t-SNE analysis

Helping to reduce dimensionality and visualize relationships in a non-linear fashion

Use the t-SNE (t-distributed Stochastic Neighbor Embedding) tab to visualize high-dimensional data in a low-dimensional map, typically 2D.

t-SNE is particularly good at revealing local structure and clusters within your data. It works by modeling similarities between high-dimensional data points and representing them as probabilities, then finding a low-dimensional embedding that preserves these similarities.

Unlike PCA, t-SNE uses a non-linear algorithm. This often makes it better suited for visualizing complex datasets where relationships aren't linear, such as identifying distinct cell populations in single-cell RNA sequencing (scRNA-seq) data.

Keep in mind:

• t-SNE is primarily for visualization, not necessarily for preserving global distances accurately. The distances between clusters in a t-SNE plot might not be meaningful.

• The resulting plot can depend heavily on the chosen parameters (like perplexity).

1. t-SNE Setup

Configure the t-SNE calculation and visualization using the options in the side panel. For general setup like initial column selection and standard preprocessing, refer to the main documentation sections.

1. t-SNE Hyperparameter Setup

These parameters control the core t-SNE algorithm. Finding optimal values often requires experimentation, but PANDORA may provide automatic optimization or reasonable defaults.

• Perplexity:

  • Related to the number of nearest neighbors considered for each point. It balances attention to local vs. global aspects of the data.

  • Typical values range from 5 to 50. Lower values emphasize local structure; higher values consider more neighbors.

• Exaggeration Factor:

  • Controls how much the natural clusters in the data are separated from each other during the initial optimization phase. Higher values can create more space between clusters.

  • Typical values might range from 4 to 30.

• Theta:

  • Controls the trade-off between speed and accuracy for the Barnes-Hut approximation used in t-SNE.

  • Lower values (e.g., 0) are more accurate but slower. Higher values (e.g., 0.5 to 1) are faster but less accurate.

• Max Iterations:

  • The maximum number of optimization steps the algorithm will run.

  • Should be high enough for the embedding to stabilize (often 1000 or more). PANDORA allows up to 50,000.

• Learning Rate (Eta):

  • Controls the step size during the optimization process.

  • Typical values might be around 200. If the learning rate is too high, the embedding might diverge; if too low, it might take many iterations to converge.

2. Clustered t-SNE Settings

These settings apply specifically when generating the Clustered t-SNE Plot, which runs a clustering algorithm on the 2D t-SNE results.

• Clustering Algorithm: Choose the method used to identify clusters in the 2D t-SNE map:

  • Louvain: Community detection algorithm often used with KNN graphs.

    • K (for KNN graph): The number of nearest neighbors used to build the graph for Louvain clustering.

  • Hierarchical Clustering: Builds a hierarchy of clusters.

    • Clustering Method (Linkage): Select the linkage method (e.g., ward, complete, average).

  • Mclust: Model-based clustering assuming Gaussian mixture models.

    • epsQuantile: Parameter related to density or neighborhood size (shared with Density-based).

  • Density-based clustering (e.g., DBSCAN): Groups points based on density.

    • epsQuantile: Parameter controlling the density threshold or neighborhood size. Higher values increase the considered neighborhood.

3. Dataset Analysis Settings (Post-Clustering Analysis)

Perform further analysis on the identified clusters from the Clustered t-SNE.

• Dataset Analysis Type: Select how to visualize the characteristics of the identified clusters using the original high-dimensional data:

  • Heatmap: Shows the mean expression/value of original variables within each cluster.

  • Hierarchical Clustering: Performs clustering on the cluster means or representative profiles.

• Grouped Display: (Typically used with Heatmap) Display the mean values of the original variables for each identified t-SNE cluster.

4. Optional Visualization Settings

Control how points are colored in the main t-SNE plots:

• Grouping Variable:

  • Select a categorical variable from your metadata (e.g., 'cell_type', 'treatment').

  • Points in the t-SNE plot will be colored according to this variable.

  • Important: This variable is excluded from the t-SNE calculation itself and used only for visualization.

