Efficient duration and hierarchical modeling for human activity recognition

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Fine et al. [10] were the first to introduce the HHMM, generalizing the HMM by viewing each state as an autonomous probabilistic HMM model itself.

“Fine et al. [10] were the first to introduce the HHMM, generalizing the HMM by viewing each state as an autonomous probabilistic HMM model itself.”

• cites [10] Fine, 1998, The hierarchical hidden Markov model: Analysis and applications, Machine Learning sourceSupported

Probably not a substantial claim: may not pass S3 (load-bearing).

The semantics of the proposed switching HSMM is somewhat similar to the switching linear dynamic system (SLDS) proposed by [28] for the bee-dance tracking problem.

“The semantics of our proposed switching HSMM is somewhat similar to the switching linear dynamic system (SLDS) proposed by [28] for the bee-dance tracking problem.”

• cites [28] S. Min Oh, J.M. Rehg, T. Balch, F. Dellaert, Learning and inference in parametric switching linear dynamic systems, in: International Conference on Computer Vision (ICCV-2005), Beijing, China, 2005 sourceSupported

Classified as probably not a substantial claim.

In a two-layer HHMM, the duration of a bottom-level state i in ch(p) follows a geometric distribution.

“In this two-layer HHMM, the duration of a bottom-level state i ∈ ch(p), denoted as D p,i , follows a geometric distribution.”

• cites [3] Bui, 2004, Hierarchical hidden Markov models with general state hierarchyNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [10] Fine, 1998, The hierarchical hidden Markov model: Analysis and applications, Machine Learning sourceSupported

May combine two claims.

The CxSHSMM significantly outperforms the HHMM (without duration model) and the MuSHSMM (multinomial duration).

“The experiments show that the CxSHSMM significantly outperforms the HHMM (without duration model) and the MuSHSMM (multinomial duration).”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

The Coxian parameterization requires a relatively small number of phases.

“Furthermore, the Coxian parameterization requires a relatively small number of phases.”

May combine two claims.

The Coxian comes second at 91.39% when K=5, achieved with a significant speedup (about 10 times faster than the MuHSMM in this case).

“The Coxian comes second at 91.39% when K = 5, however, it was achieved with a significant speedup (about 10 times faster than the MuHSMM in this case).”

May combine two claims.

The Multinomial was able to learn both dominant modes in the data and fitted best in this example.

“The Multinomial was able to learn both dominant modes in the data and fitted best in this example.”

May combine two claims.

In this case, multinomial parameterization would require over 100 parameters, whereas the Coxian requires less than 10.

“We also note that, in this case, multinomial parameterization would requires over 100 parameters whilst it is less than 10 for the Coxian.”

May combine two claims.

The empirical speedup factor goes from 7 times for the first four sequences to 10 times for the next three sequences.

“The empirical speedup factor goes from 7 times for the first four sequences, which are from activity (a.1) whose lengths are shortest among the three activity types, to 10 times for the next three sequences taken from activity (a.2), whose lengths are generally the longest.”

May combine two claims.

The HMM performs worst with only 68% average classification accuracy, and the PsHSMM is almost equally poor at 69%.

“The result shows that the HMM performs worst with only 68% in average classification accuracy; the performance of the PsHSMM is almost equally poor (69%).”

May combine two claims.

Among the Coxian models, performance varies as the number of phases increases, and a good performance is observed when K=5 in terms of both recognition and early detection rates.

“Among the Coxian models, performance varies as the number of phases increases.We observe a good performance when K = 5 in terms of both recognition and early detection rates as shown in Table 2.”

May combine two claims.

Being weakly multi-modal, the Coxian has learned the first dominant mode in the data well and smoothed out the less dominant one.

“Being weakly multi-modal, the Coxian has learned the first dominant mode in the data well and smoothed out the less dominant one.”

May combine two claims.

Starting from K=3, Coxian-based models begin to increase their performances and outperform the baseline models quickly.

“Starting from K = 3, Coxian-based models begin to increase their performances and outperform these baseline models quickly.”

May combine two claims.

Most models generally detect activity (a.1) accurately and early, while sometimes confusing the other two activities.

“It is further observed that most models generally detect activity (a.1) accurately and early, while sometimes confusing the other two activities.”

May combine two claims.

As the number of phases increases, the mode of the learned Coxian gradually shifts to the right, showing a sign of going from underfitting to good fitting and overfitting; starting from K=5, it matches reasonably well with the dominant mode from the empirical distribution.

