Generalized Separable Nonnegative Matrix Factorization

Nonnegative matrix factorization (NMF) is a linear dimensionality technique for nonnegative data with applications such as image analysis, text mining, audio source separation and hyperspectral unmixing. Given a data matrix $M$ and a factorization rank $r$, NMF looks for a nonnegative matrix $W$ with $r$ columns and a nonnegative matrix $H$ with $r$ rows such that $M \approx WH$. NMF is NP-hard to solve in general. However, it can be computed efficiently under the separability assumption which requires that the basis vectors appear as data points, that is, that there exists an index set $\mathcal{K}$ such that $W = M(:,\mathcal{K})$. In this paper, we generalize the separability assumption: We only require that for each rank-one factor $W(:,k)H(k,:)$ for $k=1,2,\dots,r$, either $W(:,k) = M(:,j)$ for some $j$ or $H(k,:) = M(i,:)$ for some $i$. We refer to the corresponding problem as generalized separable NMF (GS-NMF). We discuss some properties of GS-NMF and propose a convex optimization model which we solve using a fast gradient method. We also propose a heuristic algorithm inspired by the successive projection algorithm. To verify the effectiveness of our methods, we compare them with several state-of-the-art separable NMF algorithms on synthetic, document and image data sets.Comment: 31 pages, 12 figures, 4 tables. We have added discussions about the identifiability of the model, we have modified the first synthetic experiment, we have clarified some aspects of the contributio

Modelling Rod-like Flexible Biological Tissues for Medical Training

This paper outlines a framework for the modelling of slender rod-like biological tissue structures in both global and local scales. Volumetric discretization of a rod-like structure is expensive in computation and therefore is not ideal for applications where real-time performance is essential. In our approach, the Cosserat rod model is introduced to capture the global shape changes, which models the structure as a one-dimensional entity, while the local deformation is handled separately. In this way a good balance in accuracy and efficiency is achieved. These advantages make our method appropriate for the modelling of soft tissues for medical training applications

Sketch-based skeleton-driven 2D animation and motion capture.

This research is concerned with the development of a set of novel sketch-based skeleton-driven 2D animation techniques, which allow the user to produce realistic 2D character animation efficiently. The technique consists of three parts: sketch-based skeleton-driven 2D animation production, 2D motion capture and a cartoon animation filter. For 2D animation production, the traditional way is drawing the key-frames by experienced animators manually. It is a laborious and time-consuming process. With the proposed techniques, the user only inputs one image ofa character and sketches a skeleton for each subsequent key-frame. The system then deforms the character according to the sketches and produces animation automatically. To perform 2D shape deformation, a variable-length needle model is developed, which divides the deformation into two stages: skeleton driven deformation and nonlinear deformation in joint areas. This approach preserves the local geometric features and global area during animation. Compared with existing 2D shape deformation algorithms, it reduces the computation complexity while still yielding plausible deformation results. To capture the motion of a character from exiting 2D image sequences, a 2D motion capture technique is presented. Since this technique is skeleton-driven, the motion of a 2D character is captured by tracking the joint positions. Using both geometric and visual features, this problem can be solved by ptimization, which prevents self-occlusion and feature disappearance. After tracking, the motion data are retargeted to a new character using the deformation algorithm proposed in the first part. This facilitates the reuse of the characteristics of motion contained in existing moving images, making the process of cartoon generation easy for artists and novices alike. Subsequent to the 2D animation production and motion capture,"Cartoon Animation Filter" is implemented and applied. Following the animation principles, this filter processes two types of cartoon input: a single frame of a cartoon character and motion capture data from an image sequence. It adds anticipation and follow-through to the motion with related squash and stretch effect

Block Diagonalization of Quaternion Circulant Matrices with Applications

It is well-known that a complex circulant matrix can be diagonalized by a discrete Fourier matrix with imaginary unit $\mathtt{i}$. The main aim of this paper is to demonstrate that a quaternion circulant matrix cannot be diagonalized by a discrete quaternion Fourier matrix with three imaginary units $\mathtt{i}$, $\mathtt{j}$ and $\mathtt{k}$. Instead, a quaternion circulant matrix can be block-diagonalized into 1-by-1 block and 2-by-2 block matrices by permuted discrete quaternion Fourier transform matrix. With such a block-diagonalized form, the inverse of a quaternion circulant matrix can be determined efficiently similar to the inverse of a complex circulant matrix. We make use of this block-diagonalized form to study quaternion tensor singular value decomposition of quaternion tensors where the entries are quaternion numbers. The applications including computing the inverse of a quaternion circulant matrix, and solving quaternion Toeplitz system arising from linear prediction of quaternion signals are employed to validate the efficiency of our proposed block diagonalized results. A numerical example of color video as third-order quaternion tensor is employed to validate the effectiveness of quaternion tensor singular value decomposition

