Related papers: Automatic sorting of point pattern sets using Mink…
This paper proposes an algorithm called Forward Composition Propagation (FCP) to explain the predictions of feed-forward neural networks operating on structured classification problems. In the proposed FCP algorithm, each neuron is…
In this paper, a homogeneous system of n $\alpha$-order linear fractal differential equation is defined and the set of its fundamental solutions through the corresponding Wronskian matrix is described. Finally, the solutions of some…
The diffraction of various random subsets of the integer lattice $\mathbb{Z}^{d}$, such as the coin tossing and related systems, are well understood. Here, we go one important step beyond and consider random point sets in $\mathbb{R}^{d}$.…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
Amino acid sequence portrays most intrinsic form of a protein and expresses primary structure of protein. The order of amino acids in a sequence enables a protein to acquire a particular stable conformation that is responsible for the…
Matrices are two-dimensional data structures allowing one to conceptually organize information. For example, adjacency matrices are useful to store the links of a network; correlation matrices are simple ways to arrange gene co-expression…
While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning…
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches…
Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on…
Complex biological systems have been successfully modeled by biochemical and genetic interaction networks, typically gathered from high-throughput (HTP) data. These networks can be used to infer functional relationships between genes or…
Humans can categorize with only a few samples despite the numerous features. To mimic this ability, we propose a novel dimension-reduced category representation using a mixture of probabilistic principal component analyzers (mPPCA). Tests…
A new classification method for functional data is proposed in this paper. This work is motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded.…
The Gene or DNA sequence in every cell does not control genetic properties on its own; Rather, this is done through translation of DNA into protein and subsequent formation of a certain 3D structure. The biological function of a protein is…
Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing…
Principal Component Analysis (PCA) is a well known procedure to reduce intrinsic complexity of a dataset, essentially through simplifying the covariance structure or the correlation structure. We introduce a novel algebraic, model-based…
Multidimensional separations data have the capacity to reveal detailed information about complex biological samples. However, data analysis has been an ongoing challenge in the area since the peaks that represent chemical factors may drift…
The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from…
Principal component analysis (PCA) algorithms use neural networks to extract the eigenvectors of the correlation matrix from the data. However, if the process is non-Gaussian, PCA algorithms or their higher order generalisations provide…
Ranking over sets arise when users choose between groups of items. For example, a group may be of those movies deemed $5$ stars to them, or a customized tour package. It turns out, to model this data type properly, we need to investigate…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…