Related papers: HUMAP: Hierarchical Uniform Manifold Approximation…
Spatiotemporal (ST) image data are increasingly common and often high-dimensional (high-D). Modeling ST data can be a challenge due to the plethora of independent and interacting processes which may or may not contribute to the…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
The Mapper algorithm, a technique within topological data analysis (TDA), constructs a simplified graphical representation of high-dimensional data to uncover its underlying shape and structural patterns. The algorithm has attracted…
This paper introduces an elemental building block which combines Dictionary Learning and Dimension Reduction (DRDL). We show how this foundational element can be used to iteratively construct a Hierarchical Sparse Representation (HSR) of a…
Latent variable models represent a useful tool for the analysis of complex data when the constructs of interest are not observable. A problem related to these models is that the integrals involved in the likelihood function cannot be solved…
This paper describes an effective and efficient image classification framework nominated distributed deep representation learning model (DDRL). The aim is to strike the balance between the computational intensive deep learning approaches…
Appropriately representing elements in a database so that queries may be accurately matched is a central task in information retrieval; recently, this has been achieved by embedding the graphical structure of the database into a manifold in…
This paper describes the systematic application of local topological methods for detecting interfaces and related anomalies in complicated high-dimensional data. By examining the topology of small regions around each point, one can…
Regression discontinuity design (RDD) is widely adopted for causal inference under intervention determined by a continuous variable. While one is interested in treatment effect heterogeneity by subgroups in many applications, RDD typically…
This paper considers the problem of nonlinear dimensionality reduction. Unlike existing methods, such as LLE, ISOMAP, which attempt to unfold the true manifold in the low dimensional space, our algorithm tries to preserve the nonlinear…
Dimensionality reduction is a common method for analyzing and visualizing high-dimensional data across domains. Dimensionality-reduction algorithms involve complex optimizations and the reduced dimensions computed by these algorithms…
Empirical evidence demonstrates that every region of the neocortex represents information using sparse activity patterns. This paper examines Sparse Distributed Representations (SDRs), the primary information representation strategy in…
In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…
In ordinary Dimensionality Reduction (DR), each data instance in a high dimensional space (original space), or on a distance matrix denoting original space distances, is mapped to (projected onto) one point in a low dimensional space…
Dimensionality reduction algorithms are often used to visualise high-dimensional data. Previously, studies have used prior information to enhance or suppress expected patterns in projections. In this paper, we adapt such techniques for…
Infomap clustering finds the community structures that minimize the expected description length of a random walk trajectory; algorithms for infomap clustering run fast in practice for large graphs. In this paper we leverage the…
The ability to autonomously navigate in unknown environments is important for mobile robots. The map is the core component to achieve this. Most map representations rely on drift-free state estimation and provide a global metric map to…
This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate…
We consider the application of the DRA method to the case of several master integrals in a given sector. We establish a connection between the homogeneous part of dimensional recurrence and maximal unitarity cuts of the corresponding…
Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure.…