“It can seen that as the number of phases increases, the mode of the learned Coxian gradually shifts to the right, showing sign of going from underfitting to good fitting and overfitting.Starting from K = 5, it matches reasonably well with the dominant mode from the empirical distribution (bottom chart, marked with * ).”

May combine two claims.

The CxHSMM computation time does not increase noticeably with activity length, while the MuHSMM runs much slower as it moves from activities (a.1) to (a.2), taking more than 35 min per EM iteration.

“It is important to note that while the CxHSMM computation time does not increase noticeably with the activity length ((a.1) vs. (a.2)), the MuHSMM runs much slower as it moves from activities (a.1) to (a.2), taking more than 35 min per EM iteration.”

May combine two claims.

In the region of false alarm not greater than 10%, the 2-phase Coxian D p,i scores best with TP = 84%, compared to 82% for the 5-phase Coxian D p,i and 78% for the uniform multinomial D p,i.

“In the region of false alarm not greater than 10% (i.e.FP 10%), the 2-phase Coxian D p,i scores best with TP = 84% in comparison to 82%, and 78% from the 5-phase Coxian D p,i and the uniform multinomial D p,i , respectively.”

May combine two claims.

For K = 4, despite gaining 80% overall, the CxSHSMM failed on activity (a.5) more than 50% of the time.

“For example, for K = 4, despite of gaining 80% overall, the CxSHSMM has failed miserably on the activity (a.5) more than 50% of the time.”

May combine two claims.

With just 1% training labels, the 3-phase CxSHSMM increased its performance to 73%, compared with a rise of only 2% (from 29% to 31%) for the HHMM.

“However, when supplied with a small fraction of training labels (e.g., with just 1%), the 3-phase CxSHSMM dramatically increases its performance to 73% as compared with a modest rise of only 2% (from 29% to 31%) for the case of the HHMM (further results are shown in Table A.6 in Appendix A).”

May combine two claims.

The MuSHSMM segmented reasonably well for activities (a.1), (a.2), (a.4), (a.5), but failed on activity (a.6) one third of the time and occasionally failed on activity (a.3), resulting in 90.4% performance.

“The MuSHSMM has segmented reasonably well for the set of activities {(a.1), (a.2), (a.4), (a.5)}, but failed on activity (a.6) one third of the time, and occasionally failed on activity (a.3), resulting in a performance of 90.4%.”

May combine two claims.

The high-level activities share considerable overlappings in their trajectories, totally overlapping in some cases, and are more complicated than those in Section 5.2.

“In addition to this capturing flexibility, our high-level activities share considerable overlappings in their trajectories (totally overlap in some cases), and more complicated than those considered previously in Section 5.2.”

May combine two claims.

For unlabeled data, the 3-phase CxSHSMM significantly performed better than the HHMM, but its performance was still very low and unsatisfactory (49.4%).

“The results show that, even though the 3-phase CxSHSMM significantly perform better than the HHMM for unlabeled data, its performance was still very low and unsatisfactory (49.4%).”

May combine two claims.

With K=2, the segmentation result was less than 70% accuracy; activity (a.1) could not be recognized when K=4 and activity (a.2) when K=3.

“With K = 2, the segmentation result was less than 70% accuracy; activity (a.1) could not be recognized when K = 4 and so was activity (a.2) when K = 3.”

May combine two claims.

The background uniform multinomial D p,i seems to be the least effective, while the 2-phase Coxian D p,i produces the considerably best ROC curve.

“The background uniform multinomial D p,i seems to be the least affective, while the 2-phase Coxian D p,i pro- duces the considerably best ROC curve.”

May combine two claims.

In an example sequence with activities (a.1) to (a.6) where first two are abnormal and rest normal, the 5-phase CxSHSMM correctly detected only the first two activities as abnormal, while the HSMM continued to label the sequence as abnormal until its end.

“While the 5-phase CxSHSMM has successfully dealt with this scenario by correctly detecting only the first two activities are abnormal, the HSMM continues to label the sequence as abnormal until the sequence reaches its end.”

May combine two claims.

For small numbers of phases (K=2,3,4), the CxSHSMM had trouble distinguishing between the first two activities, showing signs of underfitting, but still delivered good segmentation performance on the remaining activities.

“Our first observation is that, for small number of phases (K = 2, 3, 4) the CxSHSMM was having trouble in distinguishing between first two activities, showing sign of underfitting, but still delivering good segmentation performance on the remaining set of activities (Table 3(a)).”

May combine two claims.

The two-layer HHMM, without duration knowledge, learned a poor transition model at the high level, resulting in low performance.

