The vast chemical space, encompassing virtually innumerable molecules and materials, presents both immense opportunities and significant challenges. The design and discovery of novel drugs and functional materials may be viewed as a search within this space; however, the sheer scale of potential candidates renders exhaustive exploration infeasible. To address this, we introduce Chemical Mapper, a framework that integrates topological data analysis with deep learning to enable the visual exploration and analysis of chemical latent spaces. At its core, Chemical Mapper employs mapper, a widely used tool in topological data analysis, to investigate the organizational principles of chemical latent spaces defined by molecular representations learned by geometric deep learning models. In doing so, Chemical Mapper not only highlights groups of molecular representations but also uncovers the relationships among them through linkages and branching structures. Our results show that Chemical Mapper reveals intrinsic patterns associated with molecular scaffolds, functional groups, and chemical properties, as well as the structural and functional evolutions of the molecules.

MOTIVATION: Accurately predicting anticancer drug response is a central challenge in precision oncology. Existing computational methods, although valuable, often depend on pairwise molecular descriptors or limited graph-based encodings that cannot fully capture the complexity of molecular structures or their interactions with cellular states. These constraints hinder their robustness and generalization across diverse drugs and biological contexts, underscoring the need for more expressive frameworks. RESULTS: To address this gap, we propose MolDr, a topological deep learning framework that represents molecules as multiscale simplicial complexes and propagates information across higher-order structures. By integrating these molecular representations with cellular profiles, MolDr unifies chemical topology and biological context within a single predictive model. Comprehensive experiments show that MolDr consistently outperforms or matches state-of-the-art baselines across multiple benchmarks. It achieves stronger accuracy and robustness on continuous drug response tasks, while also generalizing effectively to discrete classification settings. Moreover, sensitivity analysis confirms the benefit of incorporating multiple topological scales, further supporting the importance of higher-order representations. Together, these results demonstrate that MolDr delivers reliable performance across heterogeneous pharmacogenomic scenarios and highlight the promise of topological modeling for advancing drug response prediction. AVAILABILITY: Source code freely available at https://github.com/CS-BIO/MolDr.

Process mining aims to uncover, track, and enhance real-world workflows by deriving insights from event logs commonly found in modern information systems. With the growing focus on improving productivity within complex business operations, recent research has looked into developing process models to improve business performance metrics. As such, this study aims to enhance process mining from event logs by proposing a novel path-complex construction based on process mining sequential data and a path-complex-based message-passing mechanism for higher-order structural information. We adopt path-complex representations for event logs and their temporal connections developed from instance graphs. Representations are identified and optimised for 0-paths (events), 1-paths (two events in chronological order) and 2-paths (three consecutive events) to characterise intrinsic higher-order information among events. The proposed framework, Path Complex Neural Networks (PCNN), leverages the advantages of topological deep learning and obtains representations for higher-order complexes inductively. Additionally, we evaluated the results with four real-world benchmark datasets and found that PCNN outperforms existing models in analysing sequential and complex process data.

This paper explores the use of simplicial complex to construct a new structure-wise representation for videos. Complementary to the appearance-based representation, which usually involves feature extraction from video content, the proposed method captures the structural properties of a video and can be used for various video processing tasks. We demonstrate a case study of the proposed approach to automated video summarization, which relies only on the developed topological structures and requires no training phase. Experimental results show the potential of this approach to facilitate tasks involving the understanding and analysis of structural information inherent in videos.

Smart photography carries the promise of quality improvement and functionality extension in making aesthetically appealing pictures. In this article, we focus on self-portrait photographs and introduce new methods that guide a user in how to best pose while taking a selfie. While most of the current solutions use a post processing procedure to beautify a picture, the developed tool enables a novel function of recommending a good look before the photo is captured. Given an input face image, the tool automatically estimates the pose-based aesthetic score, finds the most attractive angle of the face, and suggests how the pose should be adjusted. The recommendation results are determined adaptively to the appearance and initial pose of the input face. We apply a data mining approach to find distinctive, frequent itemsets and association rules from online profile pictures, upon which the aesthetic estimation and pose recommendation methods are developed. A simulated and a real image set are used for experimental evaluation. The results show the proposed aesthetic estimation method can effectively select user-favorable photos. Moreover, the recommendation performance for the vertical adjustment is moderately related to the degree of conformity among the professional photographers’ recommendations. This study echoes the trend of instant photo sharing, in which a user takes a picture and then immediately shares it on a social network without engaging in tedious editing.

Skin cancer is one of the most common cancers in the United States. As technological advancements are made, algorithmic diagnosis of skin lesions is becoming more important. In this paper, we develop algorithms for segmenting the actual diseased area of skin in a given image of a skin lesion, and for classifying different types of skin lesions pictured in a given image. The cores of the algorithms used were based in persistent homology, an algebraic topology technique that is part of the rising field of Topological Data Analysis (TDA). The segmentation algorithm utilizes a similar concept to persistent homology that captures the robustness of segmented regions. For classification, we design two families of topological features from persistence diagrams-which we refer to as persistence statistics and persistence curves, and use linear support vector machine as classifiers.

In this paper, we investigate an important but understudied problem, gender classification from human gaits. And we have proved the ability of using GEI (Gait Energy Image) as a representation of human gait for arbitrary view angles. Using GEI as a discriminative feature, we construct angle classifiers and gender classifiers from different approaches. Experiments show that our system achieved a good performance in real-time and is able to be applied to real-world application.