• Color Variable:

  • Select a continuous variable from your dataset (e.g., expression level of a specific gene, a clinical score).

  • Points in the t-SNE plot will be colored based on the value of this variable (using a continuous color scale).

  • Important: This variable is included in the t-SNE calculation along with other selected features.

2. t-SNE Plot

The primary output of the t-SNE Analysis tab is a 2D scatter plot where each point represents one of your samples (e.g., an individual patient, a cell). The algorithm positions points such that samples that were similar in the original high-dimensional space tend to be close together in the 2D plot.

Example t-SNE plot showing sample distribution

How to Interpret the t-SNE Plot

• Identify Clusters/Trends: Look for groups of points that form distinct clusters. These clusters often represent groups of samples with similar characteristics (e.g., similar cell types, similar responses to treatment).

• Focus on Local Structure: t-SNE excels at revealing local relationships. Points close together within a cluster are likely very similar in the original data.

• Axes Are Not Directly Interpretable: Unlike PCA, the axes (labeled "t-SNE dimension 1" and "t-SNE dimension 2") do not have a specific, interpretable meaning like "variance explained". They are simply the two dimensions chosen for the visualization.

• Cluster Separation May Not Reflect True Distance: While points within a cluster are close because they are similar, the amount of space between distinct clusters doesn't necessarily reflect how dissimilar those groups are in the original data. Don't over-interpret the large-scale distances.

• Hyperparameter Dependence: The final appearance of the plot (cluster shapes, tightness, separation) is highly sensitive to the chosen hyperparameters (Perplexity, Iterations, etc.). Running t-SNE with different parameters might yield different visualizations of the same data.

Hyperparameter Display

PANDORA typically displays the specific hyperparameter values used to generate the current t-SNE plot below the visualization itself.

Example display of t-SNE hyperparameters used for the plot

This is useful for:

• Recording the exact settings used for your analysis.

• Comparing results if you experiment with different hyperparameter values.

• Understanding how the chosen parameters (either default, automatically optimized, or manually set) influenced the resulting plot.

3. t-SNE Analysis: Results Tabs

After running the t-SNE calculation, PANDORA presents the results and further analyses in several tabs or sections, often located in a results panel (e.g., on the right side).

1. t-SNE Plot(s) Tab

• Purpose: Displays the primary t-SNE visualization(s).

• Content:

  • Shows the 2D scatter plot where each point is a sample, positioned based on the t-SNE embedding.

  • If you selected a Grouping Variable or Color Variable in the setup, additional versions of the plot colored accordingly will be displayed here. This helps visualize how known categories or continuous features map onto the t-SNE structure.

• Use: Identify potential clusters and visualize the distribution of your samples based on their high-dimensional similarities.

2. Clustered t-SNE Analysis Tab

• Purpose: Shows the results after applying a clustering algorithm (chosen in the setup) to the 2D t-SNE coordinates.

• Content:

  • Displays the t-SNE plot where points are colored based on the cluster assignments determined by the selected algorithm (e.g., Louvain, Hierarchical, Mclust, Density-based).

  • May include summary statistics about the identified clusters (e.g., number of points per cluster).

• Use: Automatically identify and label distinct groups within the t-SNE map, helping to quantify and interpret the observed visual structures.

3. Dataset Analysis Tab

• Purpose: Provides deeper insights into the characteristics of the clusters identified in the Clustered t-SNE analysis by relating them back to the original high-dimensional data.

• Content: Depending on the Dataset Analysis Type selected during setup:

  • Heatmap: Displays a heatmap showing the average value (e.g., mean expression level) of the original variables (columns) for each identified t-SNE cluster. Rows might be variables, and columns would be clusters (or vice-versa).

  • Hierarchical Clustering: May show results of further clustering performed on the cluster average profiles, grouping clusters with similar overall variable patterns.

• Use: Understand what makes the identified clusters different from each other in terms of the original features (e.g., which genes are highly expressed in cluster 1 vs. cluster 2). This is crucial for biological interpretation of the t-SNE clusters.