Connectomics

connectome-graph-analysis

An exploratory analysis using graph-theoretic features and machine learning to test whether connectome patterns can support subject sex prediction for the SWU4 dataset.

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Overview

This is an exploratory analysis project extended from a course assignment that uses graph-theoretic features and machine learning to test whether connectomic features can predict subject sex in the SWU4 dataset.

The objective is to build a classifier and obtain a classification score of 70% or higher.

The data

The project starts with precomputed SWU4 weighted edge lists. Each connectome file contains three columns: two nodes and a weight. The nodes are Desikan atlas brain regions, and the weight describes the estimated strength of the structural connection between them.

The matched dataset contains 207 subjects between the ages of 17 and 27: 99 with sex label 1 and 108 with label 2. Each connectome has 70 regions, so the same region-to-region connections can be compared across subjects.

Heatmap of the mean structural connectome across 70 Desikan brain regions, with two stronger blocks visible along the diagonal
Figure 01 The average 70 × 70 connectivity matrix across all 207 subjects.

The same group-average connectome can also be represented as a network. This view below keeps only the strongest 5% of mean connections so the dominant edges remain visible.

Circular network diagram of 70 connectome regions showing the strongest five percent of mean structural connections
Figure 02 A network view of the mean connectome. Larger nodes have greater total connection strength; thicker, lighter edges have larger mean streamline counts. The circular layout is only schematic and does not represent brain anatomy.

Feature extraction

Each connectome was turned into one row of numbers. The features can be categorized into three families: graph features, topology features, and log-scaled edge weights.

Graph features

  • Global efficiency: how efficiently regions can communicate through short paths. Stronger connections are treated as shorter distances.
  • Edge-weight statistics: the mean, standard deviation, median, and 25th and 75th percentiles of connection strength.
  • Modularity: how strongly the graph separates into communities that are more connected internally than they are to the rest of the network.
  • Characteristic path length: the average weighted shortest-path distance between regions.
  • Node strength: the total connection weight attached to each region.
Four box-and-scatter plots comparing global efficiency, mean edge weight, modularity, and path length between sex codes 1 and 2
Figure 03 Raw graph summaries by sex code. The distributions differ most visibly in global efficiency and mean edge weight, but these plots are descriptive: they are not adjusted for covariates or total streamline count.

Topology features

  • Weighted clustering coefficient: whether a region's neighbors are also strongly connected to one another.
  • Betweenness centrality: how often a region lies on the shortest paths between other regions.
  • Closeness centrality: how close a region is to the rest of the network by weighted shortest paths.
  • Participation coefficient: whether a region spreads its connections across several communities instead of concentrating them within one.

Edge-weight features

While the graph and topology features summarize the network, the edge-weight features are more detailed and allow the model to capture the weight of every individual region-to-region connection.

Each weight was transformed with log10(weight + 1) so the large weights do not overwhelm the smaller connections.

Model and validation

The classifier is a random forest with 300 decision trees. The data was split into a 75% training set and a 25% holdout set, and the label proportions are similar in both. The performance is also validated using shuffled, stratified five-fold cross-validation.

Horizontal bar chart comparing cross-validated balanced accuracy for six combinations of graph, topology, and connection-weight features
Figure 04 Five-fold comparison of the feature families. Connection weights carried most of the predictive signal, while combining them with graph summaries and regional topology produced the highest mean balanced accuracy.

Results

The full feature set performed best: 81.5% ± 3.8% balanced accuracy across five-fold cross-validation and 84.6% on the holdout set.

  • Graph + topology + log edge weights: 81.5% cross-validated balanced accuracy
  • Log edge weights only: 80.6%
  • Graph features only: 75.8%
  • Topology features only: 74.7%
Confusion matrix for the holdout set showing 21 correct and 4 incorrect predictions for sex code 1, and 23 correct and 4 incorrect predictions for sex code 2
Figure 05 Holdout predictions. The model correctly classified 44 of 52 previously withheld participants (84.6%), performing similarly across both sex-code groups.

Discussion

This project demonstrates how structural connectomes can be represented as graphs, analyzed using graph-theoretic features, and used for machine-learning classification. However, this analysis is only exploratory because it includes a relatively small dataset. The results are limited by the quality and information available in the data. Overfitting is a key concern, as there are more features than subjects. A stronger follow-up study should be tested on an independent dataset and control more carefully for other baseline differences, such as age and total streamline count.