- #31
Stephen Tashi
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Let's discuss an utterly simple method. Perhaps objections to it will clarify the problem further.
Let the data points be (x_i,y_i,z_i,t_i) for i = 1 to N. If this data represented a line perfectly parallel to the y-axis then the x and z values would remain constant while the y value varied.
If we have data from an imperfect line, we could estimate the line that the data is "trying to" follow in various ways. The simplest seems to be to estimate that the \hat{x} = the average of the x values in the data and \hat{z} = the average of the z values.
We can quantify the "error" that the imperfect data has in various ways. The one that comes to my mind first
\hat{\sigma^2} = (\frac{1}{N}) { \sum_{i=1}^N ( (\hat{x} - x )^2 + (\hat{z}-z)^2)}
Of course the idea is to classify the data as a gesture parallel to the y-axis when \hat{\sigma^2} is "small". What constitutes a small or large error would have to be determined empirically. You'd have to do a different test for each axis, but this is not an elaborate computation.
One weakness of this method is that it doesn't give any more credit to data that is a perfect straight line but slightly out-of-parallel vs data that is scattered. Is this weakness the reason that you are considering sophisticated statistical methods?
Let the data points be (x_i,y_i,z_i,t_i) for i = 1 to N. If this data represented a line perfectly parallel to the y-axis then the x and z values would remain constant while the y value varied.
If we have data from an imperfect line, we could estimate the line that the data is "trying to" follow in various ways. The simplest seems to be to estimate that the \hat{x} = the average of the x values in the data and \hat{z} = the average of the z values.
We can quantify the "error" that the imperfect data has in various ways. The one that comes to my mind first
\hat{\sigma^2} = (\frac{1}{N}) { \sum_{i=1}^N ( (\hat{x} - x )^2 + (\hat{z}-z)^2)}
Of course the idea is to classify the data as a gesture parallel to the y-axis when \hat{\sigma^2} is "small". What constitutes a small or large error would have to be determined empirically. You'd have to do a different test for each axis, but this is not an elaborate computation.
One weakness of this method is that it doesn't give any more credit to data that is a perfect straight line but slightly out-of-parallel vs data that is scattered. Is this weakness the reason that you are considering sophisticated statistical methods?