Enhancing Dimension-Reduced Scatter Plots with Class and Feature Centroids

• URL: http://arxiv.org/abs/2403.20246v1
• Date: Fri, 29 Mar 2024 15:45:25 GMT
• Title: Enhancing Dimension-Reduced Scatter Plots with Class and Feature Centroids
• Authors: Daniel B. Hier, Tayo Obafemi-Ajayi, Gayla R. Olbricht, Devin M. Burns, Sasha Petrenko, Donald C. Wunsch II,
• Abstract summary: When datasets are reduced to two dimensions, each observation is assigned an x and y coordinates and is represented as a point on a scatter plot. A significant challenge lies in interpreting the meaning of the x and y axes due to the complexities inherent in dimension reduction. This study addresses this challenge by using the x and y coordinates derived from dimension reduction to calculate class and feature centroids, which can be overlaid onto the scatter plots.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Dimension reduction is increasingly applied to high-dimensional biomedical data to improve its interpretability. When datasets are reduced to two dimensions, each observation is assigned an x and y coordinates and is represented as a point on a scatter plot. A significant challenge lies in interpreting the meaning of the x and y axes due to the complexities inherent in dimension reduction. This study addresses this challenge by using the x and y coordinates derived from dimension reduction to calculate class and feature centroids, which can be overlaid onto the scatter plots. This method connects the low-dimension space to the original high-dimensional space. We illustrate the utility of this approach with data derived from the phenotypes of three neurogenetic diseases and demonstrate how the addition of class and feature centroids increases the interpretability of scatter plots.

Related papers

• Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein [56.62376364594194]
  Unsupervised learning aims to capture the underlying structure of potentially large and high-dimensional datasets. In this work, we revisit these approaches under the lens of optimal transport and exhibit relationships with the Gromov-Wasserstein problem. This unveils a new general framework, called distributional reduction, that recovers DR and clustering as special cases and allows addressing them jointly within a single optimization problem.
  arXiv  Detail & Related papers  (2024-02-03T19:00:19Z)
• Interpreting the Curse of Dimensionality from Distance Concentration and Manifold Effect [0.6906005491572401]
  We first summarize five challenges associated with manipulating high-dimensional data. We then delve into two major causes of the curse of dimensionality, distance concentration and manifold effect. By interpreting the causes of the curse of dimensionality, we can better understand the limitations of current models and algorithms.
  arXiv  Detail & Related papers  (2023-12-31T08:22:51Z)
• Improving embedding of graphs with missing data by soft manifolds [51.425411400683565]
  The reliability of graph embeddings depends on how much the geometry of the continuous space matches the graph structure. We introduce a new class of manifold, named soft manifold, that can solve this situation. Using soft manifold for graph embedding, we can provide continuous spaces to pursue any task in data analysis over complex datasets.
  arXiv  Detail & Related papers  (2023-11-29T12:48:33Z)
• Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data Visualization [20.43471678277403]
  We propose LaptSNE, a new graph-based dimensionality reduction method based on t-SNE. Specifically, LaptSNE leverages the eigenvalue information of the graph Laplacian to shrink the potential clusters in the low-dimensional embedding. We show how to calculate the gradient analytically, which may be of broad interest when considering optimization with Laplacian-composited objective.
  arXiv  Detail & Related papers  (2022-07-25T14:10:24Z)
• Intrinsic dimension estimation for discrete metrics [65.5438227932088]
  In this letter we introduce an algorithm to infer the intrinsic dimension (ID) of datasets embedded in discrete spaces. We demonstrate its accuracy on benchmark datasets, and we apply it to analyze a metagenomic dataset for species fingerprinting. This suggests that evolutive pressure acts on a low-dimensional manifold despite the high-dimensionality of sequences' space.
  arXiv  Detail & Related papers  (2022-07-20T06:38:36Z)
• A Local Similarity-Preserving Framework for Nonlinear Dimensionality Reduction with Neural Networks [56.068488417457935]
  We propose a novel local nonlinear approach named Vec2vec for general purpose dimensionality reduction. To train the neural network, we build the neighborhood similarity graph of a matrix and define the context of data points. Experiments of data classification and clustering on eight real datasets show that Vec2vec is better than several classical dimensionality reduction methods in the statistical hypothesis test.
  arXiv  Detail & Related papers  (2021-03-10T23:10:47Z)
• Tensor Laplacian Regularized Low-Rank Representation for Non-uniformly Distributed Data Subspace Clustering [2.578242050187029]
  Low-Rank Representation (LRR) suffers from discarding the locality information of data points in subspace clustering. We propose a hypergraph model to facilitate having a variable number of adjacent nodes and incorporating the locality information of the data. Experiments on artificial and real datasets demonstrate the higher accuracy and precision of the proposed method.
  arXiv  Detail & Related papers  (2021-03-06T08:22:24Z)
• Grassmannian diffusion maps based dimension reduction and classification for high-dimensional data [0.0]
  novel nonlinear dimensionality reduction technique that defines the affinity between points through their representation as low-dimensional subspaces corresponding to points on the Grassmann manifold. The method is designed for applications, such as image recognition and data-based classification of high-dimensional data that can be compactly represented in a lower dimensional subspace.
  arXiv  Detail & Related papers  (2020-09-16T08:32:02Z)
• Manifold Learning via Manifold Deflation [105.7418091051558]
  dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. Many popular methods can fail dramatically, even on simple two-dimensional Manifolds. This paper presents an embedding method for a novel, incremental tangent space estimator that incorporates global structure as coordinates. Empirically, we show our algorithm recovers novel and interesting embeddings on real-world and synthetic datasets.
  arXiv  Detail & Related papers  (2020-07-07T10:04:28Z)
• Semiparametric Nonlinear Bipartite Graph Representation Learning with Provable Guarantees [106.91654068632882]
  We consider the bipartite graph and formalize its representation learning problem as a statistical estimation problem of parameters in a semiparametric exponential family distribution. We show that the proposed objective is strongly convex in a neighborhood around the ground truth, so that a gradient descent-based method achieves linear convergence rate. Our estimator is robust to any model misspecification within the exponential family, which is validated in extensive experiments.
  arXiv  Detail & Related papers  (2020-03-02T16:40:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.