Embedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this article, we propose to combine deep neural networks (DNN) with mathematics-guided... Show moreEmbedding high-dimensional data onto a low-dimensional manifold is of both theoretical and practical value. In this article, we propose to combine deep neural networks (DNN) with mathematics-guided embedding rules for high-dimensional data embedding. We introduce a generic deep embedding network (DEN) framework, which is able to learn a parametric mapping from high-dimensional space to low-dimensional space, guided by well-established objectives such as Kullback-Leibler (KL) divergence minimization. We further propose a recursive strategy, called deep recursive embedding (DRE), to make use of the latent data representations for boosted embedding performance. We exemplify the flexibility of DRE by different architectures and loss functions, and benchmarked our method against the two most popular embedding methods, namely, t-distributed stochastic neighbor embedding (t-SNE) and uniform manifold approximation and projection (UMAP). The proposed DRE method can map out-of-sample data and scale to extremely large datasets. Experiments on a range of public datasets demonstrated improved embedding performance in terms of local and global structure preservation, compared with other state-of-the-art embedding methods. Code is available at https://github.com/tao-aimi/DeepRecursiveEmbedding. Show less
Real-life processes are characterized by dynamics involving time. Examples are walking, sleeping, disease progress in medical treatment, and events in a workflow. To understand complex behavior one... Show moreReal-life processes are characterized by dynamics involving time. Examples are walking, sleeping, disease progress in medical treatment, and events in a workflow. To understand complex behavior one needs expressive models, parsimonious enough to gain insight. Uncertainty is often fundamental for process characterization, e.g., because we sometimes can observe phenomena only partially. This makes probabilistic graphical models a suitable framework for process analysis. In this thesis, new probabilistic graphical models that offer the right balance between expressiveness and interpretability are proposed, inspired by the analysis of complex, real-world problems. We first investigate processes by introducing latent variables, which capture abstract notions from observable data (e.g., intelligence, health status). Such models often provide more accurate descriptions of processes. In medicine, such models can also reveal insight on patient treatment, such as predictive symptoms. The second viewpoint looks at processes by identifying time points in the data where the relationships between observable variables change. This provides an alternative characterization of process change. Finally, we try to better understand processes by identifying subgroups of data that deviate from the whole dataset, e.g., process workflows whose event dynamics differ from the general workflow. Show less
This monograph focuses on clustering of objects in high-dimensional data, given the restriction that the objects do not cluster on all the attributes, not even on a single subset of attributes,... Show moreThis monograph focuses on clustering of objects in high-dimensional data, given the restriction that the objects do not cluster on all the attributes, not even on a single subset of attributes, but often on different subsets of attributes in the data. With the objective to reveal such a clustering structure, Friedman and Meulman (2004) proposed a framework and a specific algorithm, called COSA. In this monograph we propose various improvements to the original COSA algorithm. The first improvement targets the optimization strategy for the tuning parameters in COSA. Further, a reformulation of the COSA criterion brings down the number of tuning parameters from two to one, enables incorporation of pre-specified initial weights for the attribute distances and allows for a solution that consists of zero-valued attribute weights. The third improvement consists of a new definition of the COSA distances that yields a better separation between objects from different clusters. We compared the `old' and the improved COSA with other state of the art methods. The comparison is based on simulated and real omics data sets. Show less
Vos, B.D. de; Berendsen, F.F.; Viergever, M.A.; Sokooti, H.; Staring, M.; Isgum, I. 2019
Image registration, the process of aligning two or more images, is the core technique of many (semi-)automatic medical image analysis tasks. Recent studies have shown that deep learning methods,... Show moreImage registration, the process of aligning two or more images, is the core technique of many (semi-)automatic medical image analysis tasks. Recent studies have shown that deep learning methods, notably convolutional neural networks (ConvNets), can be used for image registration. Thus far training of ConvNets for registration was supervised using predefined example registrations. However, obtaining example registrations is not trivial. To circumvent the need for predefined examples, and thereby to increase convenience of training ConvNets for image registration, we propose the Deep Learning Image Registration (DLIR) framework for unsupervised affine and deformable image registration. In the DLIR framework ConvNets are trained for image registration by exploiting image similarity analogous to conventional intensity-based image registration. After a ConvNet has been trained with the DLIR framework, it can be used to register pairs of unseen images in one shot. We propose flexible ConvNets designs for affine image registration and for deformable image registration. By stacking multiple of these ConvNets into a larger architecture, we are able to perform coarse-to-fine image registration. We show for registration of cardiac cine MRI and registration of chest CT that performance of the DLIR framework is comparable to conventional image registration while being several orders of magnitude faster. (C) 2018 Elsevier By. All rights reserved. Show less
