Related papers: Using Quantum Mechanics to Cluster Time Series
Time series clustering is the process of grouping time series with respect to their similarity or characteristics. Previous approaches usually combine a specific distance measure for time series and a standard clustering method. However,…
The $k$-means algorithm (Lloyd's algorithm) is a widely used method for clustering unlabeled data. A key bottleneck of the $k$-means algorithm is that each iteration requires time linear in the number of data points, which can be expensive…
Starting from a dataset with input/output time series generated by multiple deterministic linear dynamical systems, this paper tackles the problem of automatically clustering these time series. We propose an extension to the so-called…
This paper presents the first time series clustering benchmark utilizing all time series datasets currently available in the University of California Riverside (UCR) archive -- the state of the art repository of time series data.…
Quantum computing is a promising paradigm based on quantum theory for performing fast computations. Quantum algorithms are expected to surpass their classical counterparts in terms of computational complexity for certain tasks, including…
Accurate quantum state readout is crucial for error correction and algorithms, but measurement errors are detrimental. Readout fidelity is typically limited by a poor signal-to-noise ratio (SNR) and energy relaxation ($T_1$ decay), a…
Unsupervised clustering of temporal data is both challenging and crucial in machine learning. In this paper, we show that neither traditional clustering methods, time series specific or even deep learning-based alternatives generalise well…
Time-series clustering serves as a powerful data mining technique for time-series data in the absence of prior knowledge about clusters. A large amount of time-series data with large size has been acquired and used in various research…
Time series clustering is an essential machine learning task with applications in many disciplines. While the majority of the methods focus on time series taking values on the real line, very few works consider time series defined on the…
We present a unified framework for quantum sensitivity sampling, extending the advantages of quantum computing to a broad class of classical approximation problems. Our unified framework provides a streamlined approach for constructing…
Clustering is a fundamental problem in unsupervised machine learning with many applications in data analysis. Popular clustering algorithms such as Lloyd's algorithm and $k$-means++ can take $\Omega(ndk)$ time when clustering $n$ points in…
The paper is focused on the forecasting method for time series groups with the use of algorithms for cluster analysis. $K$-means algorithm is suggested to be a basic one for clustering. The coordinates of the centers of clusters have been…
Many measurement modalities which perform imaging by probing an object pixel-by-pixel, such as via Photoacoustic Microscopy, produce a multi-dimensional feature (typically a time-domain signal) at each pixel. In principle, the many degrees…
We present a de-trending algorithm for the removal of trends in time series. Trends in time series could be caused by various systematic and random noise sources such as cloud passages, changes of airmass, telescope vibration or CCD noise.…
In this paper, we introduce a method performing clustering of time-series on the basis of their trend (increasing, stagnating/decreasing, and seasonal behavior). The clustering is performed using $k$-means method on a selection of…
Noise is the central obstacle to building large-scale quantum computers. Quantum systems with sufficiently uncorrelated and weak noise could be used to solve computational problems that are intractable with current digital computers. There…
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over…
Clustering is one of the most important tools for analysis of large datasets, and perhaps the most popular clustering algorithm is Lloyd's algorithm for $k$-means. This algorithm takes $n$ vectors $V=[v_1,\dots,v_n]\in\mathbb{R}^{d\times…
Quantum noise fundamentally limits the utility of near-term quantum devices, making error mitigation essential for practical quantum computation. While traditional quantum error correction codes require substantial qubit overhead and…
Quantum error correction can reduce the effects of noise in quantum systems, e.g. in metrology or most notably in quantum computing. Typically, this requires making measurements that provide information about the errors that have occurred…