Related papers: Interval Fisher's Discriminant Analysis and Visual…
In the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained…
Various regularized linear discriminant analysis (LDA) methods have been proposed to address the problems of the classic methods in high-dimensional settings. Asymptotic optimality has been established for some of these methods in high…
Considering the challenges posed by the space and time complexities in handling extensive scientific volumetric data, various data representations have been developed for the analysis of large-scale scientific data. Multivariate functional…
Ensembles of classifier models typically deliver superior performance and can outperform single classifier models given a dataset and classification task at hand. However, the gain in performance comes together with the lack in…
In many pattern recognition problems, a single feature vector is not sufficient to describe an object. In multiple instance learning (MIL), objects are represented by sets (\emph{bags}) of feature vectors (\emph{instances}). This requires…
Large unlabeled datasets demand efficient and scalable data labeling solutions, in particular when the number of instances and classes is large. This leads to significant visual scalability challenges and imposes a high cognitive load on…
Recent studies in the literature have paid much attention to the sparsity in linear classification tasks. One motivation of imposing sparsity assumption on the linear discriminant direction is to rule out the noninformative features, making…
The eigenvalues and eigenvectors of the Fisher information matrix (FIM) can reveal the most and least sensitive directions of a system and it has wide application across science and engineering. We present a symplectic variant of the…
In this article we present very intuitive, easy to follow, yet mathematically rigorous, approach to the so called data fitting process. Rather than minimizing the distance between measured and simulated data points, we prefer to find such…
Missingness and measurement frequency are two sides of the same coin. How frequent should we measure clinical variables and conduct laboratory tests? It depends on many factors such as the stability of patient conditions, diagnostic…
In multiple correspondence analysis, both individuals (observations) and categories can be represented in a biplot that jointly depicts the relationships across categories or individuals, as well as the associations between them. Additional…
Numerical experiments demonstrate that deep neural network classifiers progressively separate class distributions around their mean, achieving linear separability on the training set, and increasing the Fisher discriminant ratio. We explain…
Investigating relationships between variables in multi-dimensional data sets is a common task for data analysts and engineers. More specifically, it is often valuable to understand which ranges of which input variables lead to particular…
Jeroslow and Lowe gave an exact geometric characterization of subsets of $\mathbb{R}^n$ that are projections of mixed-integer linear sets, a.k.a MILP-representable sets. We give an alternate algebraic characterization by showing that a set…
Machine learning algorithms often produce models considered as complex black-box models by both end users and developers. They fail to explain the model in terms of the domain they are designed for. The proposed Iterative Visual Logical…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
For many computer vision applications, such as image description and human identification, recognizing the visual attributes of humans is an essential yet challenging problem. Its challenges originate from its multi-label nature, the large…
We introduce continuous indexed points for improved multivariate volume visualization. Indexed points represent linear structures in parallel coordinates and can be used to encode local correlation of multivariate (including multifield,…
Incremental learning is useful if an AI agent needs to integrate data from a stream. The problem is non trivial if the agent runs on a limited computational budget and has a bounded memory of past data. In a deep learning approach, the…
In large-scale distributed scenarios, increasingly complex tasks demand more intelligent collaboration across networks, requiring the joint extraction of structural representations from data samples. However, conventional task-specific…