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Boltzmann Machine (BM)

Boltzmann Machine (BM)

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In this paper, we propose a deep generative model named Multimodal Conditional Deep Belief Network (MCDBN) for cross-modal learning of 3D motion data and their non-injective 2D projections on the image plane. This model has a three sectional structure, which learns conditional probability distribution of 3D motion data given 2D projections. Two dis...

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... Boltzmann Machine (BM) which is depicted in Fig. 1 can be viewed as either a probabilistic neural network or an undirected graphical model. It consists of visible and hidden layers of the binary variables with fully connected links [31]- [32]. The variables in the visible layer represent the data while the hidden variables have the role of enlarging class of representable ...
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... each action, PCCs of every pair of 50 real motion samples have been computed which would result in 1225 PCCs. To compare the results fairly, the PCC histograms of 1225 randomly chosen pairs of regenerated movements against the PCC histograms of all real movements are depicted (Fig. 10). Two Weibull distributions are fitted to the histograms in red and blue colors for real and regenerated data, respectively. The parameters of the fitted distributions are reported in Table 5. The range of PCCs in Fig. 9 and Fig. 10 are very similar, that indicate sampling from PCCs is done unbiasedly and the sampled PCCs are ...
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... 1225 randomly chosen pairs of regenerated movements against the PCC histograms of all real movements are depicted (Fig. 10). Two Weibull distributions are fitted to the histograms in red and blue colors for real and regenerated data, respectively. The parameters of the fitted distributions are reported in Table 5. The range of PCCs in Fig. 9 and Fig. 10 are very similar, that indicate sampling from PCCs is done unbiasedly and the sampled PCCs are distributed according to the main distributions in Fig. 9. However, the shape parameters in Table 4 tend to upper values due to more sample numbers. The PCC histograms of pairwise real and regenerated motions for jumping in place action are ...
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... are very similar, that indicate sampling from PCCs is done unbiasedly and the sampled PCCs are distributed according to the main distributions in Fig. 9. However, the shape parameters in Table 4 tend to upper values due to more sample numbers. The PCC histograms of pairwise real and regenerated motions for jumping in place action are very similar (Fig. 10.a). The real data have lower mean PCC values in comparison with regenerated data. The PCC histograms of pairwise real and regenerated motions for jumping-jacks action are somehow similar (Fig. 10.b). The real data have greater standard deviation and PCC values of real data are usually lower than the regenerated data which means the ...
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... to upper values due to more sample numbers. The PCC histograms of pairwise real and regenerated motions for jumping in place action are very similar (Fig. 10.a). The real data have lower mean PCC values in comparison with regenerated data. The PCC histograms of pairwise real and regenerated motions for jumping-jacks action are somehow similar (Fig. 10.b). The real data have greater standard deviation and PCC values of real data are usually lower than the regenerated data which means the regenerated data have lower stochasticity. ...
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... that the PCC values of real data are in the range of [0.95 1] and the PCC values of regenerated data are in the range of [0. 97 1]. The fitted shape and scale parameters for these two actions in Table 5, obviously show the described situations. The PCC histogram of pairwise real and regenerated motions for clapping hands action are very similar (Fig. 10.e) and the parameters of fitted distributions are close to each other. The PCC histograms of pairwise real and regenerated motions for throwing a ball action is depicted in Fig. 10.f. The real data has greater standard deviation and PCC values of real data are usually lower than regenerated data which means regenerated data has lower ...
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... two actions in Table 5, obviously show the described situations. The PCC histogram of pairwise real and regenerated motions for clapping hands action are very similar (Fig. 10.e) and the parameters of fitted distributions are close to each other. The PCC histograms of pairwise real and regenerated motions for throwing a ball action is depicted in Fig. 10.f. The real data has greater standard deviation and PCC values of real data are usually lower than regenerated data which means regenerated data has lower stochasticity. Comparing jumping in place and jumping-jacks actions, we see that jumping in place action have more uniform distribution of PCCs in different bins of histograms (Fig. ...
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... usually lower than regenerated data which means regenerated data has lower stochasticity. Comparing jumping in place and jumping-jacks actions, we see that jumping in place action have more uniform distribution of PCCs in different bins of histograms (Fig. 8.a and Fig. 8.b). Furthermore, pairwise PCC histograms of real and regenerated motions ( Fig. 10.a and Fig. 10.b) and the parameters of fitted Weibull distributions for these actions show that the regenerated motions for jumping in place best fit the real data. We believe that fewer employed joints in the jumping in place action causes this ...
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... similar procedure is performed for CMU dataset. The only difference is that the number of samples in CMU Mocap are not equal for different actions. There are 6 samples for jumping, 9 and 81 samples for forward jump and walking, respectively. The histograms of PCCs between real and regenerated movements of CMU Mocap dataset are depicted in Fig. 11 and the statistics of results are reported in Table 6. ...
