Fig 1.
Input data is tabular, there can be missing labels. A3SOM can perform standard classification or abstained classification. In both cases, results can be visualized and interpreted.
Fig 2.
Information is propagated from the input layer to the self-organizing map and to fully-connected dense layers, to obtain class predictions. A loss composed of the categorical cross-entropy and the distortion of the SOM is computed. Then, the weights of the model are updated during backpropagation.
Fig 3.
The model predicts the class of an input sample xt as purple. This sample is represented by the prototype P(1,1) which can be visualized.
Fig 4.
Abstained classification task overview.
The abstention task is applied after the model has been trained. It produces a new set of labels that can be visualized.
Fig 5.
Plot representing the 2D points of the artificial dataset.
Each class in the dataset is represented by a different color. Some overlaps between classes can be noticed.
Table 1.
Description of the different characteristics of benchmark datasets: Size, number of features, and number of classes.
Note that some datasets are not balanced.
Fig 6.
Representation of the mean validation accuracy after 5-fold cross-validation for different percentages of labeled data used during training. The x-axis represents the percentage of labeled samples included during training, and the mean accuracy of each method can be read on the y-axis.
Table 2.
Averaged benchmark accuracies.
The results presented in Fig 6 are averaged over all percentages of labeled data. Best performance for each dataset is in bold.
Fig 7.
Evolution of performance on the artificial dataset when varying abstention thresholds.
Scores obtained using combinations of local thresholds are in blue, and those obtained using global thresholds are in pink. The areas in yellow are the regions of interest, i.e., where local thresholds perform better than global ones. In (a) and (b) we vary distance abstention thresholds between 0 and 1 (ambiguity thresholds are set to 0). In (c) and (d) we vary ambiguity abstention thresholds between 0 and 1 (distance thresholds are set to 0).
Fig 8.
Representation of labels on the artificial dataset.
(a) 2D representation of training samples, colored by their true labels. Triangles are for labels that were not used during training, and circles for labels used. (b) Representation of SOM prototypes by the true labels of the training set. (c) 2D representation of test samples, colored by their abstained label. (d) Representation of SOM prototypes by the abstained labels of the test set.
Fig 9.
Visualization of the trained SOM with different types of labels for the breast cancer dataset.
LumA, LumB and Her2 are the three breast cancer subtypes seen during training, and Basal is the fourth subtype present in the data. Distance and ambiguity are the two abstention criteria.
Table 3.
Gene signature expected for each subtype.
‘+’ means overexpression of the gene in the subtype, ‘-’ means underexpression, and ‘/’ means we have no particular expectation.
Fig 10.
Visualization of the SOM prototypes.
Each prototype is represented by its values for four genes. In the background, neurons are also colored by their abstained label, as shown in the previous figure.