Abstract Computational pathology foundation models (CPathFMs) have emerged as a powerful approach for analyzing histopathological data, leveraging self-supervised learning to extract robust feature representations from unlabeled whole-slide images. These models, categorized into uni-modal and multi-modal frameworks, have demonstrated promise in automating complex pathology tasks such as segmentation, classification, and biomarker discovery. However, the development of CPathFMs presents significant challenges, such as limited data accessibility, high variability across datasets, the necessity for domain-specific adaptation, and the lack of standardized evaluation benchmarks. This survey provides a comprehensive review of CPathFMs in computational pathology, focusing on pre-training datasets, adaptation strategies, and evaluation tasks. We analyze key techniques, such as contrastive learning, masked image modeling and multi-modal integration, and highlight existing gaps in current research. Finally, we explore future directions from four perspectives for advancing CPathFMs. This survey serves as a valuable resource for researchers, clinicians, and AI practitioners, guiding the advancement of CPathFMs toward robust and clinically applicable AI-driven pathology solutions.

Given a data matrix, unsupervised column subset selection refers to the problem of identifying a subset of columns that can be used to linearly approximate the original data matrix. This problem has many applications, such as feature selection and representative selection, but solving it optimally is known to be NP-hard. We consider multi-view unsupervised column subset selection, which extends the concept of (single-view) column subset selection to data represented in multiple views or modalities. We introduce a combinatorial search algorithm for this generalized problem. One variant of the algorithm is guaranteed to compute an optimal solution in a setting similar to the classical A* algorithm. Other suboptimal variants, in a setting similar to the weighted A* algorithm, are much faster and provide a solution along with a bound on its quality.

The common criteria for evaluating spectral clustering are NCut and RatioCut. The seemingly unrelated column subset selection (CSS) problem aims to compute a column subset that linearly approximates the entire matrix. A common criterion is the approximation error in the Frobenius norm (ApproxErr). We show that any algorithm for CSS can be viewed as a clustering algorithm that minimizes NCut by applying it to a matrix formed from graph edges. Conversely, any clustering algorithm can be seen as identifying a column subset from that matrix. In both cases, ApproxErr and NCut have the same value. Analogous results hold for RatioCut with a slightly different matrix. Therefore, established results for CSS can be mapped to spectral clustering. We use this to obtain new clustering algorithms, including an optimal one that is similar to A*. This is the first nontrivial clustering algorithm with such an optimality guarantee. A variant of the weighted A* runs much faster and provides bounds on the accuracy. Finally, we use the results from spectral clustering to prove the NP-hardness of CSS from sparse matrices.

Graph spectral clustering is a fundamental technique in data analysis, which utilizes eigenpairs of the Laplacian matrix to partition graph vertices into clusters. However, classical spectral clustering algorithms require eigendecomposition of the Laplacian matrix, which has cubic time complexity. In this work, we describe pass-efficient spectral clustering algorithms that leverage recent advances in randomized eigendecomposition and the structure of the graph vertex-edge matrix. Furthermore, we derive formulas for their efficient implementation. The resulting algorithms have a linear time complexity with respect to the number of vertices and edges and pass over the graph constant times, making them suitable for processing large graphs stored on slow memory. Experiments validate the accuracy and efficiency of the algorithms.

Cancer is a complex cellular ecosystem where malignant cells coexist and interact with immune, stromal and other cells within the tumor microenvironment (TME). Recent technological advancements in spatially resolved multiplexed imaging at single-cell resolution have led to the generation of large-scale and high-dimensional datasets from biological specimens. This underscores the necessity for automated methodologies that can effectively characterize molecular, cellular and spatial properties of TMEs for various malignancies. This study introduces SpatialCells, an open-source software package designed for region-based exploratory analysis and comprehensive characterization of TMEs using multiplexed single-cell data. The source code and tutorials are available at https://semenovlab.github.io/SpatialCells. SpatialCells efficiently streamlines the automated extraction of features from multiplexed single-cell data and can process samples containing millions of cells. Thus, SpatialCells facilitates subsequent association analyses and machine learning predictions, making it an essential tool in advancing our understanding of tumor growth, invasion and metastasis.