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... pairwise PCC histogram of real and regenerated motions for CMU Mocap dataset are depicted in Fig. 12 and the parameters of fitted distributions are reported in Table 7. Fig. 12.a show the PCC histogram of real and 60 regenerated motions and the PCC histograms of pairwise real and regenerated motions for jumping action of CMU dataset, respectively. All the PCC values are in the narrow range of [0.95 0.99]. The mean PCC value is 0.9662 ...
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... pairwise PCC histogram of real and regenerated motions for CMU Mocap dataset are depicted in Fig. 12 and the parameters of fitted distributions are reported in Table 7. Fig. 12.a show the PCC histogram of real and 60 regenerated motions and the PCC histograms of pairwise real and regenerated motions for jumping action of CMU dataset, respectively. All the PCC values are in the narrow range of [0.95 0.99]. The mean PCC value is 0.9662 and the low standard deviation (0.0161) show high confidence of the results ...
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... real and regenerated motions for jumping action of CMU dataset, respectively. All the PCC values are in the narrow range of [0.95 0.99]. The mean PCC value is 0.9662 and the low standard deviation (0.0161) show high confidence of the results in different runs. The histograms are very similar and the fitted parameters are also close to each other. Fig. 11.b shows the PCC histogram of real and 90 regenerated movements for forward jump action of CMU dataset. Two-third of the PCC values are in the range of [0.93 0.99]. The pairwise PCC values of the real motions in Fig. 12.b have greater standard deviation and lower values compared with PCC values of the regenerated data. The fitted shape ...
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... of the results in different runs. The histograms are very similar and the fitted parameters are also close to each other. Fig. 11.b shows the PCC histogram of real and 90 regenerated movements for forward jump action of CMU dataset. Two-third of the PCC values are in the range of [0.93 0.99]. The pairwise PCC values of the real motions in Fig. 12.b have greater standard deviation and lower values compared with PCC values of the regenerated data. The fitted shape and scale parameters, obviously show the situation. The results show that the MCDBN performs better in the jumping action of CMU dataset compared with forward jump action. The reason is the greater number of employed ...
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... of the PCC values in the PCC histogram of real and 810 regenerated movements for walking action of CMU dataset (Fig. 12.c) are in the range of [0.8 0.92]. The shapes of the PCC histograms of pairwise real and regenerated motions for walking action of CMU dataset are very similar and the parameters of fitted distributions are close to each other. Due to the complicatedness of walking action and other factors such as walking styles, the pairwise PCCs of real ...
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... Boltzmann Machine (BM) which is depicted in Fig. 1 can be viewed as either a probabilistic neural network or an undirected graphical model. It consists of visible and hidden layers of the binary variables with fully connected links [31]- [32]. The variables in the visible layer represent the data while the hidden variables have the role of enlarging class of representable ...
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... each action, PCCs of every pair of 50 real motion samples have been computed which would result in 1225 PCCs. To compare the results fairly, the PCC histograms of 1225 randomly chosen pairs of regenerated movements against the PCC histograms of all real movements are depicted (Fig. 10). Two Weibull distributions are fitted to the histograms in red and blue colors for real and regenerated data, respectively. The parameters of the fitted distributions are reported in Table 5. The range of PCCs in Fig. 9 and Fig. 10 are very similar, that indicate sampling from PCCs is done unbiasedly and the sampled PCCs are ...
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... 1225 randomly chosen pairs of regenerated movements against the PCC histograms of all real movements are depicted (Fig. 10). Two Weibull distributions are fitted to the histograms in red and blue colors for real and regenerated data, respectively. The parameters of the fitted distributions are reported in Table 5. The range of PCCs in Fig. 9 and Fig. 10 are very similar, that indicate sampling from PCCs is done unbiasedly and the sampled PCCs are distributed according to the main distributions in Fig. 9. However, the shape parameters in Table 4 tend to upper values due to more sample numbers. The PCC histograms of pairwise real and regenerated motions for jumping in place action are ...
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... are very similar, that indicate sampling from PCCs is done unbiasedly and the sampled PCCs are distributed according to the main distributions in Fig. 9. However, the shape parameters in Table 4 tend to upper values due to more sample numbers. The PCC histograms of pairwise real and regenerated motions for jumping in place action are very similar (Fig. 10.a). The real data have lower mean PCC values in comparison with regenerated data. The PCC histograms of pairwise real and regenerated motions for jumping-jacks action are somehow similar (Fig. 10.b). The real data have greater standard deviation and PCC values of real data are usually lower than the regenerated data which means the ...
