Unsupervised Contrastive Learning for Time Series Data Clustering

Abstract

Aiming at the problems of existing time series data clustering methods, such as the lack of similarity metric universality, the influence of dimensional catastrophe, and the limitation of feature expression ability, a time series data clustering method based on unsupervised contrasting learning (UCL-TSC) is proposed. The method first utilizes Residual, TCN, and CNN-TCN to construct multi-view representations of spatial, temporal, and spatial–temporal features of time series data, and adaptively fuses complementary information to enhance feature extraction capabilities. Subsequently, positive and negative sample pairs are constructed based on nearest neighbor and pseudo-clustering label information. Finally, a contrast loss function consisting of feature loss, clustering loss, and a regularization term is designed to facilitate the model in achieving compact intra-cluster and sparse inter-cluster clustering effects in the clustering process. The experimental results on the UCR dataset show that UCL-TSC performs well with respect to several evaluation indexes, such as clustering accuracy, normalized information degree, and purity, and is more effective in learning time series data features and achieving accurate clustering compared to traditional clustering and deep clustering methods.

1. Introduction

As one of the basic tasks in the field of data mining, clustering can classify data into different clusters based on the similarity of features and attributes of the data points, so that the points in the same cluster are more similar to each other compared to the points in other clusters. Clustering algorithms have a wide range of applications in the fields of image denoising, data dimensionality reduction, medical diagnosis, etc. A variety of clustering strategies have been developed in the face of different types of datasets. With respect to time series data clustering (TSC), existing clustering methods can be broadly categorized into six types: partitional clustering (k-means [1,2,3], k-medoids [4,5,6]), hierarchical clustering (AGNES [7], DIANA [8]), density-based clustering (DBSCAN [9,10], OPTICS [11,12], HDBSCAN [13,14,15]), graph-based clustering (spectral clustering [16,17,18], graph partitioning [19]), model-based clustering [20,21,22], and deep-learning-based clustering (contrastive learning methods [23,24,25,26,27,28], non-contrastive learning methods [29,30,31,32,33]).

Despite their widespread use in TSC tasks, traditional clustering methods, such as partitional clustering, hierarchical clustering, and density-based clustering, often struggle to handle high-dimensional time series data due to their sensitivity to noise and parameter selection. In contrast, by leveraging neural networks to capture temporal dependencies and complex patterns, deep clustering has demonstrated superior performance in clustering tasks. As a type of deep clustering method, the core idea of contrastive learning is to learn feature representations of data by maximizing the similarity between positive sample pairs and minimizing the similarity between negative sample pairs. This ultimately ensures that positive pairs are pulled closer in the embedding space while negative pairs are pushed apart. While contrastive learning has achieved remarkable success in the image domain, its direct application to TSC tasks still faces the following challenges.

First, sensitivity to the construction of positive and negative sample pairs. Traditional contrastive learning methods typically rely on data augmentation to generate positive samples. However, the dynamics and complexity of time series make it difficult for sample pairs to capture true similarities based on simple augmentation.

Second, insufficient utilization of multi-view features. Existing contrastive learning frameworks mainly focus on single-view feature representations, making it challenging to capture complementary spatial–temporal features.

Third, the disconnection between feature representation and clustering objectives. Current methods often employ generic contrastive loss functions, such as information noise contrastive estimation (InfoNCE), which are difficult to optimize specifically for clustering objectives, leading to inconsistency between the feature space and clustering structure.

To address the above problems, this paper proposes an unsupervised contrastive-learning-based clustering method (UCL-TSC) for time series data. The clustering performance is effectively improved by multi-view feature fusion, pseudo-label-guided sample pair construction, and contrastive loss function. The main contributions of this paper are as follows.

(1) Multi-view feature fusion. A multi-view representation of spatial, temporal, and spatial–temporal features of time series data is constructed using Residual, TCN, and CNN-TCN models, and complementary information is fused through adaptive weight learning to enhance the feature extraction capability of time series data.

(2) Construction of positive and negative sample pairs. The approach proposed in this study fully considers the nearest neighbor and pseudo-clustering label information to construct positive and negative sample pairs, i.e., two samples are treated as positive sample pairs if they are nearest neighbors and assigned to the same class, and as negative sample pairs otherwise.

(3) Design of the contrastive loss function. The contrastive loss function is mainly composed of three parts: feature-level loss, clustering loss, and a regularization term, which together promote compact intra-cluster and sparse inter-cluster clustering effects during the clustering process.

(4) Design of experiments. To verify the clustering performance of the model, we conduct analytical experiments and comparative experiments on several UCR datasets to validate the effectiveness of the model.

