The advantages of applying multivariate analysis to mass spectrometry imaging (MSI) data have been thoroughly demonstrated in recent decades. The identification and visualization of complex relationships between pixels in a hyperspectral data set can provide unique insights into the underlying surface chemistry. It is now recognized that most MSI data contain nonlinear relationships, which has led to increased application of machine learning approaches. Previously, we exemplified the use of the self-organizing map (SOM), a type of artificial neural network, for analyzing time-of-flight secondary ion mass spectrometry (TOF-SIMS) hyperspectral images. Recently, we developed a novel methodology, SOM-relational perspective mapping (RPM), which incorporates the algorithm RPM to improve visualization of the SOM for 2D TOF-SIMS images. Here, we use SOM-RPM to characterize and interpret 3D TOF-SIMS depth profile data, voxel-by-voxel. An organic Irganox™ multilayer standard sample was depth profiled using TOF-SIMS, and SOM-RPM was used to create 3D similarity maps of the depth-profiled sample, in which the mass spectral similarity of individual voxels is modeled with color similarity. We used this similarity map to segment the data into spatial features, demonstrating that the unsupervised method meaningfully differentiated between Irganox-3114 and Irganox-1010 nanometer-thin multilayer films. The method also identified unique clusters at the surface associated with environmental exposure and sample degradation. Key fragment ions characteristic of each cluster were identified, tying clusters to their underlying chemistries. SOM-RPM has the demonstrable ability to reduce vast data sets to simple 3D visualizations that can be used for clustering data and visualizing the complex relationships within.