Workflow from Scientific Research

The algorithm includes a soft TCN assignment module and a TCN ensemble module. First, a k -NN-based cellular spatial graph is constructed using cell spatial coordinates. Each node represents a cell and its m -dimensional attribute vector (blue) encodes the cell phenotype. m , number of cell phenotypes; n , number of cells. A basic GNN is applied to this cellular spatial graph to obtain a d -dimensional embedding vector (green) for each node. Embedding dimensions are specified according to users. A fully connected neural network is used to transform cell node embeddings to soft TCN assignments (yellow vectors) of nodes, representing the probabilities of cells belonging to c TCNs. The number of TCNs are specified according to users. The graph MinCut-based loss function ( L MinCut ) is used to learn the optimal soft TCN assignments of all nodes. This loss function can be used alone for an unsupervised learning task. In a supervised learning task, differentiable graph pooling, graph convolution and two fully connected layers with the cross-entropy loss function L CE (for sample classification, bordered by a dashed rectangular box) are added on top of the soft TCN assignment module. The overall supervised loss function is a linear combination of L MinCut and L CE with a weight parameter . In the TCN ensemble module, the first module can be run multiple times to generate multiple optimal soft TCN assignment matrices. Hard assignment is conducted for each of them and an ensemble procedure is performed on those hard TCN assignments using a majority vote strategy to determine the final robust TCNs.

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