Answers.Body: <p>There might be lots of different graph representations for a set of N data points with m features the suitability depends on your intended use for these data.</p>
  <p>For example, for unsupervised learning to detect outlier/anomaly or density-based clustering like DBSCAN or dimensionality reduction like t-SNE, one suitable graph-based model might be a <a href="https://en.wikipedia.org/wiki/Nearest_neighbor_graph" rel="nofollow noreferrer">nearest neighbor graph (NNG)</a>. This model captures <em>local</em> relationships between data points and edges can be weighted by distances or similarities. In an NNG, outliers or anomalies tend to have fewer incoming edges. You can also embed the graph into a lower-dimensional space while preserving the nearest neighbor relationships as much as possible, leading to faithful low-dimensional representations.</p>
  <blockquote>
  <p>The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG has a vertex for each point, and a directed edge from p to q whenever q is a nearest neighbor of p, a point whose distance from p is minimum among all the given points other than p itself</p>
  </blockquote>
  <p>Instead if you want to analyze feature relationships for feature selection/ranking or multicollinearity analysis or dimensionality reduction, then a <a href="https://speedml.com/plot-correlation-of-features/" rel="nofollow noreferrer">feature correlation graph</a> is most suitable where nodes represent features (not data points) and edge weights are based on statistical measures like Pearson correlation or Spearman's rank correlation computed from your data points.</p>
  
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Answers.CreationDate: 2024-12-17T05:57:09.300Z
Answers.LastActivityDate: 2024-12-17T05:57:09.300Z
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Body: <p>Let us consider a dataset consisting of N cases (data points), each described by m features. I am interested in exploring how this dataset can be effectively represented or encoded using graph structures. Specifically, what are the most suitable graph-based models that can capture the relationships within this dataset?</p>
  
Tags: <machine-learning><graph-neural-networks><data-science><feature-engineering><graph-theory>
Title: What graph structures can describe a dataset with N cases and m features
UserDisplayName: ABB
ThreadText: # What graph structures can describe a dataset with N cases and m features
  
  (Asked by: username_0 on 2024-12-16)
  
  Let us consider a dataset consisting of N cases (data points), each described by m features. I am interested in exploring how this dataset can be effectively represented or encoded using graph structures. Specifically, what are the most suitable graph-based models that can capture the relationships within this dataset?
  
  **Tags:** machine-learning, graph-neural-networks, data-science, feature-engineering, graph-theory
  
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  ## 1 answers
  
  ### Answer by username_1 on 2024-12-17. Score: 0 | Accepted answer
  
  There might be lots of different graph representations for a set of N data points with m features the suitability depends on your intended use for these data.
  
  For example, for unsupervised learning to detect outlier/anomaly or density-based clustering like DBSCAN or dimensionality reduction like t-SNE, one suitable graph-based model might be a [nearest neighbor graph (NNG)](https://en.wikipedia.org/wiki/Nearest_neighbor_graph). This model captures *local* relationships between data points and edges can be weighted by distances or similarities. In an NNG, outliers or anomalies tend to have fewer incoming edges. You can also embed the graph into a lower-dimensional space while preserving the nearest neighbor relationships as much as possible, leading to faithful low-dimensional representations.
  
  > The nearest neighbor graph (NNG) is a directed graph defined for a set of points in a metric space, such as the Euclidean distance in the plane. The NNG has a vertex for each point, and a directed edge from p to q whenever q is a nearest neighbor of p, a point whose distance from p is minimum among all the given points other than p itself
  
  Instead if you want to analyze feature relationships for feature selection/ranking or multicollinearity analysis or dimensionality reduction, then a [feature correlation graph](https://speedml.com/plot-correlation-of-features/) is most suitable where nodes represent features (not data points) and edge weights are based on statistical measures like Pearson correlation or Spearman's rank correlation computed from your data points.
  
  
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