Complex Activity Meta-Activity Profiles Dumbbell a:(Sg,S8,S7,S5,s7,s8） After that,for any two complex activities ci and cj.we add Triceps B:(s8,S8》 the distances from all three dimensions together,and obtain the Extension Y:(s5,s6,S7) overall distance between the two complex activities as follows: Upright a:(s0,s2,s3,53,S2,S1】 Barbell B:(s10,S10,S11,S10） Row Y:(s3,s8,S8) Lee=VLe(a)()+I()(+)) (8) Dumbbell a:(s0,82,s3,sg,810 Lateral 3:(s2》 Therefore,given a test complex activity c.we enumerate all Raise Y:(S2,S1,S0,s11,s0,s1》 template meta-activity profiles of all complex activities ciEC Butter a:(82》 Fly B:(S2,S1,S0,S11,s1,s2)》 and compute their distance Le then we select the category y:(s0,s2,S2,S1,S0】 of the template complex activity with the least distance as the TABLE I recognition result. EXAMPLE META-ACTIVITY PROFILES FOR THE COMPLEX ACTIVITIES V.PERFORMANCE EVALUATION sequences of strings,we leverage this term to denote the A.Experimental Setup difference between two sequences of meta-activity profiles. We have implemented a prototype system using the android In order to compute the edit distance between two pairs of phone(SAMSUNG Galaxy S5)2,which is attached to the wrist complex activities,it is essential to first consider the distance of the human subject,as shown in Fig.9.The android phone between two meta-activities.As aforementioned in Section III, is embedded with inertial sensors including accelerometers for each dimension of the angle profiles,the meta-activity and magnetometers.The lower-arm direction is consistent with is a process which is performed in a specified sector with the Y-axis of the smart phone's local coordinate system.In a specified rotation direction.When considering the distance the experiment,we let 10 volunteers perform 10 categories between two meta-activities,we should take these two issues of complex activities,they have different heights,genders, into consideration.i.e..the distance between sectors and the and ages.For each category of complex activity,20 sam- distance between rotation directions.Considering the distance ples of inertial measurements are collected for each subject. between sectors,assume the number of sectors is m,for any In order to evaluate the performance for user-independent two meta-activities mi and mj,suppose their corresponding activity sensing,we leverage the n-fold cross-validation as sector numbers are respectively si and sj(0<si<sj<m). follows:for each round of evaluation,we select one human the distance between them is defined as follows: subject as the test case,and obtain the template profiles from d.(mi;mj)=min{(sj-si)modm,(si-sj+m)modm}. n-1 of the remaining human subjects.We then evaluate the recognition accuracy and time delay for the three solutions: The distance is the minimum distance between the two sectors 1)Acceleration-based Matching (AM):It uses the DTW to si and s;either clockwise or anti-clockwise.Considering the perform waveform-based matching in terms of the acceleration distance between rotation directions(clock-wise or anti-clock- measurements.2)Angle Profiles-based Matching (APM):It wise),for any two meta-activities mi and mj,if they have the uses the DTW to perform waveform-based matching in terms same rotation direction,then we set the distance dr(mi,mj) of the angle profiles.3)Meta-Activity Recognition(MAR):It to 0.Otherwise,we set the distance dr(mi,mj)to (n= uses the least edit distance-based matching in terms of the m/4 in our implementation).Hence,considering the above meta-activity profiles. two issues,the distance between two meta-activities m;and mj is as follows: d(m,m）=d,(m,mj）+d,(m,m) (6) Therefore,for each dimension of the angles profiles,a complex activity ciC can be depicted as a sequence of the meta-activities,i.e,c=(mi,…,m）,where mj∈M. Then,for a specified dimension,considering any two com- Fig.9.Experimental Setup plex activities,e.g.,a and b,we can compute their distance B.Parameter Selection Lab(lal,b)by referring to the Levenshtein distance [7]: For the meta-activity recognition,the angle of a meta- max(i,j)×4 if min(i,j)=0, activity sector,i.e.,6,is very crucial to the performance in La.b(i,j)= La.b(i-1,j)+4 (7) terms of recognition accuracy and time efficiency.It directly min La.6(i,j-1)+u otherwise. determines the number of meta-activities within a specified La.b(i-1,j-1)+d(ai;bj) complex activity.Therefore,we conduct experiments to eval- where La.