PREM: A Simple Yet Effective Approach for Node-Level Graph Anomaly Detection

Node-level graph anomaly detection (GAD) plays a critical role in identifying anomalous nodes from graph-structured data in various domains such as medicine, social networks, and e-commerce. However, challenges have arisen due to the diversity of anomalies and the dearth of labeled data. Existing methodologies - reconstruction-based and contrastive learning - while effective, often suffer from efficiency issues, stemming from their complex objectives and elaborate modules. To improve the efficiency of GAD, we introduce a simple method termed PREprocessing and Matching (PREM for short). Our approach streamlines GAD, reducing time and memory consumption while maintaining powerful anomaly detection capabilities. Comprising two modules - a pre-processing module and an ego-neighbor matching module - PREM eliminates the necessity for message-passing propagation during training, and employs a simple contrastive loss, leading to considerable reductions in training time and memory usage. Moreover, through rigorous evaluations of five real-world datasets, our method demonstrated robustness and effectiveness. Notably, when validated on the ACM dataset, PREM achieved a 5% improvement in AUC, a 9-fold increase in training speed, and sharply reduce memory usage compared to the most efficient baseline.Comment: Accepted by IEEE International Conference of Data Mining 2023 (ICDM 2023

Beads-on-String Model for Virtual Rectum Surgery Simulation

A beads-on-string model is proposed to handle the deformation and collision of the rectum in virtual surgery simulation. The idea is firstly inspired by the observation of the similarity in shape shared by a rectum with regular bulges and a string of beads. It is beneficial to introduce an additional layer of beads, which provides an interface to map the deformation of centreline to the associated mesh in an elegant manner and a bounding volume approximation in collision handling. Our approach is carefully crafted to achieve high computational efficiency and retain its physical basis. It can be implemented for real time surgery simulation application

Augmented reality-based visual-haptic modeling for thoracoscopic surgery training systems

Background: Compared with traditional thoracotomy, video-assisted thoracoscopic surgery (VATS) has less minor trauma, faster recovery, higher patient compliance, but higher requirements for surgeons. Virtual surgery training simulation systems are important and have been widely used in Europe and America. Augmented reality (AR) in surgical training simulation systems significantly improve the training effect of virtual surgical training, although AR technology is still in its initial stage. Mixed reality has gained increased attention in technology-driven modern medicine but has yet to be used in everyday practice. Methods: This study proposed an immersive AR lobectomy within a thoracoscope surgery training system, using visual and haptic modeling to study the potential benefits of this critical technology. The content included immersive AR visual rendering, based on the cluster-based extended position-based dynamics algorithm of soft tissue physical modeling. Furthermore, we designed an AR haptic rendering systems, whose model architecture consisted of multi-touch interaction points, including kinesthetic and pressure-sensitive points. Finally, based on the above theoretical research, we developed an AR interactive VATS surgical training platform. Results: Twenty-four volunteers were recruited from the First People's Hospital of Yunnan Province to evaluate the VATS training system. Face, content, and construct validation methods were used to assess the tactile sense, visual sense, scene authenticity, and simulator performance. Conclusions: The results of our construction validation demonstrate that the simulator is useful in improving novice and surgical skills that can be retained after a certain period of time. The video-assisted thoracoscopic system based on AR developed in this study is effective and can be used as a training device to assist in the development of thoracoscopic skills for novices

Assessing the validity of SafeGraph data for visitor monitoring in Yellowstone National Park

Monitoring visitor demographics and temporal visitation patterns will help park managers allocate resources, develop infrastructure, and predict the demands of visitors. Previous studies have only validated temporal visitation patterns with big data and traditional survey data, while research on validation national park visitor demographics using mobile data is scant. This study compares SafeGraph data (a type of mobile Location-based Service data) and survey/count data, assessing visitor demographics and temporal visitation patterns in Yellowstone National Park. The comparison between two data sources suggests that SafeGraph data can serve as an additional and complementary source of information to traditional visitor use study/count data. However, biases of SafeGraph data, such as data at an aggregation level and data only in the United States, resulting in differences compared to traditional survey/count data. This study contributes to understanding visitors in national parks by validating a new data source