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Breast cancer is a type of cancer that develops in breast tissues, and, after skin cancer, it is the most commonly diagnosed cancer in women in the United States. Given that an early diagnosis is imperative to prevent breast cancer progression, many machine learning models have been developed in recent years to automate the histopathological classification of the different types of carcinomas. However, many of them are not scalable to large-scale datasets.

In this study, we propose the novel Primal-Dual Multi-Instance Support Vector Machine to determine which tissue segments in an image exhibit an indication of an abnormality. We derive an efficient optimization algorithm for the proposed objective by bypassing the quadratic programming and least-squares problems, which are commonly employed to optimize Support Vector Machine models. The proposed method is computationally efficient, thereby it is scalable to large-scale datasets. We applied our method to the public BreaKHis dataset and achieved promising prediction performance and scalability for histopathological classification.

Software is publicly available at: https://1drv.ms/u/s!AiFpD21bgf2wgRLbQq08ixD0SgRD?e=OpqEmY.

Supplementary data are available at Bioinformatics online.

 

Multi-instance learning (MIL) handles data that is organized into sets of instances known as bags. Traditionally, MIL is used in the supervised-learning setting for classifying bags which contain any number of instances. However, many traditional MIL algorithms do not scale efficiently to large datasets. In this paper, we present a novel primal–dual multi-instance support vector machine that can operate efficiently on large-scale data. Our method relies on an algorithm derived using a multi-block variation of the alternating direction method of multipliers. The approach presented in this work is able to scale to large-scale data since it avoids iteratively solving quadratic programming problems which are broadly used to optimize MIL algorithms based on SVMs. In addition, we improve our derivation to include an additional optimization designed to avoid solving a least-squares problem in our algorithm, which increases the utility of our approach to handle a large number of features as well as bags. Finally, we derive a kernel extension of our approach to learn nonlinear decision boundaries for enhanced classification capabilities. We apply our approach to both synthetic and real-world multi-instance datasets to illustrate the scalability, promising predictive performance, and interpretability of our proposed method. 

Histopathological image analysis is critical in cancer diagnosis and treatment. Due to the huge size of histopathological images, most existing works analyze the whole slide pathological image (WSI) as a bag and its patches are considered as instances. However, these approaches are limited to analyzing the patches in a fixed shape, while the malignant lesions can form varied shapes. To address this challenge, we propose the Multi-Instance Multi-Shape Support Vector Machine (MIMSSVM) to analyze the multiple images (instances) jointly where each instance consists of multiple patches in varied shapes. In our approach, we can identify the varied morphologic abnormalities of nuclei shapes from the multiple images. In addition to the multi-instance multi-shape learning capability, we provide an efficient algorithm to optimize the proposed model which scales well to a large number of features. Our experimental results show the proposed MIMSSVM method outperforms the existing SVM and recent deep learning models in histopathological classification. The proposed model also identifies the tissue segments in an image exhibiting an indication of an abnormality which provides utility in the early detection of malignant tumors. 

Linear discriminant analysis (LDA) is widely used for dimensionality reduction under supervised learning settings. Traditional LDA objective aims to minimize the ratio of squared Euclidean distances that may not perform optimally on noisy data sets. Multiple robust LDA objectives have been proposed to address this problem, but their implementations have two major limitations. One is that their mean calculations use the squared l2-norm distance to center the data, which is not valid when the objective does not use the Euclidean distance. The second problem is that there is no generalized optimization algorithm to solve different robust LDA objectives. In addition, most existing algorithms can only guarantee the solution to be locally optimal, rather than globally optimal. In this paper, we review multiple robust loss functions and propose a new and generalized robust objective for LDA. Besides, to better remove the mean value within data, our objective uses an optimal way to center the data through learning. As one important algorithmic contribution, we derive an efficient iterative algorithm to optimize the resulting non-smooth and non-convex objective function. We theoretically prove that our solution algorithm guarantees that both the objective and the solution sequences converge to globally optimal solutions at a sub-linear convergence rate. The experimental results demonstrate the effectiveness of our new method, achieving significant improvements compared to the other competing methods. 

