MicroRNAs (miRNAs) play a pivotal role in cellular processes directly correlating to the genesis and progression of various diseases, including cancer [5] . The potential for miRNAs as therapeutic targets and disease biomarkers has triggered the growth of research into miRNA clustering, facilitating the discovery of miRNA families and their biogenesis. Concomitant (concurrent) with this has been the rise of advanced computational techniques, such as Convolutional Deep Neural Networks (CDNNs), which promise tremendous potential for clustering miRNAs [6] .

miRNA clustering involves grouping them based on their sequences, expression patterns, or genes (mRNAs) they target. It provides insights into their regulatory mechanisms, biological functions, potential diseases and biomarkers therapeutic applications.

Effective computational tools are required for in-depth miRNA analysis, which led to the formation of diverse clustering approaches. Traditional methods like hierarchical clustering, k-means, and DBSCAN, among others, have been employed. However, they have limitations, such as incapacity to handle large datasets and misclassifications [7] .

These clustering techniques only use sequence characteristics to cluster miRNAs and ignore functional properties. It is essential to cluster miRNA and its related functions in terms of both functional and sequence properties.

Deep learning is a subset of machine learning and artificial intelligence known for its ability to learn unlabelled and unstructured data [8] . This marvel of technology holds a profound capacity for clustering expansive genomic data, further redefining the bioinformatics ecosystem.

Different approaches have been used in Deep Clustering in the literature. These are the pipeline-model approach that first: 1) learn data representation using different deep neural network (DNN) architectures, and 2) next apply a machine learning (ML)-based clustering algorithms [4] . Deep Embedding Clustering (DEC), and Deep Clustering Network (DCN) are examples of approaches that uses multilayer perceptrons (MLP) architecture, and k-means clustering [9] [10] . Clustering Using CNN (CCNN) [11] and clustering using pairwise constraints clustering CNN (NNCPC), are examples of approaches that use CNN architecture [12] , and k-means clustering.

Another approach is Single-Model approach that perform end-to end clustering without being preceded with representation learning step [13] .

Deep Neural Networks, specifically the convolutional variant (CNN), have been increasingly used for miRNAs clustering due to their inherent capability to extract hierarchical features from input data automatically. CNN’s unique architecture of convolutional and pooling layers works excellently in sifting through the overwhelming dimensionality and complexity of miRNAs sequences [14] .

Xie et al. has introduced Deep Embedded Clustering (DEC) algorithm to learn feature representation and assign cluster [9] . Gui et al. have introduced deep clustering framework that uses convolutional auto encoders for image clustering and learning representations [15] . Yang et al., have also proposed a method that improve K-means performance being integrated by deep learning [16] .

Deep clustering algorithms integrate feature learning and clustering into a unified framework, promising higher accuracy and robustness [9] . Autoencoder-based clustering algorithm, an iteration of deep learning, offers a two-fold operation: encoding, which compresses the input into a lower-dimensional space and decoding, which reconstructs the original input data [17] . This methodology facilitates the identification of subtle patterns and inherent structures within genomic data.

Several publications have highlighted the methodological and computational benefits of CNNs for clustering miRNAs. In a work by [18] , they successfully applied a convolutional neural network for clustering miRNA sequences and unravelling their latent taxonomy, which significantly impacted research related to the diagnosis and therapy of diseases [7] . Similarly, a study by [19] exhibited the efficacy of their novel deep learning model, DeepMirTar, to perform a binary classification for accurately predicting miRNA-target interactions. Their model outperformed traditional machine learning methods, such as SVM and Random Forest. The Convolutional Deep Neural Network (CNN) offers a potential solution to curbing the limitations of conventional miRNA clustering methods. CNNs have revolutionized numerous machine learning applications due to their ability to process large dimensional data efficiently, making them suitable for high dimensional miRNA data [20] . Their use of multiple layers for feature learning and abstract representation enhances precision and reduces misclassifications.

CDNNs are a category of Neural Networks that have shown remarkable potential in bioinformatics, specifically in sequence analysis [8] . CDNNs can automatically and adaptively learn spatial hierarchies of features from raw input data, providing a potent asset in the clustering of miRNAs.

The primary advantage of CDNNs and their suitability in classifying miRNAs is their capacity to learn abstraction from data, a skill particularly useful when dealing with complex biological data, including miRNAs. Translating raw sequence data into more abstract, high-level features, CDNNs greatly enhance the clustering process by reducing data dimensionality and capturing discriminative features [19] . Initial research into the use of CDNNs for miRNA clustering points towards positive trends. A study by [6] employed CDNNs to perform unsupervised learning of miRNA sequences, demonstrating promising results in biomarker detection, which serves to reinforce the potential of CDNNs for superior clustering of miRNA sequences and motivates further detailed exploration of this approach.

The convolutional deep neural network presents an innovative and enhanced approach to miRNA clustering. It addresses the limitations of conventional methods, effectively dealing with both functional and sequence properties of miRNAs. Hence, it provides comprehensive bioinformatics solutions that can contribute to the understanding and treatment of genetic diseases.

