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Multivariate feature analysis

The Multivariate analysis mode in AUDIT enables users to investigate how multiple features interact with each other across different datasets. It provides a two-dimensional scatter plot where each data point represents a subject, and its position is determined by two selected features. This visualization is particularly useful for detecting complex patterns, identifying correlations, and revealing dataset-specific behaviors or outliers that may not be visible in univariate analyses.

The goals of multivariate analysis are to:

  • Explore relationships between pairs of features across multiple datasets.
  • Detect hidden clusters or trends in the feature space.
  • Identify dataset shifts or feature interactions that might affect model performance.
  • Spot outliers that deviate from the main population.
  • Visually compare cohorts in a shared 2D space.

🎥 Demo video

Below is a short video that walks you through the multivariate interface:

Watch the video

⚙️ User configuration

1. Dataset Selection

Users can load and compare multiple datasets simultaneously in the Multivariate analysis mode. This enables side-by-side inspection of how a given feature varies across different cohorts — for example, across different institutions, scanner protocols, or study years.

Each dataset is automatically assigned a distinct color in all plots, ensuring an easy interpretation.

Datasets can be:

  • Selected or deselected using the dedicated selector panel on the left-hand side of the dashboard.
  • Toggled directly from the interactive Plotly legend, which allows temporary hiding/showing of datasets with a single click.

While the Plotly legend interaction is useful for quick comparisons, we recommend using the left-side dataset selector for a more stable and consistent user experience, especially when exporting plots or applying filters.

2. Feature Selection (X and Y axes)

Users must select two features, one for the X-axis and one for the Y-axis, from the available categories:

Feature Description Example
Statistical Descriptive measures derived from intensity distributions. Mean, standard deviation, maximum
Texture Quantitative descriptors of local intensity patterns (GLCM-based). Entropy, contrast, homogeneity
Spatial Anatomical or geometric positioning of segmented regions. Center of mass (x, y, z)
Tumor Morphological properties extracted from segmentation masks. Lesion volume, tumor location

The combination of different types of features (e.g., texture vs. spatial) can help uncover intricate data patterns or technical biases.

Some features depend heavily on the imaging modality, and comparisons between datasets are only meaningful when extracted from preprocessed MRIs. Texture features in particular are highly sensitive to variations in acquisition protocols and preprocessing pipelines. This sensitivity arises because descriptors like entropy, contrast, and energy are affected by voxel size and image spacing, intensity range and quantization strategy, and other technical aspects related to the scanners. Such technical differences are especially relevant in multi-center studies, where spatial resolution and image quality may vary substantially.

Other features, such as tumor volume, center of mass, or spatial location, are typically derived from segmentation masks that take into account the voxel spacing, and are independent of intensity information. These are more robust to differences in acquisition and preprocessing, making them suitable for comparisons even across heterogeneous cohorts.

Info

More technical details can be found in our publication and within the API reference.

3. Color Feature

In addition to selecting the X and Y axes, users can define a third variable to control the color of each data point in the scatter plot. This feature enables a richer multivariate exploration by adding a visual encoding of an additional dimension, effectively transforming the 2D plot into a pseudo-3D representation.

The available options include:

  • Dataset (default): Colors each point based on the dataset it belongs to. This is particularly useful when comparing cohorts, such as data from different hospitals, protocols, or population groups. Patterns of separation, overlap, or clustering between datasets can provide insight into dataset shifts or cohort-specific trends.

  • Any other available feature: Users may also choose to color points based on the value of a specific feature, such as tumor volume, center of mass, texture entropy, or any other scalar variable present in the dataset. This allows researchers to visually explore how a third variable distributes over the 2D feature space and whether it aligns with certain regions, clusters, or gradients.

Colorbars are dynamically generated when using feature-based coloring, providing a reference scale for interpretation. Continuous variables use a sequential or diverging colormap, while categorical features are represented using distinct colors.

Tip

When coloring by a continuous feature, watch for visual patterns such as localized extremes. These often indicate a non-trivial interaction between the color feature and the selected X/Y pair, which may warrant deeper investigation or stratified modeling approaches.

4. Highlight Subject

The Highlight subject option allows users to trace the behavior of an individual patient (or subject) across plots. By entering a specific subject ID and specifying the corresponding dataset, the selected subject will be visually highlighted in the dashboard, where the subject appears as a clearly marked point (e.g., with a different color or shape).

This feature is particularly valuable in contexts such as detecting whether a subject is an outlier or aligns with cohort expectations or verifying how individuals from different cohorts are distributed in shared feature space.

Tip

When analyzing extreme values, this feature can help determine whether a subject truly deviates from the cohort or lies within natural variability.

📊 Visualization

The Multivariate analysis mode displays an interactive 2D scatter plot:

2D scatter plot of multivariate features across datasets 2D scatter plot of multivariate features across datasets Figure 1: A scatter plot showing the relationship between two selected features across datasets. Each point represents a subject and is colored by dataset.

3D scatter plot of multivariate features across datasets 3D scatter plot of multivariate features across datasets Figure 2: A scatter plot showing the relationship between three selected features across datasets. X-axis and Y-axis represent Kurtosis and Skewness fo FLAIR sequence intensity pixels. Color represents tumor location for enhancing region.

All plots are interactive, powered by Plotly, allowing users to:

  • Toggle datasets on and off
  • Zoom and pan within plots
  • Export high-resolution images
  • Hover to inspect exact values

Whether you're debugging unexpected results or preparing figures for publication, this analysis mode is a core part of the AUDIT toolkit.