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LOWESS and RLOWESS as smoother functions have the following limitations:
there is no sliding window (at each point, the K nearest neighbors are fetched)
only one kernel is available (tricube)
the bandwidth of the kernel is variable and is equal to the distance between the current tick and the furthest neighbor
On the other hand, the family of smoother mappers of the type mapper.kernel.* have the following limitations:
the computation of the smoother weights is discretized
the bandwidth of the kernel is fixed and is computed from the parameters
the semantic of parameters bandwidth and step can be misleading
only regression using weighted average is available
These limitations do not overlap.
To answer all these limitations, we may deprecate mapper.kernel.* and implement another family, for example coined mapper.smoother.*, or mapper.regression.* such that:
the computation of weights is exact (instead of precomputed on a discrete set of values)
they took a parameter bandwidth expressed in time unit, for which 0 means 'maximize the bandwidth automatically at each point' (like in the case of LOWESS and RLOWESS)
they took a parameter degree for the degree of the polynomial fit, (0 means 'weighted averages' like current behavior)
LOWESS and RLOWESS have a feature that can be interesting for MAP, namely, creating the window at each point using the K nearest neighbors. This could be also implemented in MAP, or as a variant, for example MAP.NEAR, by reusing the code of MAP except for computing the window (instead of pre and post parameters, MAP.NEAR could have k and max.neighbor.distance parameters).
The text was updated successfully, but these errors were encountered:
LOWESS and RLOWESS as smoother functions have the following limitations:
On the other hand, the family of smoother mappers of the type
mapper.kernel.*
have the following limitations:bandwidth
andstep
can be misleadingThese limitations do not overlap.
mapper.kernel.*
and implement another family, for example coinedmapper.smoother.*
, ormapper.regression.*
such that:bandwidth
expressed in time unit, for which 0 means 'maximize the bandwidth automatically at each point' (like in the case of LOWESS and RLOWESS)degree
for the degree of the polynomial fit, (0 means 'weighted averages' like current behavior)pre
andpost
parameters, MAP.NEAR could havek
andmax.neighbor.distance
parameters).The text was updated successfully, but these errors were encountered: