Building Mapper Lenses and Overlapping Covers for Price Point Clouds
Summary
The article develops the first two stages of the Mapper topological data analysis pipeline for price point clouds: assign each point a scalar lens value, then divide the lens range into overlapping intervals called a cover. It describes three lenses: eccentricity, based on mean distance to other points; density, based on Gaussian-weighted distances; and a coordinate projection. The cover records which points belong to each interval, preparing the data for later clustering and graph construction.
A circle example shows why lens choice matters: eccentricity and density can be constant across a symmetric cloud, producing a zero range, while a coordinate lens varies and allows the shape to be sliced. The demo reports lens ranges and interval memberships as checks, including increased total membership when intervals overlap. The article suggests starting cover resolution around 5 to 15 and gain around 0.2 to 0.5. These are implementation guidelines, not trading-performance evidence; the graph stage and empirical market validation are outside its scope.
Key ideas
- Mapper first assigns one scalar lens value to each point and then covers the lens range with overlapping intervals.
- Eccentricity, density, and coordinate lenses describe peripheral position, local crowding, and a chosen coordinate respectively.
- Intrinsic lenses may be constant on symmetric point clouds, so a coordinate lens can reveal structure they miss.
- With positive overlap, the summed interval memberships should exceed the number of points because some points appear in multiple intervals.
- The article builds lenses and covers only; clustering points into graph nodes and connecting those nodes are subsequent steps.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.