“Finally, as expected, the two-layer HHMM, without duration knowledge, has learned a poor transition model at the high level, resulting a low performance (i.e., it occasionally detecting some activities such as (a.2) or (a.3) correctly, while generally failing to detect the others).”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

There are major overlappings between chS(5) and chS(6), and between chE(5) and chE(6), as sweeping starts and ends around the stove area.

“There are also major overlappings between chS(5) and chS(6), and between chE(5)and chE(6) as sweeping starts and ends around the stove area.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Emptying the bin takes noticeably less time than sweeping the floor or watching television.

“For instance, emptying the bin takes noticeably less time than sweeping the floor or watching television, and thus is possibly overlooked by the model.”

May combine two claims.

There is no significant difference between the Coxian and the multinomial; both have learned reasonable transitions from activities (a.2) to (a.3) or (a.4), from (a.3) to (a.4) or (a.6), and from (a.5) to (a.3) or (a.6).

“In particular, there is no significant difference between the Coxian and the multinomial.They both have learned reasonable transitions: from activities (a.2) to (a.3) or (a.4), from activities (a.3) to (a.4) or (a.6) and from activities (a.5) to (a.3) or (a.6).”

May combine two claims.

On a workstation with 3.2 GHz CPU and 2 GB memory, the 5-phase Coxian took approximately 20 min per EM iteration on one training sequence, while the MuSHSMM took approximately 19 hours (57 times slower).

“on a workstation configured with 3.2 GHz CPU, 2 GB memory the 5-phase Coxian took approximately 20 min per one EM iteration on one single training sequence, while the MuSHSMM took approximately 19 hours (57 times slower); therefore its results are not reported.”

May combine two claims.

Starting from K=5 onward, the CxSHSMM resolved the problem and produced consistent segmentation accuracy across all activities, achieving more than 96% accuracy on average; optimal performance was at K=5 with segmentation accuracy 97.73% and early detection rate 7.56%.

“However, starting from K = 5 onward, the CxSHSMM has successfully resolved this problem and produced consistent segmentation accuracy across all activities, achieving more than 96% accuracy on average.The optimal performance is again marked at K = 5 in terms of segmentation accuracy (97.73%) and early detection rate (7.56%) (Table 3).”

May combine two claims.

In the unconstrained setting, more than 35% of tracks were lost, affecting every sequence recorded in the dataset.

“This setting has created a significant portion of the tracks being lost (more than 35%), and affecting every sequence recorded in the dataset.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

ch(5) is a subset of ch(6), as cleaning-stove concentrates only around the stove area while sweeping-floor is done on the whole floor.

“We observe that ch(5) ⊂ ch(6) as cleaning-stove concentrates only around the stove area while sweeping-floor is done on the whole floor.”

May combine two claims.

Both the Coxian and the multinomial SHSMMs can capture the patterns in the training data adequately, while the two-layer HHMM has failed to do so.

“We found that while both the Coxian and the multinomial SHSMMs can capture the patterns in the training data adequately, the two-layer HHMM has failed to do so (Table 4).”

May combine two claims.

The best baseline method is the smoothed MuSHSMM; its segmentation accuracy is comparable to the Coxian model for the first five activities, but it performs much poorly on the last activity, making its average performance approximately 3% lower than the optimal performance of the Coxian.

“The best performance among the baseline methods is the MuSHSMM with smoothing.The segmentation accuracy is comparable to the Coxian model for the first five activities.However, it performs much poorly on the last activity, making its average performance approximately 3% lower the optimal performance of the Coxian.”

May combine two claims.

The filtering computations per time slice for K=5 is 0.73 s, improved by four times per time slice compared with the multinomial (about 3 s).

“With respect to the running time, the filtering computations per time slice for K = 5 is 0.73 s, improved by four times per time slice compared with the multinomial (about 3 s).”

May combine two claims.

When K=2, the CxSHSMM occasionally segmented activity (a.1) earlier than its true ending time, while the 4-phase always did so, leading to poor performance on this activity for K=2 and 4.

“It shows that when K = 2 the CxSHSMM has occasionally segmented activity (a.1) earlier than its true ending time while the 4-phase always does so, leading to the poor performance on this activity for K = 2 and 4.”

May combine two claims.

The occupant does not strictly follow the sequential order from activity (a.1) to (a.7), but occasionally deviates, such as cleaning the stove before/after watching television.

“The occupant does not strictly follow the sequential order from activity (a.1) to (a.7), but occasionally makes a deviation such as choosing to clean the stove (a.5) before/after watching television (a.4).”

May combine two claims.

With K > 4, there is no noticeable performance difference for the CxSHSMM when data is labeled with 4%, 8%, or 16%, except in segmentation accuracy when trained with 16% labeled data.

