Clustering Input Signals Based Identification Algorithms for Two-Input Single-Output Models with Autoregressive Moving Average Noises

Abstract

This study focused on the identification problems of two-input single-output system with moving average noises based on unsupervised learning methods applied to the input signals. The input signal to the autoregressive moving average model is proposed to be arriving from a source with continuous technical and environmental changes as two separate featured input signals. These two input signals were grouped in a number of clusters using the K-means clustering algorithm. The clustered input signals were supplied to the model in an orderly fashion from cluster-1 up to cluster-K. To ensure that the output signal can be best predicted from the input signal which in turn leads to selecting good enough model for its intended use, the magnitude-squared coherence (MSC) measure is applied to the input/output signals in the cases of clustered and nonclustered inputs, which indicates best correlation coefficient when measured with clustered inputs. From collected input-output signals, we deduce a K-means clustering based recursive least squares method for estimating the parameter of autoregressive moving average system. The simulation results indicate that the suggested method is effective.

Perspective Chapter: Insights from Kalman Filtering with Correlated Noises Recursive Least-Square Algorithm for State and Parameter Estimation

“…The expressions "F≕X" or "X≔F " indicate that "F " is defined as "X: " The symbol "q"represents a unit back-shift operator, where q À1 xt ðÞdenotes xtÀ 1 ðÞ . The superscript "T" denotes the transpose of vectors/matrices [29].…”

K-ARMA Models for Clustering Time Series Data

“…Model-based time series clustering methods have proven to be useful in many real-world situations. They have been used to cluster gene expression data [1], to understand within-person dynamics [2], to better understand currency exchange dynamics [3], to cluster input signals [4], and more. We study the time series clustering problem using new modelbased clustering methods focusing on the general class of Autoregressive Moving Average models.…”