Preliminaries

In this section, we first formally define the problem formulation of transferable clustering task and then present the key challenges involved in designing an effective transferable deep clustering model.

In our study, we focus on a collection of datasets denoted as 𝒟=D1,D2,…,Dm. Each dataset Dj is sampled from a joint probability distribution p(𝒟). Within each sampled dataset Dj, we have a set of high-dimensional feature vectors denoted as Dj=xiji=1Nj, where xij represents the feature vector for the i-th sample. Our objective is to learn shared knowledge in clustering from a subset of datasets, referred to as the training set Ds (source), and utilize this acquired knowledge to predict the clustering patterns on newly sampled unseen datasets, serving as the test set Dt (target).

To achieve this, we aim to learn a clustering model denoted as f, trained on the source datasets Ds. The model f partitions each source dataset xisi=1Ns into K clusters in an unsupervised manner, where K is the desired number of clusters. Our goal is to maximize the intra-cluster similarities and minimize the inter-cluster similarities by learning the clustering rule from the training datasets. Subsequently, we evaluate the clustering performance of the learned function f on the test target sets Dt. By leveraging the knowledge acquired during training, we aim to accurately predict the cluster patterns in the test datasets.