Principal Curves and Chaos
Sandeep Rajput · AIP conference proceedings · 2003
A Principal Curve is a hypercurve that passes through the center of the data cloud. We adapt and expand the principal curve algorithm to develop a non‐parametric approach called Cluster‐linked Principal Curves (CLPC) that locally approximates the structure and scatter in a distribution of data points. The iterative algorithm is based on Expectation‐Maximization (E‐M) principle. The projections of data points on the principal curve or arc lengths are capable of characterizing the data in fewer dimensions and with greater accuracy than PCA. The distribution of arc lengths is used for gauging stationarity and reversibility, and monitoring. For illustration we use the embeddings formed from chaotic gas pressure time series measurements collected before an electrified capillary nozzle that injects bubbles into a liquid‐filled column.