# Clustering of Series via Dynamic Mode Decomposition and the Matrix Pencil Method

## TL;DR

This paper introduces a novel feature extraction algorithm combining Dynamic Mode Decomposition and the Matrix Pencil method, enabling efficient analysis of multidimensional sequences by estimating frequencies and amplitudes across datasets.

## Contribution

The paper presents a new least-squares, model-based approach that considers entire datasets simultaneously, improving feature extraction over traditional sequence-specific methods.

## Key findings

- Effective extraction of complex frequencies from multidimensional data
- Simultaneous analysis of multiple sequences improves feature accuracy
- Application to microscopy images demonstrates practical utility

## Abstract

In this paper, a new algorithm for extracting features from sequences of multidimensional observations is presented. The independently developed Dynamic Mode Decomposition and Matrix Pencil methods provide a least-squares model-based approach for estimating complex frequencies present in signals as well as their corresponding amplitudes. Unlike other feature extraction methods such as Fourier Transform or Autoregression which have to be computed for each sequence individually, the least-squares approach considers the whole dataset at once. It invokes order reduction methods to extract a small number of features best describing all given data, and indicate which frequencies correspond to which sequences. As an illustrative example, the new method is applied to regions of different grain orientation in a Transmission Electron Microscopy image.