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... to upper values due to more sample numbers. The PCC histograms of pairwise real and regenerated motions for jumping in place action are very similar (Fig. 10.a). The real data have lower mean PCC values in comparison with regenerated data. The PCC histograms of pairwise real and regenerated motions for jumping-jacks action are somehow similar (Fig. 10.b). The real data have greater standard deviation and PCC values of real data are usually lower than the regenerated data which means the regenerated data have lower stochasticity. ...
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... that the PCC values of real data are in the range of [0.95 1] and the PCC values of regenerated data are in the range of [0. 97 1]. The fitted shape and scale parameters for these two actions in Table 5, obviously show the described situations. The PCC histogram of pairwise real and regenerated motions for clapping hands action are very similar (Fig. 10.e) and the parameters of fitted distributions are close to each other. The PCC histograms of pairwise real and regenerated motions for throwing a ball action is depicted in Fig. 10.f. The real data has greater standard deviation and PCC values of real data are usually lower than regenerated data which means regenerated data has lower ...
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... two actions in Table 5, obviously show the described situations. The PCC histogram of pairwise real and regenerated motions for clapping hands action are very similar (Fig. 10.e) and the parameters of fitted distributions are close to each other. The PCC histograms of pairwise real and regenerated motions for throwing a ball action is depicted in Fig. 10.f. The real data has greater standard deviation and PCC values of real data are usually lower than regenerated data which means regenerated data has lower stochasticity. Comparing jumping in place and jumping-jacks actions, we see that jumping in place action have more uniform distribution of PCCs in different bins of histograms (Fig. ...
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... usually lower than regenerated data which means regenerated data has lower stochasticity. Comparing jumping in place and jumping-jacks actions, we see that jumping in place action have more uniform distribution of PCCs in different bins of histograms (Fig. 8.a and Fig. 8.b). Furthermore, pairwise PCC histograms of real and regenerated motions ( Fig. 10.a and Fig. 10.b) and the parameters of fitted Weibull distributions for these actions show that the regenerated motions for jumping in place best fit the real data. We believe that fewer employed joints in the jumping in place action causes this ...
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... similar procedure is performed for CMU dataset. The only difference is that the number of samples in CMU Mocap are not equal for different actions. There are 6 samples for jumping, 9 and 81 samples for forward jump and walking, respectively. The histograms of PCCs between real and regenerated movements of CMU Mocap dataset are depicted in Fig. 11 and the statistics of results are reported in Table 6. ...
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... pairwise PCC histogram of real and regenerated motions for CMU Mocap dataset are depicted in Fig. 12 and the parameters of fitted distributions are reported in Table 7. Fig. 12.a show the PCC histogram of real and 60 regenerated motions and the PCC histograms of pairwise real and regenerated motions for jumping action of CMU dataset, respectively. All the PCC values are in the narrow range of [0.95 0.99]. The mean PCC value is 0.9662 ...
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... pairwise PCC histogram of real and regenerated motions for CMU Mocap dataset are depicted in Fig. 12 and the parameters of fitted distributions are reported in Table 7. Fig. 12.a show the PCC histogram of real and 60 regenerated motions and the PCC histograms of pairwise real and regenerated motions for jumping action of CMU dataset, respectively. All the PCC values are in the narrow range of [0.95 0.99]. The mean PCC value is 0.9662 and the low standard deviation (0.0161) show high confidence of the results ...
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... real and regenerated motions for jumping action of CMU dataset, respectively. All the PCC values are in the narrow range of [0.95 0.99]. The mean PCC value is 0.9662 and the low standard deviation (0.0161) show high confidence of the results in different runs. The histograms are very similar and the fitted parameters are also close to each other. Fig. 11.b shows the PCC histogram of real and 90 regenerated movements for forward jump action of CMU dataset. Two-third of the PCC values are in the range of [0.93 0.99]. The pairwise PCC values of the real motions in Fig. 12.b have greater standard deviation and lower values compared with PCC values of the regenerated data. The fitted shape ...
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... of the results in different runs. The histograms are very similar and the fitted parameters are also close to each other. Fig. 11.b shows the PCC histogram of real and 90 regenerated movements for forward jump action of CMU dataset. Two-third of the PCC values are in the range of [0.93 0.99]. The pairwise PCC values of the real motions in Fig. 12.b have greater standard deviation and lower values compared with PCC values of the regenerated data. The fitted shape and scale parameters, obviously show the situation. The results show that the MCDBN performs better in the jumping action of CMU dataset compared with forward jump action. The reason is the greater number of employed ...
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... of the PCC values in the PCC histogram of real and 810 regenerated movements for walking action of CMU dataset (Fig. 12.c) are in the range of [0.8 0.92]. The shapes of the PCC histograms of pairwise real and regenerated motions for walking action of CMU dataset are very similar and the parameters of fitted distributions are close to each other. Due to the complicatedness of walking action and other factors such as walking styles, the pairwise PCCs of real ...

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