The remaining sections of this paper are specifically structured as follows. Section 2 provides a description of the TSC task. Section 3 details our proposed clustering method based on unsupervised contrastive learning (UCL-TSC). Section 4 describes the dataset used to validate the model, the evaluation metrics, the experiments conducted, and the specific conclusions. Section 5 summarizes the article.

2. Task Setting

TSC aims to classify series with similar dynamic patterns, trend characteristics, or structural properties into the same category based on the intrinsic similarities between time series data, while series from different categories are significantly distinct. The core task of TSC is the process of mining data for dependencies and pattern differences, mapping them to corresponding clusters. Analyzed mathematically, this process can be expressed in the form of the following equation.

$$C=f(X)$$

(1)

where C denotes the grouping information of the time series data, $X=\{X_1,X_2,\dots ,X_n\}$ denotes a set of time series, and each time series X_i consists of a vector $(x_{i1},x_{i2},\dots ,x_{im})$ of length m. The value of C obtained after clustering needs to satisfy the following conditions.

$${\displaystyle \underset{l=1}{\overset{K}{\cup }}{C}_l}=X$$

(2)

$$C_p\cap C_q=\varnothing ,p\ne q$$

(3)

3. The Proposed Method

Our proposed clustering model for time series data based on unsupervised comparative learning is shown in Figure 1. The model consists of three main modules: multi-view feature fusion, positive and negative sample pair construction, and clustering. In the remainder of this section, we provide a detailed description of these three modules, the overall target loss, and the training strategy.

3.1. Multi-View Feature Fusion

In this paper, we consider extracting the temporal, spatial, and spatial–temporal features of the data separately, based on which we learn a consensus representation shared by the three features in order to obtain a unique clustering result. Specifically, let $f^s$, $f^t$, and $f^{st}$ denote the network models for extracting temporal features, spatial features, and spatial–temporal features, respectively, and let ${\theta }^s$, ${\theta }^t$, and ${\theta }^{st}$ be the parameters of the corresponding network models.

For temporal feature extraction, a temporal convolutional neural network (TCN) is used in this paper for the smoothing and compression of time series data. TCN is a network model that can handle time series data with the core of dilated causal convolution, proposed by Shaojie Bai et al. in 2018. The exponential multiplicative expansion of the dilated causal convolution’s sense field enables it to cover all valid inputs of the time series, leading to better fusion of information and effective modeling of long-term patterns in the series. Given the input $x_i$, the temporal features extracted by the TCN are represented as in Equation (4).

$$x_i^t=f^t(x_i,{\theta }^t)$$

(4)

For spatial feature extraction, a 1D convolutional neural network (CNN) is used to smooth and compress the time series data, introducing residual connections to strengthen the spatial feature extraction capability of the model. Given the input $x_i$, the spatial features extracted by the Residual module are represented as in Equation (5).

$$x_i^s=f^s(x_i,{\theta }^s)$$

(5)

For spatial–temporal feature extraction, this paper adopts the structure of TCN and CNN fusion for the smoothing and compression of time series data, as shown in Figure 2. Given the input $x_i$, the spatial–temporal features extracted by TCN-CNN are represented as in Equation (6).

$$x_i^{st}=f^{st}(x_i,{\theta }^{st})$$

(6)

To enable each network model to capture valuable deep features, this paper introduces a reconstructed loss with reference to the autoencoder, as shown in Equation (7).

$$L_{rec}={\displaystyle \sum _{i=1}^N\left({‖x_i-x_i^t‖}^2+{‖x_i-x_i^s‖}^2+{‖x_i-x_i^{st}‖}^2\right)}$$

(7)

After obtaining separate feature representations, an adaptive fusion mechanism is introduced to fuse the three features to obtain a consensus, and the fused feature representation is shown in Equation (8).

$${\widehat{x}}_i={\alpha }_1{x}_i^t+{\alpha }_2{x}_i^s+{\alpha }_3{x}_i^{st}$$

(8)

where ${\alpha }_r$ denotes the weight of the feature representation, which is adaptively determined by the trainable parameter $w_r$ of each network model. The specific formula is ${\alpha }_r={\displaystyle \frac{\exp (w_r)}{{\displaystyle {\sum }_{c=1}^3\exp (w_l)}}}$. The weights are updated based on the feature distribution of the training data, such a distribution enabling the model to automatically adjust the importance of each view feature according to different input data. This adaptive mechanism helps to avoid drastic changes in feature representation, thus stabilizing the model’s learning process.

3.2. Positive and Negative Sample Pair Construction

In contrastive learning, the construction of positive and negative sample pairs plays a crucial role. In the task of TSC, traditional comparative learning methods usually treat the original data and the augmented data as a pair of positive samples, while all other data are treated as negative samples. This violates the principle of intra-class compactness. Literature [34] considers the construction of positive and negative sample pairs by combining nearest-neighbor and pseudo-clustering label information, and the effectiveness of the method is confirmed by simulation experiments. In this paper, we cite the positive–negative sample pair construction method in the literature and first construct the nearest neighbor graph G of each sample as follows.

$$G_{i,j}=\left\{\begin{array}{ll}1& (x_i\in \phi (x_j))or(x_j\in \phi (x_i))\\ 0& otherwise\end{array}\right.$$

(9)

where $\phi (x_i)$ denotes the set of instances closest to $x_i$.

