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https://issues.apache.org/jira/browse/SPARK-23266?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=16346398#comment-16346398
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Chandan Misra commented on SPARK-23266:
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Kriging is a geostatistical method for interpolating known attribute values of
scattered data points to predict unknown attribute values at some other points.
It is based on kriging weight calculation which has the equation of the form
Cw=D. To get the weight vector, we need one matrix inversion and one
matrix-vector multiplication. The size of C (covariance matrix), w vector and D
vector are nxn, nx1 and nx1 respectively, where n is the number of
interpolating points (input points) and interpolation is done for a single
output point.
Now, when the output points change, we only require to change matrix D (vector
for single point), and thus do not have to do the inverse again and again. We
require matrix-vector multiplication on several nodes which is quick i.e.
O(n^2) and easy.
> Matrix Inversion on BlockMatrix
> -------------------------------
>
> Key: SPARK-23266
> URL: https://issues.apache.org/jira/browse/SPARK-23266
> Project: Spark
> Issue Type: New Feature
> Components: MLlib
> Affects Versions: 2.2.1
> Reporter: Chandan Misra
> Priority: Minor
>
> Matrix inversion is the basic building block for many other algorithms like
> regression, classification, geostatistical analysis using ordinary kriging
> etc. A simple Spark BlockMatrix based efficient distributed
> divide-and-conquer algorithm can be implemented using only *6*
> multiplications in each recursion level of the algorithm. The reference paper
> can be found in
> [https://arxiv.org/abs/1801.04723]
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