... constant[*]
The time spent between two successive points is $\frac{1}{25}$ second if the original training video sequence is taken at $25$ frames per second. 
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... residuals[*]
The residuals represent the difference between a pathlet and its approximation by the linear model. 
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... timings[*]
$ {\bf \delta'} = {\bf \delta} $ 
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... clusters[*]
as it is the case for the clustering algorithm based on the normalised cuts and the dynamic time warping algorithms. 
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... group[*]
remember that we select nodes that are close to each other to have better chances to group the extracted pathlets together by a linear model. 
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... interaction[*]
If we model interaction by modelling the joint probability of the two speakers, the cardinality of the resulting pathlet model set could be as large as the product of the cardinality of the pathlet model sets modelling each speaker individually. 
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... formula[*]
We used a uniform probability for the coin selection. 
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... is[*]
The particular case demonstrated above computes the probability of having the event ``the next toss is a head'' given that we have observed the sequence of event where all the previous $n$ tosses observed were heads. Thus we have $n_s=n$ because all the tosses observed were heads, $N_s=n$ because $n$ toss were observed and $\vert\Sigma\vert=2$ because there were 2 possible events for each toss: heads or tails. 
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... tree[*]
In practice we choose $n$ as well as the depth of the VLMM tree to be $10$. 
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... three[*]
note that the depth of trees learn in section 6.5.1 was limited to four in order to limit the computational cost 
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... models[*]
Note that the probabilities are not drawn on the tree of figure 7.2 for simplicity only 
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... space[*]
Since we aim for compact pathlet models, this case is frequent. 
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... seconds[*]
15 seconds correspond to the actual video displayed while the remaining corresponding to a countdown inserted at the beginning of the video. 
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... rate[*]
The full frame rate could not be used due to technical reasons. This also reduces the size of the video by half thus reducing the download time. 
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... time[*]
We are only stepping forward one step due to the monotonicity condition. 
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