The consensus representation obtained after adaptive feature fusion is subjected to k-means clustering to produce an indication matrix $Y\in R^{N\times N}$. In this matrix, $Y_{i,j}$ = 1 if and only if the ith and jth samples are assigned to the same category. The constructed set of positive sample pairs, P_i, and the set of negative sample pairs. N_i, are as follows.

$$P_i=\left\{j\right|G_{i,j}=1,Y_{i,j}=1,\forall j\in [1,n]\}$$

(10)

$$N_i=\left\{j\right|G_{i,j}=0,Y_{i,j}=0,\forall j\in [1,n]\}$$

(11)

3.3. Contrastive Loss Function

3.3.1. Clustering Loss

For a given time series dataset, assuming the number of clusters is K, we design the following clustering loss function inspired by the literature [35].

$$L_c=-{\displaystyle \frac{1}{K}}{\displaystyle \sum _{c=1}^3{\displaystyle \sum _{k=1}^K\frac{s({\mu }_k,{\mu }_k^c)}{{\tau }_1}}}+{\displaystyle \frac{1}{K}}{\displaystyle \sum _{c=1}^3{\displaystyle \sum _{k=1}^K\log }}{\displaystyle \sum _{\begin{array}{l}j=1\\ j\ne k\end{array}}^K\exp \left(\frac{s({\mu }_k,{\mu }_j)}{{\tau }_1}\right)}$$

(12)

where ${\mu }_k$ denotes the consensus feature representation of the kth cluster obtained after running three network models. ${\mu }_k^c$ denotes the features of the kth cluster obtained after running a single network model, ${\mu }_k^1$ denotes the spatial feature representation of the kth cluster, ${\mu }_k^2$ denotes the temporal feature representation of the kth cluster, and ${\mu }_k^3$ denotes the spatial–temporal feature representation of the kth cluster. ${\tau }_1$ denotes the temperature parameter. $s(\cdot ,\cdot )$ is the similarity function, which is measured here using the cosine similarity, i.e., $s({\mu }_k,{\mu }_j)={\displaystyle \frac{{\mu }_k^T{\mu }_j}{‖{\mu }_k‖‖{\mu }_j‖}}$.

3.3.2. Feature-Level Loss

Section 3.2 constructs corresponding pairs of positive and negative samples for the given time series data, for which we design the following feature-level loss to better distinguish between similar and dissimilar instances. The feature-level loss consists of a positive sample pair loss and a negative sample pair loss.

$$L_f=-{\displaystyle \frac{1}{n}}{\displaystyle \sum _{c=1}^3{\displaystyle \sum _{i=1}^n\frac{{\displaystyle \sum _{j\in P_i}s({\widehat{x}}_i,x_j^c)}}{{\tau }_2}}}+{\displaystyle \frac{1}{n}}{\displaystyle \sum _{c=1}^3{\displaystyle \sum _{i=1}^n\left({\displaystyle \sum _{j\in N_i}\exp \left(\frac{s({\widehat{x}}_i,x_j^c)}{{\tau }_2}\right)+}{\displaystyle \sum _{j\in N_i}\exp \left(\frac{s(x_i^c,x_j^c)}{{\tau }_2}\right)}\right)}}$$

(13)

where ${\tau }_2$ denotes the temperature parameter, ${\widehat{x}}_i$ denotes the consensus feature representation of the ith sample after running three network models, $x_i^c$ denotes the feature of the ith sample after running a single network model, $x_i^1$ denotes the spatial feature representation of the ith sample, $x_i^2$ denotes the temporal feature representation of the ith sample, and $x_i^3$ denotes the spatial–temporal feature representation of the ith sample.

