On estimation of isotonic piecewise constant signals

Adaptive Piecewise-constant Modeling of Signals in Multidimensional Spaces

This contribution describes an analysis method for the class of problems in which data elements – e.g. measurements, event detections, etc. – are distributed over some region of space and/or time, or other coordinates (e.g., energy, redshift, category), with the goal of estimating the variation of some physical quantity. The nonparametric model is simply that the physical variable is constant o...

A Kleene Theorem for Piecewise Constant Signals Automata

In this paper, we consider timed automata for piecewise constant signals. In the model presented here, time elapses only during transitions; any constraint on clocks should be satisfied during all the duration of the transition. Signal automata are very different from un-timed and time-event automata because piecewise constant signals may be split (and spliced) in an infinite number of ways. We...

Piecewise Constant Controlled Linear Fuzzy Systems

Functional data clustering via piecewise constant nonparametric density estimation

In this paper, we present a novel way of analyzing and summarizing a collection of curves, based on piecewise constant density estimation. The curves are partitioned into clusters, and the dimensions of the curves points are discretized into intervals. The cross-product of these univariate partitions forms a data grid of cells, which represents a nonparametric estimator of the joint density of ...

Segmentation of Signals Using Piecewise Constant Linear Regression Models Submitted to Ieee Transactions on Signal Processing

The signal segmentation approach described herein assumes that the signal can be accurately modelled by a linear regression with piece-wise constant parameters. A simultaneous estimate of the change times is considered. The maximum likelihood and maximum a posteriori probability estimates are derived after marginalization of the linear regression parameters and the measurement noise variance, w...