Search

Principal component analysis (PCA) is the most commonly used statistical procedure for dimension reduction. An important issue for applying PCA is to determine the rank, which is the number of dominant eigenvalues of the covariance matrix. The Akaike information criterion (AIC) and Bayesian information criterion (BIC) are among the most widely used rank selection methods. Both use the number of free parameters for assessing model complexity. In this work, we adopt the generalized information criterion (GIC) to propose a new method for PCA rank selection under the high-dimensional framework. The GIC model complexity takes into account the sizes of covariance eigenvalues and can be better adaptive to practical applications. Asymptotic properties of GIC are derived and the selection consistency is established under the generalized spiked covariance model., Comment: 9 figures

In this paper, we propose a dimension reduction method specifically designed for tensor-structured feature data in deep neural networks. The method is implemented as a hidden layer, called the TensorProjection layer, which transforms input tensors into output tensors with reduced dimensions through mode-wise projections. The projection directions are treated as model parameters of the layer and are optimized during model training. Our method can serve as an alternative to pooling layers for summarizing image data, or to convolutional layers as a technique for reducing the number of channels. We conduct experiments on tasks such as medical image classification and segmentation, integrating the TensorProjection layer into commonly used baseline architectures to evaluate its effectiveness. Numerical experiments indicate that the proposed method can outperform traditional downsampling methods, such as pooling layers, in our tasks, suggesting it as a promising alternative for feature summarization.

The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for developing efficient large-scale SVD algorithms. Randomized SVD was proposed, and its potential was demonstrated for computing a low-rank SVD (Rokhlin et al., 2009). In this article, we provide a consistency theorem for the randomized SVD algorithm and a numerical example to show how the random projections to low dimension affect the consistency.

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an eigenvalue problem for the sample covariance matrix. We propose herein a two-stage dimension reduction (2SDR) method for image reconstruction from high-dimensional noisy image data. The first stage treats the image as a matrix, which is a tensor of order 2, and uses multilinear principal component analysis (MPCA) for matrix rank reduction and image denoising. The second stage vectorizes the reduced-rank matrix and achieves further dimension and noise reduction. Simulation studies demonstrate excellent performance of 2SDR, for which we also develop an asymptotic theory that establishes consistency of its rank selection. Applications to cryo-EM (cryogenic electronic microscopy), which has revolutionized structural biology, organic and medical chemistry, cellular and molecular physiology in the past decade, are also provided and illustrated with benchmark cryo-EM datasets. Connections to other contemporaneous developments in image reconstruction and high-dimensional statistical inference are also discussed., Comment: 29 pages, 8 figures and 3 tables

Surgical robots have been introduced to operating rooms over the past few decades due to their high sensitivity, small size, and remote controllability. The cable-driven nature of many surgical robots allows the systems to be dexterous and lightweight, with diameters as low as 5mm. However, due to the slack and stretch of the cables and the backlash of the gears, inevitable uncertainties are brought into the kinematics calculation. Since the reported end effector position of surgical robots like RAVEN-II is directly calculated using the motor encoder measurements and forward kinematics, it may contain relatively large error up to 10mm, whereas semi-autonomous functions being introduced into abdominal surgeries require position inaccuracy of at most 1mm. To resolve the problem, a cost-effective, real-time and data-driven pipeline for robot end effector position precision estimation is proposed and tested on RAVEN-II. Analysis shows an improved end effector position error of around 1mm RMS traversing through the entire robot workspace without high-resolution motion tracker., Comment: 6 pages, 10 figures, ICRA2020(under review)

Exploration of metal clusters (MCs) adaptive to both aqueous and oil phases without disturbing their size is promising for a broad scope of applications. The state-of-the-art approach via ligand-binding may perturb MC size due to varied metal-ligand binding strength when shuttling between solvents of different polarity. Herein, we applied physical confinement of a series of small noble MCs (less than 1 nm) inside ionic organic cages (I-Cages), which by means of anion exchange enables reversible transfer of MCs between aqueous and hydrophobic solutions without varying their ultrasmall size. Moreover, the MCs(at)I-Cage hybrid serves as a recyclable, reaction-switchable catalyst featuring high activity in liquid-phase catalysis., Comment: 26 pages, 45 figures

In mainstream computer vision and machine learning, public datasets such as ImageNet, COCO and KITTI have helped drive enormous improvements by enabling researchers to understand the strengths and limitations of different algorithms via performance comparison. However, this type of approach has had limited translation to problems in robotic assisted surgery as this field has never established the same level of common datasets and benchmarking methods. In 2015 a sub-challenge was introduced at the EndoVis workshop where a set of robotic images were provided with automatically generated annotations from robot forward kinematics. However, there were issues with this dataset due to the limited background variation, lack of complex motion and inaccuracies in the annotation. In this work we present the results of the 2017 challenge on robotic instrument segmentation which involved 10 teams participating in binary, parts and type based segmentation of articulated da Vinci robotic instruments.

Many malaria-endemic areas experience seasonal fluctuations in case incidence as Anopheles mosquito and Plasmodium parasite life cycles respond to changing environmental conditions. While most existing maps of malaria seasonality use fixed thresholds of rainfall, temperature, and/or vegetation indices to identify suitable transmission months, we develop a statistical modelling framework for characterising the seasonal patterns derived directly from case data. The procedure involves a spatiotemporal regression model for estimating the monthly proportions of total annual cases and an algorithm to identify operationally relevant characteristics such as the transmission start and peak months. A seasonality index combines the monthly proportion estimates and existing estimates of annual case incidence to provide a summary of "how seasonal" locations are relative to their surroundings. An advancement upon past seasonality mapping endeavours is the presentation of the uncertainty associated with each map, which will enable policymakers to make more statistically sound decisions. The methodology is illustrated using health facility data from Madagascar.