DeepTrust Clustering (DPCl) is a method that transforms gene expression time series into images and applies deep clustering techniques to group genes effectively. By converting time series data into images, DPCl leverages advancements in deep learning for image processing, enhancing pattern recognition and learning. This approach improves data representation and clustering performance by transforming data into a higher-dimensional space through image conversion [2] .

An experiment investigated whether DNN architecture can serve a comparable function. The Pan-Cancer Analysis Project, collected data from thousands of patients with primary tumors that occurred in various body sites and covered 12 tumor types, provided the random subset of the dataset used. The experiment showed five types of cancer patients with reasonably high distinctive patterns. Patients with BRCA, COAD, and LUAD are particularly distinctly clustered, whereas patients with PRAD and KIRC are somewhat mixed and not well separated. When utilizing Convolutional Autoencoder (CAE)-based Latent Features (LFs), the Agglomerative Clustering (AC) final output is marginally superior to when using one alone. According to the optimal base clustering algorithm (in this case, the AC algorithm). The cause is that Long Short-Term Memory (LSTM)-Autoencoders (AEs) learned Latent Features (LF) are of higher quality than raw GE data, which ultimately improves the Gene Expression (GE) profiles' separability a little bit. Only some of these patterns are easily discernible in the raw GE profiles, as the t-SNE plot illustrates [4] .

Deep convolutional clustering algorithms combine Convolutional Neural Networks (CNNs) with clustering techniques to extract and leverage spatial hierarchies in data, which is particularly useful for image data but can also be adopted for other types of structured data, including biological data such as miRNA expression profiles [9] [15] .

DPCl is a framework uses architecture that transform time series data to image for data representation, and then apply deep convolutional clustering algorithm that uses convolutional neural networks (CNNs), and next apply k-means clustering. The conversion of expression data to image to enrich data representation. The method has shown an outperformance compared to traditional machine learning clustering algorithms.

DPCl involves converting gene expression and time series into images and applying deep clustering techniques to create reliable gene clusters. This study implies DPCl algorithm, as illustrated in Figure 1 , on a miRNA expression dataset with multiple samples.

We concentrated on the Multiple Myeloma information on GEO page GSE16558. We focused on GPL8965, which contains miRNA expression profiles that correspond to various stages of myeloma pathology. The total number of miRNA expression profiles targeted in this study were 296.

We make use of recurrence plots for encoding miRNA expression dataset that contains multiple samples for each miRNA as images. The recurrence plot (RP) is a graphical tool for displaying the temporal properties of dynamical systems. To be more exact, an RP is a phase space representation of the trajectories of dynamical systems [21] [22] .

An RP is a binary N × N image defined as:

$R_{i,j}=\left\{\begin{array}{cc}1& ℰ-\Vert {\stackrel{\to }{x}}_{\left(i\right)}-{\stackrel{\to }{x}}_{\left(j\right)}\Vert \ge 0\\ 0& \text{otherwise}\end{array}\right\}$ (1)

where $R_{i,j}$ is the pixel value of the ith row and jth column, $ℰ$ is the radius of the $ℰ$-tube defining the largest acceptable distance between trajectories to be considered as recurrent and ${\stackrel{\to }{x}}_{\left(i\right)}$ is the ith element in input data

$R_{i,j}=\Vert {\stackrel{\to }{x}}_{\left(i\right)}-{\stackrel{\to }{x}}_{\left(j\right)}\Vert$ (2)

Equation 1 becomes Equation 2 if thresholding operation is omitted. The new image is known as a global recurrence plot since it is unthresholded and consequently non-binary. We restrict ourselves to global recurrence plots Equation 2. The dynamic behavior traits are reflected in patterns on RP.

One of the common problems with agglomerative clustering is determining the number k of clusters. We chose to use the elbow approach [22] and found that eight miRNA clusters (k) were needed to favor a meaningful result.

The convolutional autoencoder used in the DPCl algorithm’s parameters was set as follows: 1) network structure that contains three connected convolutional layers with (32, 64, 128) filters, 2) (5, 5, 3) kernel size and 3) same stride length (2) for all convolutional layers. The dimensions of the embedded space are equal to 8, which is the number of miRNAs clusters. The decoder part of the network is symmetric to the encoder part. In the decoder part, we used convolutional transpose layers with stride. We used the ReLU [23] activation function on all convolutional layers to add non-linearity to our model and avoid the vanishing gradient problem. We trained the model for 300 epochs using ADAM optimizer [24] .

Several DNN architectures are used in deep clustering. Also, since augmenting a vanilla autoencoder with convolutional units takes the spatial structures into account, it is straightforward and improves visual imagery performance [23] [25] . Using the autoencoder’s activations on its bottleneck layer, embeddings, as the inputs is a simple strategy for convolutional autoencoder-based clustering, which can be achieved in two steps: i) loading of cluster centroids, ii) iterative clustering through modification of centroids. The loading is created by mapping n gene expression recurrence plots into a lower-dimensional latent space Z, which is done by training a convolutional autoencoder. Each recurrence plot is passed through the autoencoder, and standard k-means is performed in the embedding space Z after the training is finished. These operations result with K initial centroids μ_j where $j=1,\dots ,K$. After the auto encoder is trained, the decoder part is detached from the network, we are only interested in the generation of better embeddings from the encoder part.