The problem of nonlinear dimensionality reduction is considered. We focus on problems where prior information is available, namely, semi-supervised dimensionality reduction. It is shown that basic nonlinear dimensionality reduction algorithms, such as Locally Linear Embedding (LLE), Isometric feature mapping (ISOMAP), and Local Tangent Space Alignment (LTSA), can be modified by taking into account prior information on exact mapping of certain data points. The sensitivity analysis of our algorithms shows that prior information will improve stability of the solution. We also give some insight on what kind of prior information best improves the solution. We demonstrate the usefulness of our algorithm by synthetic and real life examples.
We improve the over-parametrization size over two beautiful results [Li and Liang' 2018] and [Du, Zhai, Poczos and Singh' 2019] in deep learning theory.
Lung field segmentation in the posterior-anterior (PA) chest radiograph is important for pulmonary disease diagnosis and hemodialysis treatment. Due to high shape variation and boundary ambiguity, accurate lung field segmentation from chest radiograph is still a challenging task. To tackle these challenges, we propose a joint shape and appearance sparse learning method for robust and accurate lung field segmentation. The main contributions of this paper are: 1) a robust shape initialization method is designed to achieve an initial shape that is close to the lung boundary under segmentation; 2) a set of local sparse shape composition models are built based on local lung shape segments to overcome the high shape variations; 3) a set of local appearance models are similarly adopted by using sparse representation to capture the appearance characteristics in local lung boundary segments, thus effectively dealing with the lung boundary ambiguity; 4) a hierarchical deformable segmentation framework is proposed to integrate the scale-dependent shape and appearance information together for robust and accurate segmentation. Our method is evaluated on 247 PA chest radiographs in a public dataset. The experimental results show that the proposed local shape and appearance models outperform the conventional shape and appearance models. Compared with most of the state-of-the-art lung field segmentation methods under comparison, our method also shows a higher accuracy, which is comparable to the inter-observer annotation variation.
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