In Equation (13), all pairs of negative samples have the same weight. This can cause the model to ignore the treatment of difficult negative and false-negative samples during training, leading to the possibility of overdispersion of similar samples and under-separation of dissimilar samples. To achieve intra-cluster compactness and inter-cluster sparsity, this paper dynamically adjusts the weights of negative sample pairs according to the cluster center similarity, i.e., the weights of negative samples within the same cluster are reduced, and the weights of negative samples between different clusters are increased. The adjusted feature-level loss is as follows.

$$L_f=-{\displaystyle \frac{1}{n}}{\displaystyle \sum _{c=1}^3{\displaystyle \sum _{i=1}^n\frac{{\displaystyle \sum _{j\in P_i}s({\widehat{x}}_i,x_j^c)}}{{\tau }_2}}}+{\displaystyle \frac{1}{n}}{\displaystyle \sum _{c=1}^3{\displaystyle \sum _{i=1}^n{\omega }_{ij}\left({\displaystyle \sum _{j\in N_i}\exp \left(\frac{s({\widehat{x}}_i,x_j^c)}{{\tau }_2}\right)+}{\displaystyle \sum _{j\in N_i}\exp \left(\frac{s(x_i^c,x_j^c)}{{\tau }_2}\right)}\right)}}$$

(14)

$${\omega }_{ij}={\displaystyle \frac{\exp (s(q_{centers}^{(i)},q_{centers}^{(j)})/{\tau }_2)}{{\displaystyle {\sum }_{l=1}^K\exp (s(q_{centers}^{(i)},q_{centers}^{(l)})/{\tau }_2)}}}$$

(15)

where $q_{centers}^{(i)}$ denotes the clustering center of the cluster to which the ith sample belongs.

3.3.3. Regularization Term

To prevent the clustering center from degrading and to improve the clustering performance, we introduce a regularization term. Through this regularization term, the model can learn a more discriminative and uniformly distributed feature representation, which is calculated as follows.

$$L_r={\displaystyle \sum _{c=1}^3\log \frac{1}{n^2}{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n\exp (s(x_i^c,x_j^c))}}}$$

(16)

Combining the three loss functions, the contrastive loss values during training are as follows.

$$L_{CL}=L_{rec}+\beta L_c+\gamma L_f+L_r$$

(17)

where $\beta$ and $\gamma$ are the weights of clustering loss and feature-level loss, respectively. From the theoretical point of view, the reconstructed loss, L_rec, is a convex function of the mean square error, which can be stabilized and converged by the gradient descent method during the optimization process. The design of the clustering loss, L_c, and the feature-level loss, L_f, draws on the framework of contrastive learning, forming a clear optimization direction by maximizing the similarity of the positive sample pairs and minimizing the similarity of the negative sample pairs. The regularization term, L_r, avoids clustering center degradation by constraining the uniformity of feature distribution.

3.4. Training Process

In the initial phase of training, the TCN, Residual, and CNN-TCN modules are first trained to obtain better ${\theta }^s$, ${\theta }^t$, and ${\theta }^{st}$ parameters, and the loss function is the reconstructed loss in Equation (7). Finally, the k-means algorithm is executed on the consensus representation to obtain the final clustering results. The training process of the model is shown in Algorithm 1.

Algorithm 1 Training Algorithm

Input: Time series data X, number of cluster K, batch size B. Output: The clustering results. 1: Initialization. Initialize parameters ${\theta }^s,{\theta }^t,\mathrm{and}{\theta }^{st}$ of the TCN, Residual, and CNN-TCN modules by minimizing Lrec. 2: Repeat  3:   Randomly gather B samples from X; 4:    for each xi in B, do the following: 5:     $x_i^t=\mathrm{TCN}(x_i)$; 6:     $x_i^s=\mathrm{Residual}(x_i)$; 7:     $x_i^{st}=\text{CNN-TCN}(x_i)$; 8:     ${\widehat{x}}_i=adaptivefusion(x_i^t,x_i^s,x_i^{st})$; 9:     calculate clustering centers; 10:      calculate Lrec, Lf, Lc, Lr; 11:   End 12:   Calculate LCL; 13:   Use the Adam optimizer to update all parameters by minimizing the LCL; 14: Until reaching max epochs. 15: Return: The clustering results.

4. Experimental Evaluation

4.1. Experimental Dataset and Evaluation Indicators

To evaluate the performance of UCL-TSC, we conducted experiments on the publicly available UCR dataset (https://www.cs.ucr.edu/~eamonn/time_series_data_2018/, accessed on 15 February 2025). Each dataset consists of two parts, the training set and the test set. We fused the two datasets and used the entire data in our experiments. The UCR datasets come from multiple subject areas. Twelve datasets are selected here to cover diverse domains, varying sequence lengths, and complex category structures, as shown in

Table 1. Introduction to the selected UCR datasets.

Type	Name	Train	Test	Class	Length
ECG	ECG200	100	100	2	96
EOG	EOGHorizontalSignal	362	362	12	1250
EPG	InsectEPGRegularTrain	62	249	3	601
Image	Fish	175	175	7	463
Image	Herring	64	64	2	512
Image	ProximalPhalanxOutlineAgeGroup	400	205	3	80
Motion	GunPointOldVersusYoung	136	315	2	150
Sensor	Lightning7	70	73	7	319
Sensor	DodgerLoopWeekend	20	138	2	288
Sensor	Plane	105	105	7	144
Spectro	Coffee	28	28	2	286
Spectro	Meat	60	60	3	448

, to verify the model’s generalization ability. The selection criteria are as follows.