“We also observe from Fig. 18(a) that, with K > 4, there is no noticeable performance difference for the CxSHSMM when the data is labeled with 4%, 8% or 16% with an exception in segmentation accuracy when trained with 16% labeled data (Fig. 18(b)).”

May combine two claims.

For this experiment setting, the CxSHSMM requires a small increase in computation cost compared with the two-layer HHMM (multiplied by a factor equal to the optimal K = 4), but has dramatically increased performance overall.

“For this particular experiment setting, it requires a small increase in computation cost as compared with the two-layer HHMM (multiplied by a factor equal to the optimal K = 4), but has dramatically increased the performance over all.”

May combine two claims.

The CxHSMM achieves competitive performance close to the MuHSMM while gaining substantial improvement in computation time.

“In addition, it achieves a competitive performance close to that of the MuHSMM, whilst gaining a substantial improvement in computation time.”

May combine two claims.

The model can learn what an occupant normally does during the day from unsegmented training data and then perform online activity classification, segmentation and abnormality detection.

“The model can learn what an occupant normally does during the day from unsegmented training data and then perform online activity classification, segmentation and abnormality detection.”

Classified as probably not a substantial claim. May combine two claims.

Two popular classes of extensions to the HMM have been proposed: one relaxes the strong Markov assumption by modeling state duration, and the other enriches the basic HMM by introducing hierarchical structure.

“To overcome these limitations, two popular classes of extensions to the HMM have been proposed.The first relaxes the strong Markov assumption by modeling state duration, and the second enriches the basic HMM by introducing hierarchical structure.”

May combine two claims.

HMM performance seriously degrades when the range of activities becomes more complex, or the activities exhibit long-term temporal dependencies that are difficult to deal with under the strong Markov assumption.

“While using HMMs is suitable and efficient for learning simple sequential data, its performance seriously degrades when the range of activities becomes more complex, or the activities exhibit long-term temporal dependencies that are difficult to deal with under the strong Markov assumption.”

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

If the state duration distribution is non-geometric, the corresponding semi-Markov model is strictly non-Markov.

“If the state duration distribution is non-geometric, the corresponding semi-Markov model is strictly non-Markov.”

May combine two claims.

The work of [29] extended SLDS to incorporate duration at the top level, but duration is modeled explicitly as a multinomial which leads to the same complexity problems as outlined previously.

“This work has recently been extended to incorporate duration at the top level [29].However, duration is modeled explicitly as a multinomial which leads to the same complexity problems as we have outlined previously.”

• cites [29] S. Min Oh, J.M. Rehg, F. Dellaert, Parameterized duration modeling for switching linear dynamic systems, in: International Conference on Computer Vision and Pattern Recognition (CVPR 2006), New York, USA, 2006 sourceNot checked — no full text of the source

May combine two claims.

The DBN representation of the HSMM enables it to be viewed as a member of the exponential family, and hence the HSMM parameter set θ can be estimated using the EM algorithm.

“Similar to the HMM case, the DBN representation of the HSMM enables it to be viewed as a member of the exponential family.Hence, in the learning phase, the HSMM parameter set θ can be estimated using the Expectation Maximization (EM) algorithm.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

In [19], the authors used a Coxian to model the duration of stay of the elderly in the hospital, and the resulting best number of phases is small (equals 3), consistent with the conclusion in this paper.

“In [19], the authors used a Coxian to model the duration of stay of the elderly in the hospital.Based on the data collected from the patients, the model is fitted with different number of phases using a series of likelihood ratios testing to find the best fit model.The resulting best number of phases is small (equals 3) and it is consistent with the conclusion in this paper.”

• cites [19] Marshall, 2004, Using coxian phase-type distributions to identify patient characteristics for duration of stay in hospital, Health Care Management Science sourceNot checked — no full text of the source

Classified as probably not a substantial claim.

The original HMM has an inference/learning complexity of O(|Q|^2 T).

“the original HMM, whose state space is |Q |, has an inference/learning complexity of O (|Q | 2 T )”

May combine two claims.

Inference in the proposed switching HSMM can be done exactly, whereas inference in SLDS is intractable and needs to be approximated.

“inference in ours can be done exactly, whilst that in the SLDS is intractable, and needs to be approximated.”

May combine two claims.

There has been no attempt to formulate a model combining hierarchical and semi-Markov extensions, or to empirically demonstrate the usefulness of such joint modeling over other existing methods.

“However, there has been no attempt to formulate such a model, or to empirically demonstrate the usefulness of such joint modeling over other existing methods.”

May combine two claims.

