No GPU support for mstump

[barroca8]

First of all, congratulations! I am a huge fan of your work in stumpy @seanlaw !

I noticed that there is no GPU support for mstump ( #262 (comment) ) and I was wondering if there is anything I can do to go around this.

My data has 3 dimensions in 3 columns ("x", "y", "z") and I was wondering if there was any way to do the equivalent of what would be stumpy.gpu_mstump for these 3 dimensions. Example:

mps, indices = stumpy.gpu_mstump(df, m)

The GPU part is really important for me because simply doing this with mstump takes me more than 2 hours and eventually crashes the computer.

If I do this process individually does it return the same results? Example:

window_size = 1000
mp_x, indices_x = stumpy.gpu_stump(df["x"].astype(float), m=window_size,ignore_trivial=True)
mp_y, indices_y = stumpy.gpu_stump(df["y"].astype(float), m=window_size,ignore_trivial=True)
mp_z, indices_z = stumpy.gpu_stump(df["z"].astype(float), m=window_size,ignore_trivial=True)

[seanlaw]

@barroca8 Thank you for your question/kinds words and welcome to the STUMPY community!

I noticed that there is no GPU support for mstump ( #262 (comment) ) and I was wondering if there is anything I can do to go around this.

You're correct. There is a long-standing open issue #90 for eventually adding a gpu_mstump function but it is non-trivial. PRs are certainly welcome!

If I do this process individually does it return the same results?

No, multi-dimensional matrix profiles are NOT equivalent to computing individual 1D matrix profiles and stacking them together. I recommend reading the MSTUMP tutorial in order to understand the difference. Given that you've asked this question, perhaps mstump isn't what you need? The interpretation may not be as straightforward as you may think.

My data has 3 dimensions in 3 columns ("x", "y", "z") and I was wondering if there was any way to do the equivalent of what would be stumpy.gpu_mstump for these 3 dimensions.

Computing multi-dimensional matrix profiles can be very expensive. You may try subsampling your data, say, every 10th or 100th data point instead to reduce the computational time and memory requirements.

[barroca8]

Thank you for the quick answer! I think in this case it really is 3 dimensions instead of 3 1D stacked, because this data comes from an accelerometer, measuring the acceleration in X, Y and Z every 2 microseconds. I am using Google Colab for this task because they have a GPU system, but I can try to subsample my data, given that it is more or less 500,000 rows, I can try to reduce it to 50,000 rows or even 5,000 if it's necessary

[NimaSarajpoor]

@barroca8
So, if you have just three dimensions and if you think all three are meaningful (and I think they are because they are (x,y,z) coordinates of a point in R3 space), then you may want to avoid using mstump as what it does is to capture the meaningful dimensions (and as @seanlaw said, it is computationally expensive). In my opinion, three dimensions is not that much and I think they are all meaningful here.

So, I THINK you should try to modify stump or gpu_stump so it can calculate the matrix profile by considering all three dimensions together. Modifying gpu_stump may not be easy. I think stump (no support for GPU) is easier. So, I assume you can reduce 500_000 time stamps to 50_000 time stamps. Then, you can try to modify stump or aamp:

• if you want to z-normalize each dimension: then, you can modify stump to accept three time series T_Ax, T_Ay, T_Az, and then you can do:

Replace

# see line 188 in stumpy/stump.py
pearson = cov * Σ_T_inverse[i + k] * σ_Q_inverse[i]

with:

pearson_x = cov_x * Σ_T_inverse_x[i + k] * σ_Q_inverse_x[i]
pearson_y = cov_y * Σ_T_inverse_y[i + k] * σ_Q_inverse_y[i]
pearson_z = cov_z * Σ_T_inverse_z[i + k] * σ_Q_inverse_z[i]

pearson = (pearson_x + pearson_y + pearson_z) / 3

And I hope you can get the idea here. You first need to repeat pearson = cov * Σ_T_inverse[i + k] * σ_Q_inverse[i] for three dimensions and then take their average. So, each time you are updating pearson in each dimension, and you do it for all three dimensions. Then, just take their average.

It can mathematically be proved that: $EDznorm = \sqrt{\frac{EDznorm_{x}^{2} + EDznorm_{y}^{2} + EDznorm_{z}^{2}}{3}}$ is the same as $EDznorm$ that corresponds to a pearson value that is average of the three pearson values pearson_x, pearson_y, and pearson_z. However, if you want to combine distances of three dimensions like this: $EDzorm = \frac{EDznorm_{x} + EDznorm_{y} + EDznorm_{z}}{3}$, then you cannot use the aforementioned trick! So, it depends on how you want to combine the EDznorm distances of the three dimensions. I think using square root of average of squares is reasonable as you are trying to avoid large distance in one dimension. (this is similar to manhattan vs euclidean distance)

• if you do not want to z-normalize subseq before calculating the distance, then just modify aamp (non-normalized version of stump) and I think it would be less complicated to modify that function.