Tabular data contains rich structural semantics and plays a crucial role in organizing and manipulating information. To better capture these structural semantics, this paper introduces the HybrId-modal Preference oPtimizatiOn (HIPPO) model, which represents tables using both text and image, and optimizes MLLMs to effectively learn more comprehensive table information from these multiple modalities. Specifically, HIPPO samples model responses from hybrid-modal table representations and designs a modality-consistent sampling strategy to enhance response diversity and mitigate modality bias during DPO training. Experimental results on table question answering and table fact verification tasks demonstrate the effectiveness of HIPPO, achieving a 4% improvement over various table reasoning models. Further analysis reveals that HIPPO not only enhances reasoning abilities based on unimodal table representations but also facilitates the extraction of crucial and distinct semantics from different modal representations. All data and codes are available at https://github.com/NEUIR/HIPPO.

The K-means one-step dimensionality reduction clustering method has made some progress in addressing the curse of dimensionality in clustering tasks. However, it combines the K-means clustering and dimensionality reduction processes for optimization, leading to limitations in the clustering effect due to the introduced hyperparameters and the initialization of clustering centers. Moreover, maintaining class balance during clustering remains challenging. To overcome these issues, we propose a unified framework that integrates manifold learning with K-means, resulting in the self-supervised graph embedding framework. Specifically, we establish a connection between K-means and the manifold structure, allowing us to perform K-means without explicitly defining centroids. Additionally, we use this centroid-free K-means to generate labels in low-dimensional space and subsequently utilize the label information to determine the similarity between samples. This approach ensures consistency between the manifold structure and the labels. Our model effectively achieves one-step clustering without the need for redundant balancing hyperparameters. Notably, we have discovered that maximizing the $\ell_{2,1}$-norm naturally maintains class balance during clustering, a result that we have theoretically proven. Finally, experiments on multiple datasets demonstrate that the clustering results of Our-LPP and Our-MFA exhibit excellent and reliable performance.

Fuzzy K-Means clustering is a critical technique in unsupervised data analysis. However, the performance of popular Fuzzy K-Means algorithms is sensitive to the selection of initial cluster centroids and is also affected by noise when updating mean cluster centroids. To address these challenges, this paper proposes a novel Fuzzy K-Means clustering algorithm that entirely eliminates the reliance on cluster centroids, obtaining membership matrices solely through distance matrix computation. This innovation enhances flexibility in distance measurement between sample points, thus improving the algorithm's performance and robustness. The paper also establishes theoretical connections between the proposed model and popular Fuzzy K-Means clustering techniques. Experimental results on several real datasets demonstrate the effectiveness of the algorithm.

Anchor-based methods are a pivotal approach in handling clustering of large-scale data. However, these methods typically entail two distinct stages: selecting anchor points and constructing an anchor graph. This bifurcation, along with the initialization of anchor points, significantly influences the overall performance of the algorithm. To mitigate these issues, we introduce a novel method termed Anchor-free Clustering based on Anchor Graph Factorization (AFCAGF). AFCAGF innovates in learning the anchor graph, requiring only the computation of pairwise distances between samples. This process, achievable through straightforward optimization, circumvents the necessity for explicit selection of anchor points. More concretely, our approach enhances the Fuzzy k-means clustering algorithm (FKM), introducing a new manifold learning technique that obviates the need for initializing cluster centers. Additionally, we evolve the concept of the membership matrix between cluster centers and samples in FKM into an anchor graph encompassing multiple anchor points and samples. Employing Non-negative Matrix Factorization (NMF) on this anchor graph allows for the direct derivation of cluster labels, thereby eliminating the requirement for further post-processing steps. To solve the method proposed, we implement an alternating optimization algorithm that ensures convergence. Empirical evaluations on various real-world datasets underscore the superior efficacy of our algorithm compared to traditional approaches.

For diagnosing melanoma, hematoxylin and eosin (H&E) stained tissue slides remains the gold standard. These images contain quantitative information in different magnifications. In the present study, we investigated whether deep convolutional neural networks can extract structural features of complex tissues directly from these massive size images in a patched way. In order to face the challenge arise from morphological diversity in histopathological slides, we built a multicenter database of 2241 digital whole-slide images from 1321 patients from 2008 to 2018. We trained both ResNet50 and Vgg19 using over 9.95 million patches by transferring learning, and test performance with two kinds of critical classifications: malignant melanomas versus benign nevi in separate and mixed magnification; and distinguish among nevi in maximum magnification. The CNNs achieves superior performance across both tasks, demonstrating an AI capable of classifying skin cancer in the analysis from histopathological images. For making the classifications reasonable, the visualization of CNN representations is furthermore used to identify cells between melanoma and nevi. Regions of interest (ROI) are also located which are significantly helpful, giving pathologists more support of correctly diagnosis.