By taking advantage of the determinism of m_t, the complexity of HSMM can be reduced to O(|Q|^2 M T), or even better to O((|Q|M+|Q|^2)T).

“By taking advantage of the determinism of m t (i.e.conditionally on a given state, m t+1 = m t -1), the complexity can be reduced to O (|Q | 2 M T ), or even better to O ((|Q |M +|Q | 2 )T )”

• cites [43] Yu, 2003, An efficient forward-backward algorithm for an explicit-duration hidden Markov model, IEEE Signal Processing Letters sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

If M is set to the observation length T, the problem is then to predetermine the maximum value for T.

“If M is set to the observation length T , the problem is then to predetermine the maximum value for T .”

Probably not a substantial claim: may not pass S3 (load-bearing).

The most common choice for modeling the state duration is the multinomial due to its simplicity.

“The most common choice for modeling the state duration is the multinomial [18,21,34,43] due to its simplicity.”

• cites [18] S. Luhr, S. Venkatesh, G. West, H.H. Bui, Duration abnormality detection in sequences of human activity, Technical report, Department of Computing, Curtin University of Technology, May 2004 sourceNot checked — no full text of the source
• cites [21] Mitchell, 1999, On the complexity of explicit duration HMMs, IEEE Transactions on Speech and Audio Processing sourceNot checked — no full text of the source
• cites [34] L.R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, in: Procs. IEEE, vol. 77, 1989, pp. 257–286 sourceNot checked — no full text of the source
• cites [43] Yu, 2003, An efficient forward-backward algorithm for an explicit-duration hidden Markov model, IEEE Signal Processing Letters sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing).

If the state duration distribution D_i is a geometric random variable, the HSMM reduces to an HMM.

“Clearly, if D i is a geometric random variable (or exponential as in the case of continuous time), the HSMM reduces to an HMM.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Luhr et al. [17] were the first to employ the HHMM in modeling and recognizing human activities.

“Luhr et al. [17] were the first to employ the HHMM in modeling and recognizing human activities.”

• cites [17] S. Luhr, H.H. Bui, S. Venkatesh, G. West, Recognition of human activity through hierarchical stochastic learning, in: Int. Conf. on Pervasive Computing and Communication, 2003, pp. 416–422 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

Traditionally, the state duration D_i is modeled as the multinomial, or more generally, a member of the exponential family.

“Traditionally, D i is usually modeled as the multinomial, or more generally, a member of the exponential family.”

Probably not a substantial claim: may not pass S4 (based).

The CxSHSMM can capture normal duration patterns of atomic activities spent at each location.

“As the CxSHSMM can capture normal duration patterns of atomic activities spent at each location”

Probably not a substantial claim: may not pass S3 (load-bearing).

In a standard HMM, the duration for a state can be viewed as a geometric random variable parameterized by the corresponding diagonal entry in the transition matrix.

“In a standard hidden Markov model [34], the (random) duration for a state can be viewed as a geometric random variable parameterized by the corresponding diagonal entry in the transition matrix.”

• cites [34] L.R. Rabiner, A tutorial on hidden Markov models and selected applications in speech recognition, in: Procs. IEEE, vol. 77, 1989, pp. 257–286 sourceNot checked — no full text of the source

May combine two claims.

Discrete distribution parameterization such as Poisson can be estimated in closed-form, whereas continuous distribution such as Gamma requires numerical approximation during learning.

“In addition, whereas the discrete distribution parameterization (e.g., Poisson) can be estimated in a closed-form, the continuous distribution (e.g., the Gamma) requires numerical approximation during learning.”

May combine two claims.

The proposed switching HSMM differs from SLDS in that its state spaces are discrete, whereas SLDS is continuous at the lower level, and thus SLDS cannot model duration information.

“While both having two layers and their top layers switch in a similar manner, they are at least different in two fundamental ways: our state spaces are discrete, whilst the SLDS is continuous at the lower level, and thus SLDS cannot model duration information”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

In HHMM and related models, the state hierarchy is restricted to a tree structure and does not allow sharing of lower-level states by states at higher levels.

“Nevertheless, in these models the state hierarchy in the HHMM is restricted to a tree structure.It does not allow the sharing of lower-level states by states at higher levels.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Bui et al. [3] introduced the concept of structure sharing to allow overlapping of common substructures in the HHMM topology, providing more flexibility.

“Bui et al. [3] introduced the concept of structure sharing to allow the overlapping of common substructures in the HHMM topology, thus providing more flexibility in the model.”

