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In recent years, balanced clustering has garnered significant attention within its research domain. Previous studies have often employed various regularization terms to achieve balanced clustering. However, they inevitably bring extra hyper-parameters and suffer from high computational complexity. In this paper, we propose an efficient balanced graph cut model called Harmonic Cut. Harmonic cut is inspired by two key factors: harmonic mean and anchors' labels are instances' labels. The former elegantly derives a balance constraint. And the latter efficiently provides an idea for obtaining clustering labels. Unlike conventional spectral clustering methods, Harmonic cut directly acquires all cluster assignments, eliminating the need for additional k-means steps and significantly enhancing efficiency. We tackle the optimization problem associated with the Harmonic cut model using an efficient and heuristic algorithm, whose computational complexity scales linearly with the data size, denoted as n. Finally, extensive experiments conducted on various real-world datasets demonstrate that Harmonic cut not only achieves comparable or even superior results, but also ensures both balance and efficiency. The code is available at https://github.com/DuannYu/HarmonicCut. [ABSTRACT FROM AUTHOR]

The accurate identification of the same user across different e-commerce platforms is crucial for cross-platform recommendations. Given the complexity of the feature space of heterogeneous e-commerce platforms and the sparsity of explicit user behavior data, we propose a heterogeneous e-commerce network alignment model based on multidimensional joint representation and implicit behavior compensation. First, in response to the complexity of the feature space of heterogeneous e-commerce platforms, the UBN2vec model was constructed. The model generates independent embeddings for multidimensional features of "user attributes-behaviors-neighborhood", and integrates them using an attention mechanism. Furthermore, through joint optimization of user multidimensional features, low-rank dense user overall embedding vectors are generated, effectively representing the complex features of e-commerce users. Second, to alleviate the sparsity issue of user behavior data on an e-commerce bookstore platform, we propose a method for compensating implicit user behavior data based on item association. This method predicts potential user behavior information by mining the latent correlations between items. It effectively captures user preferences and improves alignment accuracy. Finally, to reduce the computational complexity of the user-matching process, a user interest group block indexing method based on user interest preferences is developed. This method reduces matching times among users with significantly different interests, thereby reducing the computational complexity of the heterogeneous e-commerce bookstore user alignment algorithm. Experiments show that the proposed model can accurately and efficiently identify the same user across e-commerce bookstore platforms. • A implicit behavior data compensation method based on item association is proposed. • A multi-dimensional feature joint representation model "UBN2vec" is proposed. • A block indexing method based on user interest groups is proposed. [ABSTRACT FROM AUTHOR]