First, the diversity of domains is considered. The datasets cover different sources such as ECG, EOG, image, sensor, and motion to avoid domain bias.

Second, the range of sequence lengths is considered. Sequence lengths span from 80 to 1250 to test the model’s ability to model long- and short-term dependencies.

Third, the difference in the number of categories is considered. The number of categories ranges from two to 12 to evaluate the model’s clustering stability under different category complexities.

Fourth, sample size is considered. Different sample sizes are used to validate the model’s adaptability to data sparsity.

To better quantify the model performance and compare it with that of other methods, unsupervised clustering accuracy (ACC), normalized mutual information (NMI), purity (PUR), F-score, Rand Index, reconstructed loss, and contrastive loss are selected as evaluation indicators in this paper. For these metrics, higher values indicate better model performance.

4.2. Experimental Details

We compared the UCL-TSC algorithm with traditional clustering and deep clustering methods. We ran k-means, Randomnet [32], KSC [36], k-shape [37], SPF [38], SPIRAL [39], kDBA [40], IDEC [41], DTC [42], and MiniRocket [43] on the same UCR dataset. Among the above methods, k-means, KSC, k-shape, and kDBA are clustering techniques based on raw data, while Randomnet, IDEC, DTC, and MiniRocket are deep learning clustering methods.

The experiments conducted in this paper are in the Python language, version 3.8, accelerated by NVIDIA GeForce RTX2080 GPU and CUDA 12.2, using a pytorch deep learning framework. The parameter settings for the UCL-TSC algorithm are shown in

Table 2. Parameter settings for the UCL-TSC algorithm.

Parameters	Values	Parameters	Values
TCN channels	[32, 32, 32, 32]	Epoch of initialization	200
TCN kernel_size	2, 4, 6	Epoch of clustering	100
CNN kernel_size	3	${\tau }_1$	0.5
CNN block_number	3	${\tau }_2$	0.5
Activation function	Relu	Batch size	32
Optimizer	Adam (lr = 0.0001)	$\beta$	{1, 0.1, 0.01, 0.001, 0.0001}
Number of clusters	{2, 3, 4, 5, 7, 10}	$\gamma$	{1, 0.1, 0.01, 0.001, 0.0001}

.

4.3. Experimental Results

4.3.1. Analysis of UCL-TSC Performance

To visualize the performance of UCL-TSC, this section focuses on the twelve datasets listed in this paper. The corresponding ACC, NMI, PUR, F-score, and Rand Index values are provided, the graph of contrastive loss with respect to the epoch is plotted, and the clustering results are visualized using the T-SNE algorithm. The evaluation metrics of UCL-TSC with respect to the twelve example datasets are shown in

Table 3. Comparison of evaluation metrics for the twelve example datasets.

Type	Name	ACC	NMI	PUR	F_Score	Rand_Index
ECG	ECG200	0.510	0.352	0.795	0.689	0.672
EOG	EOGHorizontalSignal	0.490	0.481	0.492	0.368	0.888
EPG	InsectEPGRegularTrain	1.000	1.000	1.000	1.000	1.000
Image	Fish	0.571	0.415	0.586	0.416	0.831
Image	Herring	0.547	0.004	0.602	0.510	0.501
Image	ProximalPhalanxOutlineAgeGroup	0.797	0.545	0.797	0.736	0.804
Motion	GunPointOldVersusYoung	1.000	1.000	1.000	1.000	1.000
Sensor	Lightning7	0.511	0.510	0.588	0.426	0.820
Sensor	DodgerLoopWeekend	0.981	0.870	0.981	0.968	0.963
Sensor	Plane	0.929	0.901	0.929	0.875	0.965
Spectro	Coffee	1.000	1.000	1.000	1.000	1.000
Spectro	Meat	1.000	1.000	1.000	1.000	1.000

.

From Table 3, it can be seen that the UCL-TSC algorithm achieves better clustering results for data with different time series lengths, different sample sizes, and different numbers of clusters. In particular, all the indexes for the InsectEPGRegularTrain, Coffee, and Meat datasets can reach 1.000.

A visual illustration of the clustering results for the 12 datasets is provided in Figure 3. When the number of clusters is two, three, four and seven, the UCL-TSC algorithm is able to cluster the corresponding time series samples and identify the correct clusters. When the number of clusters is 12, although the UCL-TSC algorithm is able to identify the correct clusters, there is a situation where individual samples are far from the center of the corresponding cluster. In this paper, we analyze the datasets with a Rand Index value lower than 0.9 after clustering and find that these datasets generally have high intra-class variability and relatively low cluster separability, resulting in the phenomenon of overlapping clusters and, therefore, relatively low classification results. Combined with Figure 3, although the Rand indexes of these datasets are lower than 0.9 after clustering, UCL-TSC is able to better identify the clustering centers of the clusters and classify the corresponding data into the clusters to which they belong.

