partition: Partition a sequence into adjacent windows and apply a metric...
In zatonovo/lambda.tools: Tools for Modeling Data with Functional Programming

Description Arguments Value Usage Details Author(s) Examples

This function transforms a sequence into a rolling set of adjacent windows separated by a pivot point. Each window is passed to a metric function that yields a scalar value. The result is effectively a coordinate pair that represents the two adjacent windows.

`x`	A sequence
`metric`	A function that maps a vector to a real-valued scalar
`radius`	The extent of the neighborhood about the index point

A length(x)-1 by 2 matrix where each row represents the value of the metric applied to left and right neighborhoods about an index point.

partition(x, metric, radius) partition(x, metric=median, radius=10)

Many analysis approaches explore ways to reduce the dimensionality of a data set to make it easier to model. The opposite situation is when there is not enough information in the data structure as is. This circumstance requires a technique that can add dimensionality to a data structure, which is what this function does.

The idea is that a sequence can yield additional information by comparing the neighborhoods around a given point. For this function, a point is an index of the sequence. In the 1D case, given an index k and a radius r, the left neighbohood is defined by [k-r+1, k] and the right neighborhood is defined by [k+1, k+r]. The values associated with each neighborhood are then applied to a metric function m: A^r -> R. This output becomes the coordinate pair (left, right).

At the edges of the sequence the above formalism is not completely accurate. This is because at the edge, the neighborhood will be smaller than the radius, with a minimum size of 1. Hence the first iteration on a sequence will yield a left neighborhood of 1, while the right neighborhood will be [2, 1+r]. Whether this is acceptable is case-specific.

In the future, a wrap parameter might be included that would emulate a loop instead of a sequence. This would be useful if a sequence represented a stationary time series.

Brian Lee Yung Rowe