• cites [3] Bui, 2004, Hierarchical hidden Markov models with general state hierarchyNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

The semi-Markov extension overcomes the limitation of the standard HMM by allowing more flexible duration distributions.

“The semi-Markov extension overcomes this limitation by allowing more flexible duration distributions.”

May combine two claims.

Duration information is important in activity modeling and can be effectively exploited by the Coxian parameterization.

“We demonstrate that duration information is important in activity modeling and can be effectively exploited by the Coxian parameterization.”

Probably not a substantial claim: may not pass S4 (based).

K is typically much smaller than the maximum duration M in practice.

“where K is typically much smaller than the maximum duration M in practice”

Probably not a substantial claim: may not pass S4 (based).

The hierarchical HMM variants have been reported to successfully exploit the hierarchical structures in human activities.

“The hierarchical HMM variants have been reported to successfully exploit the hierarchical structures in human activities.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In multinomial durations, M must be determined in advance.

“In addition, M must be determined in advance.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Previous work has recognized the need for combining both the hierarchical and semi-Markov extensions into a unified framework.

“We note that previous work [14] has also recognized the need for combining both the hierarchical and semi-Markov extensions into a unified framework.”

• cites [14] H. Kautz, O. Etzioni, D. Fox, D. Weld, Foundations of assisted cognition systems, Technical report, University of Washington, CSE, March 2003Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The number of free parameters for the Coxian duration model is |Q|(2K-1), which is usually much smaller than |Q|(M-1) for the explicit duration model, where M can be potentially as large as T.

“Finally, note that the number of free parameters for the Coxian duration model is |Q |(2K -1) which is usually much smaller than |Q |(M -1) for the explicit duration model, where M can be potentially as large as T .”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The work in [37] considers fitting web server traffic data using Coxian phase-type distributions, and its model training method can be viewed as a special case of the CxSHSMM when the starting and ending indices at the top level are known.

“The work in [37] considers the problem of fitting web server traffic data using the Coxian phasetype distributions.The model training method presented in that paper can be viewed as a special case of the CxSHSMM when the starting and ending indices at the top level are known.”

• cites [37] Riska, 2002, Matrix-analytic analysis of a map/ph/1 queue fitted to web server data sourceNot checked — no full text of the source

May combine two claims.

The CxHSMM scales linearly with the standard HMM multiplied by its number of phases K, whereas the MuHSMM and exponential family duration distribution HSMMs scale by the maximum duration length M.

“Regarding time complexity, the CxHSMM, as mentioned earlier, scales linearly with the standard HMM multiplied by its number of phases K , whereas the MuHSMM and the exponential family duration distribution HSMM (including PsHSMM and IgHSMM) scale by the maximum duration length M.”

May combine two claims.

If duration is modeled by multinomial or exponential family distributions, the complexity is O(|Q*|^2 |Q|^2 M T), where M is the maximum duration length and typically M >> K; thus, when the model becomes hierarchical, a greater computational factor is saved by using the Coxian duration model.

“Again, if the duration is modeled by the multinomial or exponential family distributions, the complexity will be O (|Q * | 2 |Q | 2 M T ), where M is the maximum duration length and typically M K .Thus, when the model becomes more complex (i.e.hierarchical), a greater computational factor is saved by using the Coxian duration model.”

May combine two claims.

The Coxian does not require a state to execute in a sequence of phases but allows entry into any arbitrary phase via the prior phase probability μ_m.

“In addition the Coxian does not require a state to execute in a sequence of phases but allows entry into any arbitrary phase via the prior phase probability μ m .”

May combine two claims.

For K << M, the CxHSMM can achieve significant speedup and avoid the problem of determining M in advance.

“For K M we can achieve significant speedup and at the same time avoided the problem of determining M in advance.”

May combine two claims.

In comparison with PsHSMM and IgHSMM, CxHSMM is better in both performance and running time; in comparison with MuHSMM, CxHSMM retains slightly worse performance but at a small fraction of computational time.

“Therefore, in comparison with the PsHSMM and the IgHSMM, the CxHSMM is better not only in performance but also in running time; whereas in comparison with the MuHSMM, the CxHSMM retains a slightly worse performance but at a small fraction of the computational time.”

Classified as probably not a substantial claim.

The study employs a leave-one-out cross validation strategy for training and testing.

“To ensure an objective result, we employ a leave-one-out cross validation strategy for training and testing.”

May combine two claims.

Because within a given state the phase variables are constrained so that m_{t+1} ∈ {m_t, m_t-1}, the full joint probability of m_t and m_{t+1} can be represented in O(K) space instead of O(K^2), reducing the overall complexity to O(|Q|^2 K T) (or O(|Q|^2 K) per filtering step).

“However, since within a given state the phase variables are constrained so that m t+1 ∈ {m t , m t -1}, the full joint probability of m t and m t+1 can be represented in just O (K ) space instead of O (K 2 ).This reduces the overall complexity to O (|Q | 2 K T ) (or O (|Q | 2 K ) per filtering step).”

Probably not a substantial claim: may not pass S3 (load-bearing).

The mean and variance of a Coxian distribution can be derived in closed-form expressions.

“The mean and variance of a Coxian distribution can also be derived in closed-form expressions [9,24]”

• cites [9] T.V. Thi Duong, Efficient duration modelling in the hierarchical hidden semi-Markov models and their applications. PhD thesis, Department of Computing, Curtin University of Technology, 2008Not checked — no full text of the source
• cites [24] Neuts, 1981Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

The Coxian duration model can be viewed as a special state-tying mechanism where a state is split into K sub-states each controlling a separate Coxian phase.

“The Coxian duration model can also be viewed as a special statetying mechanism where a state is split into K sub-states each controlling a separate Coxian phase.”

May combine two claims.

The state space of S_t in the CxSHSMM is O(|Q*||Q|K), and the recursive complexity of the smoothing distribution is O(|Q*|^2 |Q|^2 K T).

“The state space of S t is now O (|Q * ||Q |K ), therefore, the recursive complexity of the smoothing distribution is O (|Q * | 2 |Q | 2 K T ).”

Probably not a substantial claim: may not pass S3 (load-bearing).

An observation model is estimated offline with manually labeled ground truth.

“This tracking module, however, sometimes returns a neighboring position instead of the actual position occupied by the person, so an observation model is estimated offline with manually labeled ground truth [26].”

• cites [26] N.T. Nguyen, S. Venkatesh, G. West, H.H. Bui, Learning people movement model from multiple cameras for behaviour recognition, in: Joint IAPR International Workshops on Structural and Syntactical Pattern Recognition and Statistical Techniques in Pattern Recognition, Lisbon, Portugal, 2004, pp. 315–324 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

For K = 1, the CxSHSMM is equivalent to a HHMM.

“Finally, note that for K = 1, the CxSHSMM is equivalent to a HHMM.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The K-multinomial distribution is a special case of the Coxian if all λ_i is set to 1.

“The K -multinomial distribution is also a special case if all λ i is set to 1”

Classified as probably not a substantial claim. May combine two claims.

For the CxHSMM, six variants are trained by varying K from 2 to 7, and cross-validated performance on unseen data is measured to select the most suitable K.

“For the CxHSMM, we train six different variants by varying K from 2 to 7 (note that for K = 1, the CxHSMM reduces to a HMM).We measure the model's cross-validated performance in terms of classification accuracy and early detection rate (defined in the next section) on unseen data to select the most suitable K .”

May combine two claims.

The Multinomial has learned a rather 'spiky' distribution, showing a potential cause of concern for overfitting, whereas the Coxian seems to have the right fit, being able to pick up the most dominant mode and provide a smoother distribution.

“To illustrate this matter further, Fig. 10 plots another example where the Multinomial has learned a rather 'spiky' distribution, showing a potential cause of concern for overfitting, whereas the Coxian seems to have the right fit, being able to pick up the most dominant mode and provide a smoother distribution.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

[2] did not provide any empirical evaluation, nor did it address the issue of model selection.

“In addition, [2] did not provide any empirical evaluation, nor did it address the issue of model selection.”

• cites [2] J.A. Bilmes, What HMMs can do, in: IEICE Transactions on Information and Systems, 2006, pp. 869–891 sourceNot checked — no full text of the source

Probably not a substantial claim: may not pass S4 (based).

Since the CxHSMM can be represented as a DBN, existing learning and inference methods for DBNs can be readily applied to our problem.

“Since the CxHSMM can be represented as a DBN, existing learning and inference methods for DBNs can be readily applied to our problem.”

Probably not a substantial claim: may not pass S3 (load-bearing).

When K=1, the CxHSMM is equivalent to an HMM.

“We note that when K = 1 the model is equivalent to a HMM.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

A very long duration would ideally require more phases while a short one can have as small as one phase.

“A very long duration would ideally require more phases while a short one can have as small as one phase (which, in this case, reduces to a single geometric).”

May combine two claims.

The recursive calculation of α_t is performed efficiently via dynamic programming, and in an identical fashion to that of the HMM, resulting in an inference complexity of O(|Q|^2 K^2 T), or O(|Q|^2 K^2) for each filtering step.

