Glyphboard: Visual Exploration of High-Dimensional Data Combining Glyphs with Dimensionality Reduction.

Rigorous data science is interdisciplinary at its core. In order to make sense of high-dimensional data, data scientists need to enter into a dialogue with domain experts. We present Glyphboard, a visualization tool that aims to support this dialogue. Glyphboard is a zoomable user interface that combines well-known methods such as dimensionality reduction and glyph-based visualizations in a novel, seamless, and integrated tool. While the dimensionality reduction affords a quick overview over the data, glyph-based visualizations are able to show the most relevant dimensions in the data set at one glance. We contribute an open-source prototype of Glyphboard, a general exchange format for high-dimensional data, and a case study with nine data scientists and domain experts from four exemplary domains in order to evaluate how the different visualization and interaction features of Glyphboard are used.

Trace Quotient with Sparsity Priors for Learning Low Dimensional Image Representations.

This work studies the problem of learning appropriate low dimensional image representations. We propose a generic algorithmic framework, which leverages two classic representation learning paradigms, i.e., sparse representation and the trace quotient criterion, to disentangle underlying factors of variation in high dimensional images. Specifically, we aim to learn simple representations of low dimensional, discriminant factors by applying the trace quotient criterion to well-engineered sparse representations. We construct a unified cost function, coined as the SPARse LOW dimensional representation (SparLow) function, for jointly learning both a sparsifying dictionary and a dimensionality reduction transformation. The SparLow function is widely applicable for developing various algorithms in three classic machine learning scenarios, namely, unsupervised, supervised, and semi-supervised learning. In order to develop efficient joint learning algorithms for maximizing the SparLow function, we deploy a framework of sparse coding with appropriate convex priors to ensure the sparse representations to be locally differentiable. Moreover, we develop an efficient geometric conjugate gradient algorithm to maximize the SparLow function on its underlying Riemannian manifold. Performance of the proposed SparLow algorithmic framework is investigated on several image processing tasks, such as 3D data visualization, face/digit recognition, and object/scene categorization.

Reconstructible Nonlinear Dimensionality Reduction via Joint Dictionary Learning.

This paper presents a parametric low-dimensional (LD) representation learning method that allows to reconstruct high-dimensional (HD) input vectors in an unsupervised manner. Under the assumption that the HD data and its LD representation share the same or similar local sparse structure, the proposed method achieves reconstructible dimensionality reduction via jointly learning dictionaries in both the original HD data space and its LD representation space. By regarding the sparse representation as a smooth function with respect to a specific dictionary, we construct an encoding-decoding block for learning LD representations from sparse coefficients of HD data. It is expected that this learning process preserves the desirable structure of HD data in the LD representation space, and simultaneously allows a reliable reconstruction from the LD space back to the original HD space. In addition, the proposed single layer encoding-decoding block can be easily extended to deep learning structures. Numerical experiments on both synthetic data sets and real images show that the proposed method achieves strongly competitive and robust performance in data DR, reconstruction, and synthesis, even on heavily corrupted data. The proposed method can be used as an alternative approach to compressive sensing (CS); however, it can outperform the traditional CS methods in: 1) task-driven learning problems, such as 2-D/3-D data visualization, and 2) data reconstruction at a lower dimensional space.

Model-based learning of local image features for unsupervised texture segmentation.

Features that capture well the textural patterns of a certain class of images are crucial for the performance of texture segmentation methods. The manual selection of features or designing new ones can be a tedious task. Therefore, it is desirable to automatically adapt the features to a certain image or class of images. Typically, this requires a large set of training images with similar textures and ground truth segmentation. In this work, we propose a framework to learn features for texture segmentation when no such training data is available. The cost function for our learning process is constructed to match a commonly used segmentation model, the piecewise constant Mumford-Shah model. This means that the features are learned such that they provide an approximately piecewise constant feature image with a small jump set. Based on this idea, we develop a two-stage algorithm which first learns suitable convolutional features and then performs a segmentation. We note that the features can be learned from a small set of images, from a single image, or even from image patches. The proposed method achieves a competitive rank in the Prague texture segmentation benchmark, and it is effective for segmenting histological images.

Dynamical Textures Modeling via Joint Video Dictionary Learning.

Video representation is an important and challenging task in the computer vision community. In this paper, we consider the problem of modeling and classifying video sequences of dynamic scenes which could be modeled in a dynamic textures (DTs) framework. At first, we assume that image frames of a moving scene can be modeled as a Markov random process. We propose a sparse coding framework, named joint video dictionary learning (JVDL), to model a video adaptively. By treating the sparse coefficients of image frames over a learned dictionary as the underlying "states", we learn an efficient and robust linear transition matrix between two adjacent frames of sparse events in time series. Hence, a dynamic scene sequence is represented by an appropriate transition matrix associated with a dictionary. In order to ensure the stability of JVDL, we impose several constraints on such transition matrix and dictionary. The developed framework is able to capture the dynamics of a moving scene by exploring both the sparse properties and the temporal correlations of consecutive video frames. Moreover, such learned JVDL parameters can be used for various DT applications, such as DT synthesis and recognition. Experimental results demonstrate the strong competitiveness of the proposed JVDL approach in comparison with the state-of-the-art video representation methods. Especially, it performs significantly better in dealing with DT synthesis and recognition on heavily corrupted data.

Analysis operator learning and its application to image reconstruction.

Exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems. The synthesis model, which assumes that images can be decomposed into a linear combination of very few atoms of some dictionary, is now a well established tool for the design of image reconstruction algorithms. An interesting alternative is the analysis model, where the signal is multiplied by an analysis operator and the outcome is assumed to be sparse. This approach has only recently gained increasing interest. The quality of reconstruction methods based on an analysis model severely depends on the right choice of the suitable operator. In this paper, we present an algorithm for learning an analysis operator from training images. Our method is based on l(p)-norm minimization on the set of full rank matrices with normalized columns. We carefully introduce the employed conjugate gradient method on manifolds, and explain the underlying geometry of the constraints. Moreover, we compare our approach to state-of-the-art methods for image denoising, inpainting, and single image super-resolution. Our numerical results show competitive performance of our general approach in all presented applications compared to the specialized state-of-the-art techniques.

Local convergence analysis of FastICA and related algorithms.

The FastICA algorithm is one of the most prominent methods to solve the problem of linear independent component analysis (ICA). Although there have been several attempts to prove local convergence properties of FastICA, rigorous analysis is still missing in the community. The major difficulty of analysis is because of the well-known sign-flipping phenomenon of FastICA, which causes the discontinuity of the corresponding FastICA map on the unit sphere. In this paper, by using the concept of principal fiber bundles, FastICA is proven to be locally quadratically convergent to a correct separation. Higher order local convergence properties of FastICA are also investigated in the framework of a scalar shift strategy. Moreover, as a parallelized version of FastICA, the so-called QR FastICA algorithm, which employs the QR decomposition (Gram-Schmidt orthonormalization process) instead of the polar decomposition, is shown to share similar local convergence properties with the original FastICA.