4.3.2. Analysis of Contrastive Loss

In Section 3.3, the contrastive loss function is proposed. To visualize the role of the contrast loss function for clustering, the curves of reconstruction loss and contrastive loss with respect to epochs are given in Figure 4 and Figure 5. Figure 6 and Figure 7 show the results of feature visualization corresponding to the 1st, 25th, 50th, and 100th epoch of the Fish and Lightning7 datasets during the training process.

From Figure 4, it can be seen that, with the increase in epochs, the reconstruction loss during the training process of different datasets gradually decreases. When the epoch = 50, the change in the reconstruction loss of several datasets tends to stabilize. When the epoch = 125, the reconstruction loss during the training process of all ten datasets tends to stabilize. This shows that the UCL-TSC algorithm proposed in the paper can better extract the features of time series data, laying a good foundation for subsequent clustering. As can be seen in

Table 4. Means and standard deviations of contrastive loss values from multiple experiments.

Dataset	Average Loss Value	Standard Deviation
ECG200	6.33	1.64 × 10−8
EOGHorizontalSignal	33.66	2.47 × 10−7
InsectEPGRegularTrain	9.63	2.86 × 10−8
Fish	10.22	2.17 × 10−7
Herring	3.82	2.41 × 10−7
ProximalPhalanxOutlineAgeGroup	14.63	1.87 × 10−7
GunPointOldVersusYoung	7.86	3.44 × 10−7
Lightning7	.397	3.56 × 10−8
DodgerLoopWeekend	4.59	2.61 × 10−7
Plane	6.21	1.94 × 10−7
Coffee	1.80	4.18 × 10−8
Meat	3.97	2.77 × 10−7

, the standard deviation of the loss values for multiple experiments for each dataset is below 1 × 10⁻⁶, indicating that the model convergence is stable.

Figure 5 presents the plot of contrastive loss as epochs change during the training process for the ten datasets. It can be seen that the change in contrast loss tends to stabilize with the increase in epochs. Combined with Figure 6 and Figure 7, it can be observed that, with the increase in epochs, the distance between different clusters gradually increases, and the distribution of the samples within the same cluster becomes more and more compact. This indicates that the contrast loss function proposed in the paper plays an important role in the clustering of time series data.

4.3.3. Comparison Experiment

In this section, we compare the performance of the UCL-TSC algorithm proposed in this paper with that of ten other clustering algorithms, namely k-means, KSC, k-shape, SPF, SPIRAL, kDBA, IDEC, DTC, MiniRocket, and Randomnet, using the same dataset for the Rand Index. A larger Rand Index indicates better clustering performance. The partial results obtained are shown in

Table 5. Comparison of the Rand Index with (a) k-means, k-shape, KSC, SPF, and SPIRAL and with (b) kDBA, IDEC, DTC, MiniRocket, and Randomnet.

(a)
Dataset	K-Means	K-Shape	KSC	SPF	SPI.	Ours
ECG200	0.618	0.613	0.613	0.604	0.618	0.672
EOGHorizontalSignal	0.857	0.877	0.422	0.869	0.866	0.888
InsectEPGRegularTrain	0.639	0.709	0.523	0.718	0.767	1.000
Fish	0.786	0.777	0.797	0.861	0.711	0.831
Herring	0.500	0.504	0.499	0.504	0.506	0.501
ProximalPhalanxOutlineAgeGroup	0.690	0.780	0.780	0.696	0.806	0.804
GunPointOldVersusYoung	0.589	0.518	0.506	0.500	0.509	1.000
Lightning7	0.675	0.631	0.676	0.816	0.642	0.693
DodgerLoopWeekend	0.790	0.794	0.555	0.809	0.796	0.820
Plane	0.975	0.499	0.963	0.707	0.817	0.963
Coffee	0.872	0.920	0.945	0.992	0.952	0.965
Meat	0.704	0.877	0.525	0.989	0.717	0.894
(b)
Dataset	kDBA	IDEC	DTC	MiniR.	Rand.	Ours
ECG200	0.556	0.644	0.517	0.537	0.604	0.672
EOGHorizontalSignal	0.797	0.082	0.855	0.569	0.874	0.888
InsectEPGRegularTrain	0.648	0.596	0.613	0.753	1.000	1.000
Fish	0.776	0.764	0.793	0.823	0.800	0.831
Herring	0.499	0.504	0.489	0.502	0.508	0.501
ProximalPhalanxOutlineAgeGroup	0.688	0.390	0.770	0.700	0.792	0.804
GunPointOldVersusYoung	0.519	0.507	0.534	1.000	0.619	1.000
Lightning7	0.468	0.674	0.722	0.657	0.677	0.693
DodgerLoopWeekend	0.796	0.789	0.805	0.812	0.814	0.820
Plane	0.950	0.551	0.622	0.963	0.715	0.963
Coffee	0.918	0.892	0.946	0.995	0.995	0.965
Meat	0.888	0.671	0.725	0.750	0.983	0.894

, with the optimal and sub-optimal results highlighted in bold and underlined, respectively.

