Fig. 6: The case for implementing FC to CAMPA.
From: Graph Fourier transform for spatial omics representation and analyses of complex organs
a The first column shows pixel clustering concepts. In this bipartite graph (second column), pixel clustering can be formulated as a many-to-one mapping problem, where the source node represents the pixel, the target node represents the subcellular organelle, and the edges denote the corresponding mapping relationships. Regarding the modified workflow of CAMPA (third column), we have made a modification to the original loss function. The modified term aims to measure the spreading of graph signals in the reconstructed image. In the frequency domain, this spreading can be quantified using spreading entropy (see the “Methods” section). A spreading graph signal corresponds to high entropy, while a non-spread graph signal corresponds to low entropy. Therefore, the new regularizer term aims to minimize the spreading entropy. In the evaluation (fourth column), we used the validation loss, which was calculated using the same loss function and validation dataset to examine the contribution of the spreading entropy to the model training. The y-axis is the validation loss value, and the x-axis is the number of epochs for training the CAMPA model. b. UMAP shows five-pixel clusters predicted by the baseline model using the Leiden clustering algorithm at 0.2 resolution. c UMAP shows seven-pixel clusters predicted by the modified model using the Leiden clustering algorithm at 0.2 resolution. Two rare clusters were circled in this panel. d The Sanky plot shows the cluster changes from baseline model prediction to modified model prediction. e The heatmap shows the annotation of each cluster (modified model at resolution 0.2) using a human protein atlas. The column of the heatmap is the protein intensity in the cell nucleus, and the row corresponds to clusters. f–h The three figures showcase the overview of predicted pixel clusters, cluster 6, and marker protein for cell 224081. i–k The three figures showcase the overview of predicted pixel clusters, cluster 5, and marker protein for cell 367420.
