Despite the widespread use of k-means time series clustering in various
domains, there exists a gap in the literature regarding its comprehensive
evaluation with different time series normalization approaches. This paper
seeks to fill this gap by conducting a thorough performance evaluation of
k-means time series clustering on real-world open-source time series datasets.
The evaluation focuses on two distinct normalization techniques:
z-normalization and NP-Free. The former is one of the most commonly used
normalization approach for time series. The latter is a real-time time series
representation approach, which can serve as a time series normalization
approach. The primary objective of this paper is to assess the impact of these
two normalization techniques on k-means time series clustering in terms of its
clustering quality. The experiments employ the silhouette score, a
well-established metric for evaluating the quality of clusters in a dataset. By
systematically investigating the performance of k-means time series clustering
with these two normalization techniques, this paper addresses the current gap
in k-means time series clustering evaluation and contributes valuable insights
to the development of time series clustering.

该论文对 k-means 时间序列聚类进行了全面评估，重点研究了两种不同的标准化技术：z - 标准化和 NP-Free，并通过实验使用轮廓分数评估了它们对聚类质量的影响，填补了这方面研究的空白，为时间序列聚类的发展提供了有价值的见解。

基于 z 归一化和 NP-Free 的 k-means 时间序列聚类评估

Evaluation of k-means time series clustering based on z-normalization  and NP-Free

As more connected devices are implemented in a cyber-physical world and data
is expected to be collected and processed in real time, the ability to handle
time series data has become increasingly significant. To help analyze time
series in data mining applications, many time series representation approaches
have been proposed to convert a raw time series into another series for
representing the original time series. However, existing approaches are not
designed for open-ended time series (which is a sequence of data points being
continuously collected at a fixed interval without any length limit) because
these approaches need to know the total length of the target time series in
advance and pre-process the entire time series using normalization methods.
Furthermore, many representation approaches require users to configure and tune
some parameters beforehand in order to achieve satisfactory representation
results. In this paper, we propose NP-Free, a real-time Normalization-free and
Parameter-tuning-free representation approach for open-ended time series.
Without needing to use any normalization method or tune any parameter, NP-Free
can generate a representation for a raw time series on the fly by converting
each data point of the time series into a root-mean-square error (RMSE) value
based on Long Short-Term Memory (LSTM) and a Look-Back and Predict-Forward
strategy. To demonstrate the capability of NP-Free in representing time series,
we conducted several experiments based on real-world open-source time series
datasets. We also evaluated the time consumption of NP-Free in generating
representations.

该文章提出了一种新的表示法 ——NP-Free 用于实时处理无限长度的时间序列数据，它基于长短时记忆和一种回溯和预测策略将原始数据转换为一系列均方根误差值。文章在多个真实世界的时间序列数据集上验证了 NP-Free 的效果，并对其计算时间进行了评估。