It can be found that, in most cases, the UCL-TSC model achieves a higher Rand Index than the other models. Significant performance gains over other methods were obtained on seven datasets: ECG200, EOGHorizontalSignal, InsectEPGRegularTrain, GunPointOldVersusYoung, Lightning7, Coffee, and Meat. The Rand Index improved by 4.35%, 1.25%, 30.38%, 61.55%, 0.74%, 19.90%, and 16.28%, respectively, compared to the sub-optimal results. Compared to other methods, UCL-TSC shows superior performance in learning time series data features and clustering. Specifically, when dealing with long and high-dimensional data sequences, UCL-TSC can effectively capture long-term dependencies and achieve superior clustering performance. For data with significant category differences, UCL-TSC can also enforce intra-class compactness through contrastive loss. However, there is still room for improvement on datasets with small class differences or sparse samples.

The reasons are analyzed as follows. Most of the ten compared clustering algorithms use a single metric or feature extraction method, making it difficult to handle the complex dependencies in time series data. UCL-TSC effectively captures the dynamic patterns and complex dependencies of time series data by combining Residual, TCN, and CNN-TCN models to extract temporal, spatial, and spatial–temporal features, adaptively fusing multi-view information. This mechanism significantly improves feature expression capabilities and overcomes the limitations of traditional methods that rely on a single statistical feature or linear distance metric. The introduction of the contrastive loss function enables UCL-TSC to distinguish between difficult negative samples and false-positive samples, enhancing intra-cluster compactness and inter-cluster separation.

Further analysis reveals that UCL-TSC takes full advantage of the structure of contrastive learning. The ten clustering algorithms compared tend to focus only on the local features or global features of the data, ignoring the relative relationships between the data points. Contrastive learning can learn the relative feature representations between data points by constructing pairs of positive and negative samples. Specifically, during training, the model tries to bring the feature representations of positive sample pairs closer together and the feature representations of negative sample pairs farther apart. This approach enables the model to learn the discriminative features of the data, improving the effectiveness of clustering.

4.3.4. Hyperparametric Experiment

In order to analyze the effects of the hyperparameters $\alpha$ and $\beta$ and the number of clusters k on clustering performance, experiments were conducted on two representative datasets, Plane and Meat. Figure 8 illustrates the effect of changes in $\alpha$ and $\beta$ on the clustering performance when the number of clusters k is a constant value. It can be observed that for the Plane dataset, changes in $\alpha$ and $\beta$ have little effect on the clustering performance, and the Rand Index values are all higher than 0.95. For the Meat dataset, the clustering performance of the model varies significantly with different combinations of $\alpha$ and $\beta$. Figure 9 depicts the effect of changes in k on the clustering performance when $\alpha$ and $\beta$ are constant values. It can be observed that, for both datasets, the changes in the k value has less effect on the clustering performance of the model. In summary, our proposed UCL-TSC model shows good robustness to the choice of hyperparameters, and the clustering performance is more consistent under different hyperparameter settings.

4.3.5. Ablation Experiment

In this section, we set up ablation experiments to analyze the effects of multi-view feature fusion and the contrastive loss function on the clustering performance of the model. The NMI and Rand Index of twelve datasets under different cases are compared, and the obtained experimental results are shown in

Table 6. Comparison of NMI and Rand Index across different cases. (a) Experiments on Coffee, Meat, Herring, and Lightning7. (b) Experiments on DodgerLoopWeekend, ECG200, Plane, and InsectEPGRegularTrain. (c) Experiments on Fish, GunPointOldVersusYoung, ProximalPhalanxOutlineAgeGroup, and EOGHorizontalSignal.

