Abstract
Imaging Mass Cytometry (IMC) combines laser ablation and mass spectrometry to quantitate metal-conjugated primary antibodies incubated in intact tumor tissue slides. This strategy allows spatially-resolved multiplexing of dozens of simultaneous protein targets with 1μm resolution. Each slide is a spatial assay consisting of high-dimensional multivariate observations (m-dimensional feature space) collected at different spatial positions and capturing data from a single biological sample or even representative spots from multiple samples when using tissue microarrays. Often, each of these spatial assays could be characterized by several regions of interest (ROIs). To extract meaningful information from the multi-dimensional observations recorded at different ROIs across different assays, we propose to analyze such datasets using a two-step graph-based approach. We first construct for each ROI a graph representing the interactions between the m covariates and compute an m dimensional vector characterizing the steady state distribution among features. We then use all these m-dimensional vectors to construct a graph between the ROIs from all assays. This second graph is subjected to a nonlinear dimension reduction analysis, retrieving the intrinsic geometric representation of the ROIs. Such a representation provides the foundation for efficient and accurate organization of the different ROIs that correlates with their phenotypes. Theoretically, we show that when the ROIs have a particular bi-modal distribution, the new representation gives rise to a better distinction between the two modalities compared to the maximum a posteriori (MAP) estimator. We applied our method to predict the sensitivity to PD-1 axis blockers treatment of lung cancer subjects based on IMC data, achieving 97.3% average accuracy on two IMC datasets. This serves as empirical evidence that the graph of graphs approach enables us to integrate multiple ROIs and the intra-relationships between the features at each ROI, giving rise to an informative representation that is strongly associated with the phenotypic state of the entire image.
Highlights
Consider multi-feature observations collected at different spatial positions
The first step consists of extracting the steady state distribution of the random walk on the graph, which captures the mutual relations between the covariates of each regions of interest (ROIs)
We theoretically show that when the ROIs have a two-class structure, our method accentuates the distinction between the classes
Summary
Consider multi-feature observations collected at different spatial positions Data structure of this type requires analysts to address two immediate natural questions. Second is how to organize the observations from different spatial positions into an informative representation We approach these two questions from the standpoint of manifold learning, which is a class of nonlinear dimensionality reduction techniques for high-dimensional data [1,2,3,4]. The common assumption in manifold learning is that the multi-feature observations lie on a hidden lower-dimensional manifold. Such an assumption facilitates the incorporation of geometric concepts such as metrics, geodesic distances, and embedding, into useful data analysis techniques. The data samples form the graph nodes and the edges of the graph are determined according to some similarity notion that is usually application-specific
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