(i,j)is the distance between the first i meta- uate the performance with different values of 6.We set the activities of a and the first j meta-activities of b.u is the av- number of human subjects in template construction to 5. erage distance between any two meta-activities (u=0.75 x m in our implementation),and d(ai,bj)is the distance between 2As COTS smart watches are still not embedded with magnetometers to help build the body coordinate system,so in this paper we choose to use the the ith meta-activity of a and the jth meta-activity of b. android phone as the testing wearable devices.Complex Activity Meta-Activity Profiles Dumbbell α : hS9, S8, S7, S5, s7, s8i Triceps β : hs8, S8i Extension γ : hs5, s6, S7i Upright α : hs0, s2, s3, S3, S2, S1i Barbell β : hs10, S10, S11, S10i Row γ : hs3, s8, S8i Dumbbell α : hs0, s2, s3, s9, s10i Lateral β : hs2i Raise γ : hS2, S1, S0, s11, s0, s1i Butter α : hs2i Fly β : hS2, S1, S0, S11, s1, s2i γ : hs0, s2, S2, S1, S0i TABLE I EXAMPLE META-ACTIVITY PROFILES FOR THE COMPLEX ACTIVITIES sequences of strings, we leverage this term to denote the difference between two sequences of meta-activity profiles. In order to compute the edit distance between two pairs of complex activities, it is essential to first consider the distance between two meta-activities. As aforementioned in Section III, for each dimension of the angle profiles, the meta-activity is a process which is performed in a specified sector with a specified rotation direction. When considering the distance between two meta-activities, we should take these two issues into consideration, i.e., the distance between sectors and the distance between rotation directions. Considering the distance between sectors, assume the number of sectors is m, for any two meta-activities mi and mj , suppose their corresponding sector numbers are respectively si and sj (0 ≤ si ≤ sj < m), the distance between them is defined as follows: ds(mi , mj ) = min{(sj − si)modm,(si − sj + m)modm}. The distance is the minimum distance between the two sectors si and sj either clockwise or anti-clockwise. Considering the distance between rotation directions (clock-wise or anti-clock￾wise), for any two meta-activities mi and mj , if they have the same rotation direction, then we set the distance dr(mi , mj ) to 0. Otherwise, we set the distance dr(mi , mj ) to Ω (Ω = m/4 in our implementation). Hence, considering the above two issues, the distance between two meta-activities mi and mj is as follows: d(mi , mj ) = ds(mi , mj ) + dr(mi , mj ). (6) Therefore, for each dimension of the angles profiles, a complex activity ci ∈ C can be depicted as a sequence of the meta-activities, i.e., ci = hmj1 , · · · , mjk i, where mj ∈ M. Then, for a specified dimension, considering any two com￾plex activities, e.g., a and b, we can compute their distance La,b(|a|, |b|) by referring to the Levenshtein distance [7]: La,b(i, j) =    max(i, j) × µ if min(i, j) = 0, min    La,b(i − 1, j) + µ La,b(i, j − 1) + µ otherwise. La,b(i − 1, j − 1) + d(ai , bj ) (7) where La,b(i, j) is the distance between the first i meta￾activities of a and the first j meta-activities of b, µ is the av￾erage distance between any two meta-activities (µ = 0.75×m in our implementation), and d(ai , bj ) is the distance between the ith meta-activity of a and the jth meta-activity of b. After that, for any two complex activities ci and cj , we add the distances from all three dimensions together, and obtain the overall distance between the two complex activities as follows: Lci,cj = q L 2 ci(α),cj (α) + L 2 ci(β),cj (β) + L 2 ci(γ),cj (γ) . (8) Therefore, given a test complex activity ci , we enumerate all template meta-activity profiles of all complex activities cj ∈ C and compute their distance Lci,cj , then we select the category of the template complex activity with the least distance as the recognition result. V. PERFORMANCE EVALUATION A. Experimental Setup We have implemented a prototype system using the android phone (SAMSUNG Galaxy S5)2 , which is attached to the wrist of the human subject, as shown in Fig.9. The android phone is embedded with inertial sensors including accelerometers and magnetometers. The lower-arm direction is consistent with the Y -axis of the smart phone’s local coordinate system. In the experiment, we let 10 volunteers perform 10 categories of complex activities, they have different heights, genders, and ages. For each category of complex activity, 20 sam￾ples of inertial measurements are collected for each subject. In order to evaluate the performance for user-independent activity sensing, we leverage the n-fold cross-validation as follows: for each round of evaluation, we select one human subject as the test case, and obtain the template profiles from n − 1 of the remaining human subjects. We then evaluate the recognition accuracy and time delay for the three solutions: 1) Acceleration-based Matching (AM): It uses the DTW to perform waveform-based matching in terms of the acceleration measurements. 2) Angle Profiles-based Matching (APM): It uses the DTW to perform waveform-based matching in terms of the angle profiles. 3) Meta-Activity Recognition (MAR): It uses the least edit distance-based matching in terms of the meta-activity profiles. Z-axis Y-axis X-axis Fig. 9. Experimental Setup B. Parameter Selection For the meta-activity recognition, the angle of a meta￾activity sector, i.e., δ, is very crucial to the performance in terms of recognition accuracy and time efficiency. It directly determines the number of meta-activities within a specified complex activity. Therefore, we conduct experiments to eval￾uate the performance with different values of δ. We set the number of human subjects in template construction to 5. 2As COTS smart watches are still not embedded with magnetometers to help build the body coordinate system, so in this paper we choose to use the android phone as the testing wearable devices