Adding correlation distance metric in oneDAL primitives

[richardnorth3]

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[icfaust]

oneDAL/cpp/oneapi/dal/backend/primitives/reduction/reduction.hpp

Line 94 in 272269d

inline sycl::event reduce_by_columns(sycl::queue& q,

https://github.com/uxlfoundation/oneDAL/blob/main/cpp/oneapi/dal/backend/primitives/stat/cov.hpp#L34
should help you in calculating the means for each row (column_wise reduction to generate the sum, then calculate the mean using the second function)

this will leverage the GPUs capabilities

[icfaust]

Thanks for writing this up @richardnorth3 ! https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.correlation.html should be a good reference for the means necessary. The mean doesn't need to be a single value, but a vector the size of a single sample with each being the mean value for each feature (i.e. for each row). This will then be a vector subtraction. Let me know if I am misunderstanding things about your implementation. Good progress.

[icfaust]

Hey sorry about that, the definition is the mean of the 1d array, so my recommendations have been a little bit wrong.

[richardnorth3]

https://github.com/richardnorth3/oneDAL/blob/9b09822dd84b8eb2ee555e08b4576c8ce7d9c0e2/cpp/oneapi/dal/backend/primitives/distance/correlation_distance_dpc.cpp#L50-L95

After heavily mediating over numerous drafts and codebase reviews, I ultimately came back to your original advice @icfaust after an epiphany. This version of the correlation distance reuses most of the cosine distance code but calculates the deviations first, passes those values to get_inversed_norms(), and proceeds with the same functionality as the cosine distance computation.