“The recursive calculation of αt (s) is performed efficiently via dynamic programming, and in an identical fashion to that of the HMM.That results in an inference complexity of O (|Q | 2 K 2 T ), or O (|Q | 2 K 2 ) for each filtering step.”

May combine two claims.

Model performance slightly decreases when K=6 and 7, a sign of starting to overfit the training data; thus K=5 is the optimal number of phases selected for this experiment.

“The model performance slightly decreases when K = 6 and 7, a sign of starting to overfit the training data.Thus, K = 5 is the optimal number of phases selected for this experiment.”

May combine two claims.

In this experiment, K is optimal at 5, M varies from 100 to 120, and thus the Coxian is faster than other baseline models by a theoretical factor of 20 to 24 times.

“In this experiment, K is optimal at 5, whereas M varies from 100 to 120 depending on each activity.Thus, the Coxian is faster than other baseline models by a theoretical factor of 20 to 24 times.”

May combine two claims.

This makes the HSMM less flexible and unable to isolate abnormal segments in a sequence.

“This makes the HSMM less flexible and unable to isolate the abnormal segments in a sequence.”

May combine two claims.

The proposed scheme automatically constructs a general abnormal model for each normal activity class and does not require adding new abnormal models in response to unseen data.

“automatically constructing a general abnormal model for each normal activity class, our scheme offers three advantages.Firstly, it does not require the addition of new abnormal models in response to unseen data.”

May combine two claims.

The HSMM cannot segment the sequence into the six high-level activities, so it learns only a normal duration model at each cell location for the entire morning routine.

“Since the HSMM cannot segment the sequence into the six high-level activities, it learns only a normal duration model at each cell location for the entire morning routine.”

• Also stated in: § 6. Conclusion · plain

  “We note that the flat HSMM cannot be used for high-level segmentation.”

May combine two claims.

The 2-phase Coxian is chosen to represent abnormal data because it involves least computation and is known to have a high variance [32] suiting the variable characteristics of abnormality.

“The 2-phase Coxian is chosen to represent the abnormal data, not only because it involves least computation, but it is known to have a high variance [32] suiting the variable characteristics of abnormality.”

• cites [32] T. Osogami, M. Harchol-Balter, A closed-form solution for mapping general distributions to minimal PH-distributions, in: Int. Conf. on Modelling Tools and Techniques for Computer and Communication System Performance Evaluation, 2003, pp. 200–217 sourceNot checked — no full text of the source

Classified as probably not a substantial claim.

To ensure an objective evaluation, three different data sets (A, B, and C) are constructed, each consisting of 40 training and 22 testing sequences randomly partitioned from the 62 sequences.

“To ensure an objective evaluation, we construct three different data sets (A, B, and C), each consisting of 40 training and 22 testing sequences randomly partitioned from the 62 sequences.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

One possible explanation for the K=3 misclassification is that activities (a.2) and (a.3) share many common children states and have identical starting children sets.

“One possible explanation is that, these two activities share many common children states, in addition to the fact that their starting children sets are identical.”

May combine two claims.

When applied to ADLs, the CxSHSMM can learn what an occupant normally does from unsegmented training data and then perform online activity classification and segmentation.

“When applying this model to the ADLs domain, the model can learn what an occupant normally does from unsegmented training data, and then performs online activity classification and segmentation.”

May combine two claims.

The Coxian parameterization is more robust than the multinomial because it has significantly fewer free parameters, thus delivering more stable performances across activities.

“The improvements in both recognition rate and abnormality detection in our experiments confirm our belief that both duration and hierarchy information are crucial in the accurate modeling of ADLs; they further show that the Coxian parameterization is more robust as compared to the multinomial by having a significantly fewer number of free parameters, thus delivering more stable performances across”

May combine two claims.

The CxHSMM has three significant advantages over existing models: computational efficiency, low dimensionality of parameter space, and existence of closed-form parameter estimation.

“Our first main contribution is the innovative use of the Coxian distribution to efficiently model the duration information, resulting in a novel form of stochastic model, the CxHSMM, which has three significant advantages over existing models: its computational efficiency, low dimensionality of parameter space, and the existence of closed-form parameter estimation.”

May combine two claims.

Improvements in both recognition rate and abnormality detection in the experiments confirm that both duration and hierarchy information are crucial in accurate modeling of ADLs.

“The improvements in both recognition rate and abnormality detection in our experiments confirm our belief that both duration and hierarchy information are crucial in the accurate modeling of ADLs; they further show that the Coxian parameterization is more robust as compared to the multinomial by having a significantly fewer number of free parameters, thus delivering more stable performances across”