Hotspot identification for Mapper graphs

• URL: http://arxiv.org/abs/2012.01868v1
• Date: Thu, 3 Dec 2020 12:22:25 GMT
• Title: Hotspot identification for Mapper graphs
• Authors: Ciara Frances Loughrey, Nick Orr, Anna Jurek-Loughrey, and Pawe{\l} D{\l}otko
• Abstract summary: Mapper algorithm can be used to build graph-based representations of high-dimensional data capturing structurally interesting features such as loops, flares or clusters. In many applications, such as precision medicine, Mapper graph has been used to identify unknown compactly localized subareas. We propose a new algorithm for detecting hotspots in Mapper graphs. It allows automatizing of the hotspot detection process.
• Score: 2.330913682033217
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Mapper algorithm can be used to build graph-based representations of high-dimensional data capturing structurally interesting features such as loops, flares or clusters. The graph can be further annotated with additional colouring of vertices allowing location of regions of special interest. For instance, in many applications, such as precision medicine, Mapper graph has been used to identify unknown compactly localized subareas within the dataset demonstrating unique or unusual behaviours. This task, performed so far by a researcher, can be automatized using hotspot analysis. In this work we propose a new algorithm for detecting hotspots in Mapper graphs. It allows automatizing of the hotspot detection process. We demonstrate the performance of the algorithm on a number of artificial and real world datasets. We further demonstrate how our algorithm can be used for the automatic selection of the Mapper lens functions.

Related papers

• Linear Transformer Topological Masking with Graph Random Features [52.717865653036796]
  We show how to parameterise topological masks as a learnable function of a weighted adjacency matrix. Our efficient masking algorithms provide strong performance gains for tasks on image and point cloud data.
  arXiv  Detail & Related papers  (2024-10-04T14:24:06Z)
• A distribution-guided Mapper algorithm [0.3683202928838613]
  We introduce a distribution guided Mapper algorithm named D-Mapper. Our proposed algorithm is a probabilistic model-based approach, which could serve as an alternative to non-prababilistic ones. Our numerical experiments indicate that the D-Mapper outperforms the classical Mapper algorithm in various scenarios.
  arXiv  Detail & Related papers  (2024-01-19T17:07:05Z)
• $G$-Mapper: Learning a Cover in the Mapper Construction [0.7852714805965528]
  The Mapper algorithm is a visualization technique in topological data analysis (TDA) that outputs a graph reflecting the structure of a given dataset. We present an algorithm that optimize the cover of a Mapper graph by splitting a cover repeatedly according to a statistical test for normality. Our algorithm is based on $G$-means clustering which searches for the optimal number of clusters in $k$-means by iteratively applying the Anderson-Darling test.
  arXiv  Detail & Related papers  (2023-09-12T22:51:16Z)
• Sketch-Based Anomaly Detection in Streaming Graphs [89.52200264469364]
  Given a stream of graph edges from a dynamic graph, how can we assign anomaly scores to edges and subgraphs in an online manner? Our method is the first streaming approach that incorporates dense subgraph search to detect graph anomalies in constant memory and time.
  arXiv  Detail & Related papers  (2021-06-08T16:10:36Z)
• GraphMI: Extracting Private Graph Data from Graph Neural Networks [59.05178231559796]
  We present textbfGraph textbfModel textbfInversion attack (GraphMI), which aims to extract private graph data of the training graph by inverting GNN. Specifically, we propose a projected gradient module to tackle the discreteness of graph edges while preserving the sparsity and smoothness of graph features. We design a graph auto-encoder module to efficiently exploit graph topology, node attributes, and target model parameters for edge inference.
  arXiv  Detail & Related papers  (2021-06-05T07:07:52Z)
• Pseudoinverse Graph Convolutional Networks: Fast Filters Tailored for Large Eigengaps of Dense Graphs and Hypergraphs [0.0]
  Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs.
  arXiv  Detail & Related papers  (2020-08-03T08:48:41Z)
• Graph Pooling with Node Proximity for Hierarchical Representation Learning [80.62181998314547]
  We propose a novel graph pooling strategy that leverages node proximity to improve the hierarchical representation learning of graph data with their multi-hop topology. Results show that the proposed graph pooling strategy is able to achieve state-of-the-art performance on a collection of public graph classification benchmark datasets.
  arXiv  Detail & Related papers  (2020-06-19T13:09:44Z)
• Structural Temporal Graph Neural Networks for Anomaly Detection in Dynamic Graphs [54.13919050090926]
  We propose an end-to-end structural temporal Graph Neural Network model for detecting anomalous edges in dynamic graphs. In particular, we first extract the $h$-hop enclosing subgraph centered on the target edge and propose the node labeling function to identify the role of each node in the subgraph. Based on the extracted features, we utilize Gated recurrent units (GRUs) to capture the temporal information for anomaly detection.
  arXiv  Detail & Related papers  (2020-05-15T09:17:08Z)
• Block-Approximated Exponential Random Graphs [77.4792558024487]
  An important challenge in the field of exponential random graphs (ERGs) is the fitting of non-trivial ERGs on large graphs. We propose an approximative framework to such non-trivial ERGs that result in dyadic independence (i.e., edge independent) distributions. Our methods are scalable to sparse graphs consisting of millions of nodes.
  arXiv  Detail & Related papers  (2020-02-14T11:42:16Z)
• ShapeVis: High-dimensional Data Visualization at Scale [10.007129417823858]
  We present ShapeVis, a scalable visualization technique for point cloud data inspired from topological data analysis. Our method captures the underlying geometric and topological structure of the data in a compressed graphical representation.
  arXiv  Detail & Related papers  (2020-01-15T07:59:13Z)

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.