Time series clustering is a central machine learning task with applications
in many fields. While the majority of the methods focus on real-valued time
series, very few works consider series with discrete response. In this paper,
the problem of clustering ordinal time series is addressed. To this aim, two
novel distances between ordinal time series are introduced and used to
construct fuzzy clustering procedures. Both metrics are functions of the
estimated cumulative probabilities, thus automatically taking advantage of the
ordering inherent to the series' range. The resulting clustering algorithms are
computationally efficient and able to group series generated from similar
stochastic processes, reaching accurate results even though the series come
from a wide variety of models. Since the dynamic of the series may vary over
the time, we adopt a fuzzy approach, thus enabling the procedures to locate
each series into several clusters with different membership degrees. An
extensive simulation study shows that the proposed methods outperform several
alternative procedures. Weighted versions of the clustering algorithms are also
presented and their advantages with respect to the original methods are
discussed. Two specific applications involving economic time series illustrate
the usefulness of the proposed approaches.

本文针对序列响应的类别性时间序列聚类问题，提出了基于原型聚类方法的两种距离度量，并采用模糊聚类方法提高了其计算效率和准确性，所提方法在经济学时间序列应用中具有很好的可行性。

基于两种新距离的有序时间序列模糊聚类及其经济应用

Fuzzy clustering of ordinal time series based on two novel distances  with economic applications

In the new era of internet systems and applications, a concept of detecting
distinguished topics from huge amounts of text has gained a lot of attention.
These methods use representation of text in a numerical format -- called
embeddings -- to imitate human-based semantic similarity between words. In this
study, we perform a fuzzy-based analysis of various vector representations of
words, i.e., word embeddings. Also we introduce new methods of fuzzy clustering
based on hybrid implementation of fuzzy clustering methods with an evolutionary
algorithm named Forest Optimization. We use two popular fuzzy clustering
algorithms on count-based word embeddings, with different methods and
dimensionality. Words about covid from Kaggle dataset gathered and calculated
into vectors and clustered. The results indicate that fuzzy clustering
algorithms are very sensitive to high-dimensional data, and parameter tuning
can dramatically change their performance. We evaluate results of experiments
with various clustering validity indexes to compare different algorithm
variation with different embeddings accuracy.

本研究使用模糊聚类方法和进化算法优化实现的模糊聚类方法介绍，通过应用基于计数的单词嵌入在 covid 数据集上，研究表明模糊聚类算法对高维数据非常敏感且参数调整会大大改变其性能，我们通过比较不同算法变体的不同嵌入精度来评估实验结果。