We introduce a novel self-supervised multi-modal relational item representation learning framework designed to infer substitutable and complementary items. Existing approaches primarily focus on modeling item-item associations deduced from user behaviors using graph neural networks (GNNs) or leveraging item content information. However, these methods often overlook critical challenges, such as noisy user behavior data and data sparsity due to the long-tailed distribution of these behaviors. In this paper, we propose MMSC, a self-supervised multi-modal relational item representation learning framework to address these challenges. Specifically, MMSC consists of three main components: (1) a multi-modal item representation learning module that leverages a multi-modal foundational model and learns from item metadata, (2) a self-supervised behavior-based representation learning module that denoises and learns from user behavior data, and (3) a hierarchical representation aggregation mechanism that integrates item representations at both the semantic and task levels. Additionally, we leverage LLMs to generate augmented training data, further enhancing the denoising process during training. We conduct extensive experiments on five real-world datasets, showing that MMSC outperforms existing baselines by 26.1% for substitutable recommendation and 39.2% for complementary recommendation. In addition, we empirically show that MMSC is effective in modeling cold-start items.

In Formal Concept Analysis, a base for a finite structure is a set of implications that characterizes all valid implications of the structure. This notion can be adapted to the context of Description Logic, where the base consists of a set of concept inclusions instead of implications. In this setting, concept expressions can be arbitrarily large. Thus, it is not clear whether a finite base exists and, if so, how large concept expressions may need to be. We first revisit results in the literature for mining ℰℒ⊥ bases from finite interpretations. Those mainly focus on finding a finite base or on fixing the role depth but potentially losing some of the valid concept inclusions with higher role depth. We then present a new strategy for mining ℰℒ⊥ bases which is adaptable in the sense that it can bound the role depth of concepts depending on the local structure of the interpretation. Our strategy guarantees to capture all ℰℒ⊥ concept inclusions holding in the interpretation, not only the ones up to a fixed role depth. We also consider the case of confident ℰℒ⊥ bases, which requires that some proportion of the domain of the interpretation satisfies the base, instead of the whole domain. This case is useful to cope with noisy data.