Classification and diagnosis of the samples. A sample is classified to a cancer category according to its highest committee vote (average of all ANN outputs) and placed in the corresponding plot. Plotted, for each sample, is the distance from its committee vote to the ideal vote for that diagnostic category (for example, for EWS, it is EWS = 1, RMS = NB = BL = 0). Thus a perfectly classified sample would be plotted with a distance of zero. Training samples are displayed as squares and test samples as triangles. Non-SRBCT samples are colored black. All SRBCT samples, including the 20 tests, were correctly classified. The distance corresponding to the 95th percentile for the training samples is represented by a dashed line, outside which the diagnosis of a sample is rejected. The diagnosis of all 5 non-SRBCT test samples was rejected since they lie outside their respective dashed lines. Three of the SRBCT samples (EWS-T13, TEST-10 and TEST-20) though correctly classified could not be confidently diagnosed.

Hierarchical clustering and multidimensional scaling analysis. The top 96 genes as ranked by the ANN models were used for the analysis. a, Multidimensional scaling analysis. Shown here are two projections of the MDS plot of the training samples. EWS are depicted as yellow circles, RMS as red, BL as blue and NB as green. The samples clustered closely according to the 4 different cancer categories. b, Hierarchical clustering of the samples and genes. Each row represents one of the 96 cDNA clones and each column a separate sample. A pseudo-colored representation of the relative red intensity is shown such that a red color indicates high expression and green color low expression, with scale shown below. On the right are the IMAGE id., gene symbol, class in which the gene is highly expressed (see Supplementary Methods), and the ANN rank. *, genes that have not been reported to be associated with these cancers. c, Enlargement of the hierarchical clustering dendrogram of the samples in b. All 63 training and the 20 test SRBCTs correctly clustered within their diagnostic categories. In both cases where two samples were derived from the same cell line, BL-C2 & C4, and NB-C2 and C7, each mapped adjacent to one another in the same cluster. The scale shows the Pearson correlation coefficient used to construct the dendrogram. The Pearson correlation cutoff was 0.54, when the samples clustered into the four diagnostic categories.

The artificial neural network. a, Schematic illustration of the analysis process. The entire data-set of all 88 experiments was first quality filtered (1) and then the dimensionality was further reduced by principal component analysis (PCA) to 10 PCA projections (2), from the original 6567 expression values. Next, the 25 test experiments were set aside and the 63 training experiments were randomly partitioned into 3 groups (3). One of these groups was reserved for validation and the remaining 2 groups for calibration (4). ANN models were then calibrated using for each sample the 10 PCA values as input and the cancer category as output (5). For each model the calibration was optimized with 100 iterative cycles (epochs). This was repeated using each of the 3 groups for validation (6). The samples were again randomly partitioned and the entire training process repeated (7). For each selection of a validation group one model was calibrated, resulting in a total of 3750 trained models. Once the models were calibrated they were used to rank the genes according to their importance for the classification (8). The entire process (2–7) was repeated using only top ranked genes (9). The 25 test experiments were subsequently classified using all the calibrated models. b, Monitoring the calibration of the models. The average classification error per sample (using a summed square error function) is plotted during the training iterations (epochs) for both the training and the validation samples. A pair of lines, purple (training) and gray (validation), represents one model. The decrease in the classification errors with increasing epochs demonstrates the learning of the models to distinguish these cancers. The results shown are for 200 different models, each corresponding to a random partitioning of the data. All the models performed well for both training and validation as demonstrated by the parallel decrease (with increasing epochs) of the average summed square classification error per sample. In addition, there was no sign of over-training: if the models begin to learn features in the training set, which are not present in the validation set, this would result in an increase in the error for the validation at that point and the curves would no longer remain parallel. c, Minimizing the number of genes. The average number of misclassified samples for all 3750 models is plotted against increasing number of used genes. The misclassifications minimized to zero using the 96 highest ranked genes.