (DDTW) [13], which exploits the same principle as DTW but for the input data, where, instead of the time-series of RSS, we use the time-series of derivative of RSS. For example, if A = (a1, a2, ...aM ) is a time series of RSS measurements collected over M time points, the input to DDTW is A′ = (a′1, a ′ 2, ...a ′ M ), the derivative of A which is defined as a′i = (ai − ai−1) + (ai+1 − ai−1)/2 2 1 < i < M. (2) Given two RSS profiles - A and B with lengths of M and N samples respectively, DDTW constructs a distance matrix d[M × N ] which is defined as: d(i, j) = (a′i − b ′ j) 2 (3) where a′i and b ′ j are ...

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...]. The DTW technique finds an optimal match between two sequences by allowing a non-linear mapping of one sequence to another, and minimizing the distance between two sequences [8,7,12,22]. The sequences are ’’warped’’ non-linearly to determine their similarity independent of any nonlinear variations in the time dimension. The technique wasElsevier Ltd. ial and Systems Engineering, , Piscataway, NJ 08854, USA. g).originally developed for speech recognition, but several researchers have evaluated its application in other domains and have developed several variants such as derivative DTW (DDTW) [11,21,22]. Fig. 1 shows the example of process of aligning two out of phase sequences by DTW. The methodology for DTW is as follows. Assume a sequence A of length m, Aa1, a2, y, ai, y, am and a sequence B of length n, Bb1, b2, y, bj, y, bn. We create an m-by-n path matrix where the (ith, jth) element of matrix contains the distance between the two points ai and bj such that dðai,bjÞ 99ðaibjÞ99p, where 99 99p represents the lp norm. The warping path is typically subject to several constraints such as [22]Endpoint constraint: the starting and ending points of warping path have to be the first and ...

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...slo, Norway [6] [1], handwriting recognition [17] and gesture recognition [2] [4]. The vast majority of the recent work into DTW has focused on making the algorithm more computationally efficient [6] =-=[7]-=-, with the time series in these works all being uni-dimensional signals. Proposed improvements to DTW included constraining the warping path [12] [5], lowerbounding [8] [10], numerosity reduction [19]...

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...ons are not time-synchronized, even though the different demonstrations typically do not vary largely. To deal with varying movement velocity profiles, we apply derivative dynamic time warping (DDTW) =-=[15]-=- which is able to account for local distortions in the time domain by computing a nonlinear transformation of the time axis of the individual demonstrations. Based on the aligned demonstrations, we ca...