(a)
Method	Coffee		Meat		Herring		Lightning7
	NMI	Rand Index	NMI	Rand Index	NMI	Rand Index	NMI	Rand Index
w/o CL	0.031	0.501	0.515	0.708	0.005	0.502	0.504	0.825
w/o Residual	0.023	0.501	0.939	0.978	0.007	0.500	0.515	0.825
w/o TCN	0.036	0.507	0.487	0.702	0.009	0.500	0.540	0.833
w/o CNN-TCN	0.600	0.893	0.883	0.957	0.009	0.500	0.509	0.823
UCL-TSC	1.000	1.000	1.000	1.000	0.004	0.501	0.510	0.820
(b)
Method	DodgerLoop.		ECG200		Plane		InsectEPG.
	NMI	Rand Index	NMI	Rand Index	NMI	Rand Index	NMI	Rand Index
w/o CL	0.815	0.95	0.129	0.618	0.902	0.950	0.679	0.768
w/o Residual	0.815	0.950	0.140	0.623	0.912	0.952	0.703	0.800
w/o TCN	0.815	0.950	0.121	0.613	0.929	0.965	1.000	1.000
w/o CNN-TCN	0.870	0.963	0.352	0.684	0.894	0.962	1.000	1.000
UCL-TSC	0.870	0.963	0.352	0.672	0.901	0.965	1.000	1.000
(c)
Method	Fish		GunPointOld.		Proximal.		EOGHori.
	NMI	Rand Index	NMI	Rand Index	NMI	Rand Index	NMI	Rand Index
w/o CL	0.328	0.795	0.188	0.624	0.535	0.796	0.498	0.865
w/o Residual	0.384	0.821	0.403	0.683	0.521	0.796	0.446	0.875
w/o TCN	0.412	0.838	0.379	0.654	0.520	0.797	0.500	0.890
w/o CNN-TCN	0.451	0.839	0.151	0.578	0.556	0.804	0.457	0.887
UCL-TSC	0.415	0.831	1.000	1.000	0.545	0.804	0.481	0.888

.

From the experimental results, it can be observed that the model performance is significantly degraded following the removal of network structures, such as the Residual, TCN, and CNN-TCN modules, which are used for multi-view feature fusion. Taking the Coffee dataset as an example, removing the Residual module reduces the NMI from 1.000 in the full model to 0.023, and the Rand Index from 1.000 to 0.501. Removing the TCN module results in an NMI of 0.036 and a Rand Index of 0.507. Removing the CNN-TCN module results in an NMI of 0.600, which is still significantly lower than that of the full model, and a Rand Index of 0.893. This indicates that the multi-view feature fusion mechanism plays a key role in extracting spatial, temporal, and spatial–temporal features of time series data, and the fused complementary information is crucial for enhancing the clustering performance. The absence of any part will lead to difficulty for the model in fully capturing the data features, in turn affecting the clustering performance.

When the contrastive loss function is removed, the model’s performance on each dataset declines dramatically. For example, in the ECG200 dataset, the NMI decreases from 0.352 to 0.129, and the Rand Index decreases from 0.672 to 0.618. In the Meat dataset, the NMI decreases from 1.000 to 0.515, and the Rand Index decreases from 1.000 to 0.708. This fully illustrates that the contrastive loss function plays an indispensable role in enabling the model to learn data features and optimize the clustering structure, effectively promoting intra-cluster compactness and inter-cluster sparsity by adjusting the similarity of positive and negative sample pairs. Without the contrastive loss function, the model cannot accurately distinguish between similar and dissimilar instances, and the quality of clustering is severely impaired.

5. Conclusions

In this paper, we introduce a method, referred to as UCL-TSC, for time series data clustering which effectively solves many challenges faced by traditional methods. The multi-view feature fusion mechanism fully extracts multiple features of the time series data and achieves complementary information fusion through adaptive weight learning, which effectively solves the problem of feature underutilization. By combining the nearest neighbor graph and pseudo-labels to construct positive and negative sample pairs, UCL-TSC accurately captures the intrinsic relationships within the data. The contrastive loss function fuses feature-level, clustering, and regularization terms, allowing the model to better distinguish between similar and dissimilar instances in the clustering process, explicitly optimizing intra-class compactness and inter-class separation, and effectively solving the long-standing problem of fragmentation in the feature space and clustering structure in deep clustering. Experiments on several UCR datasets show that UCL-TSC exhibits good clustering performance on data with different time series lengths, sample sizes, and numbers of clusters, outperforming the other comparative models in terms of Rand Index on most datasets. Hyperparameter experiments verify that the model is robust to hyperparameter selection. The ablation experiments further demonstrate the importance of multi-view feature fusion and contrastive loss functions on model performance.

The ability to effectively cluster time series data demonstrated by UCL-TSC enables it to be better applied in healthcare, industrial IoT, and financial fields. In healthcare settings, UCL-TSC can assist in disease typing or abnormality detection by clustering and analyzing physiological signals. In industrial IoT, UCL-TSC can capture the spatial–temporal patterns of equipment operation, allowing for early failure warning. In future work, we will focus on real-time applications and heterogeneous data fusion to further expand the practical value of this method in emerging fields. Specifically, we will explore online clustering algorithms to improve the model’s usefulness in resource-constrained scenarios. Additionally, we will extend the clustering ability of the model with respect to heterogeneous time series data from multiple sources, so that UCL-TSC can be better applied in different scenarios.