Collaborative localization is an essential capability for a team of robots such as connected vehicles to collaboratively estimate object locations from multiple perspectives with reliant cooperation. To enable collaborative localization, four key challenges must be addressed, including modeling complex relationships between observed objects, fusing observations from an arbitrary number of collaborating robots, quantifying localization uncertainty, and addressing latency of robot communications. In this paper, we introduce a novel approach that integrates uncertainty-aware spatiotemporal graph learning and model-based state estimation for a team of robots to collaboratively localize objects. Specifically, we introduce a new uncertainty-aware graph learning model that learns spatiotemporal graphs to represent historical motions of the objects observed by each robot over time and provides uncertainties in object localization. Moreover, we propose a novel method for integrated learning and model-based state estimation, which fuses asynchronous observations obtained from an arbitrary number of robots for collaborative localization. We evaluate our approach in two collaborative object localization scenarios in simulations and on real robots. Experimental results show that our approach outperforms previous methods and achieves state-of-the-art performance on asynchronous collaborative localization. 

Alzheimer’s Disease (AD) is a progressive memory disorder that causes irreversible cognitive declines, therefore early diagnosis is imperative to prevent the progression of AD. To this end, many biomarker analysis models have been presented for early AD detection. However, these models may not realize the full data potential due to their failure to integrate longitudinal (dynamic) phenotypic data with (static) genetic data. Sometimes, they may not fully utilize both labeled and unlabeled samples either. To overcome these limitations, we propose a semi-supervised enrichment learning method to learn a fixed-length vectorial representation for each participant, by which the static data record can be integrated with the dynamic data records. We have applied our new method on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) cohort and achieved 75% accuracy on multiclass AD progression prediction by one year in advance. 

Multi-instance learning (MIL) is an area of machine learning that handles data that is organized into sets of instances known as bags. Traditionally, MIL is used in the supervised-learning setting and is able to classify bags which can contain any number of instances. This property allows MIL to be naturally applied to solve the problems in a wide variety of real-world applications from computer vision to healthcare. However, many traditional MIL algorithms do not scale efficiently to large datasets. In this paper we present a novel Primal-Dual Multi-Instance Support Vector Machine (pdMISVM) derivation and implementation that can operate efficiently on large scale data. Our method relies on an algorithm derived using a multi-block variation of the alternating direction method of multipliers (ADMM). The approach presented in this work is able to scale to large-scale data since it avoids iteratively solving quadratic programming problems which are generally used to optimize MIL algorithms based on SVMs. In addition, we modify our derivation to include an additional optimization designed to avoid solving a least-squares problem during our algorithm; this optimization increases the utility of our approach to handle a large number of features as well as bags. Finally, we apply our approach to synthetic and real-world multi-instance datasets to illustrate the scalability, promising predictive performance, and interpretability of our proposed method. We end our discussion with an extension of our approach to handle non-linear decision boundaries. Code and data for our methods are available online at: https://github.com/minds-mines/pdMISVM.jl. 

Nonnegative Matrix Factorization (NMF) is broadly used to determine class membership in a variety of clustering applications. From movie recommendations and image clustering to visual feature extractions, NMF has applications to solve a large number of knowledge discovery and data mining problems. Traditional optimization methods, such as the Multiplicative Updating Algorithm (MUA), solves the NMF problem by utilizing an auxiliary function to ensure that the objective monotonically decreases. Although the objective in MUA converges, there exists no proof to show that the learned matrix factors converge as well. Without this rigorous analysis, the clustering performance and stability of the NMF algorithms cannot be guaranteed. To address this knowledge gap, in this article, we study the factor-bounded NMF problem and provide a solution algorithm with proven convergence by rigorous mathematical analysis, which ensures that both the objective and matrix factors converge. In addition, we show the relationship between MUA and our solution followed by an analysis of the convergence of MUA. Experiments on both toy data and real-world datasets validate the correctness of our proposed method and its utility as an effective clustering algorithm.