Kohonen neural network visualizations

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Yeast Expression Analysis And Visualization
Kohonen neural network visualizations Training a Kohonen neural network on the yeast gene expression profiles
Here we are training a Kohonen neural network, a self-organizing feature map, on the six known gene clusters defined in the DeRisi et al paper that are based on the gene's expression profiles for seven time points, as described previously. This particular Kohonen map was trained in seven minutes on an internal 5x5 rectangular matrix. The initial neighbourhood size changed from 3.0 to 0.3 in 100 cycles and a second neighbourhood size changed from 1.0 to 0.1 in 300 cycles. The resulting output was the original data with two new fields for the x and y positions within this 5x5 matrix corresponding to the clustering of the Kohonen network.

	Figure 1. Kohonen Map Displaying DeRisi Gene Clusters. This image presents a standard two-dimensional scatter plot with the x and y dimensions defined by the x and y Kohonen network positions ($KX and $KY). Overlayed on this image are the individual genes (only those genes defined by the known six clusters presented in the paper) as colored plus signs. Each color corresponding to a different cluster defined by each letter (B to F). In order to provide visual clarity of each Kohonen location a maximum display agitation of 0.3 was applied to both x and y positions for each gene plus sign.

	Figure 2. Kohonen Map Displaying All Expressed Genes. This image presents a standard two-dimensional scatter plot with the x and y dimensions defined by the x and y Kohonen network positions ($KX and $KY). Unlike the image above, overlayed on this image are all the individual genes provided in the source data set as colored plus signs (6153 individual genes). Each color corresponding to a different cluster defined by each letter (B to F and ?). Please note here that the colors have shifted over with blue new indicating those genes not present in one of the six DeRisi et al paper clusters that are marked by the ?. In order to provide visual clarity of each Kohonen location a maximum display agitation of 0.3 was applied to both x and y positions for each gene plus sign.

	Figure 3. Kohonen Map Displaying Newly Defined Gene Clusters. Taking the previous image displayed above, we define new clusters (new?) based on the Kohonen x and y positions and the six clusters defined by DeRisi et al. Each new cluster attempts to capture the original clusters as organized by the automatic process of the Kohonen neural network. These new clusters indicated by the individual encompassing rectangles and the new labels. The results of this approach defines other genes with similar properties not indicated to be within the original DeRisi et al clusters.

The results of the Kohonen neural network and the defined new clusters are then saved into a flat file for further analysis by other software tools AnVil Informatics has in-house.

Application of Parallel Coordinates Visualization of the Kohonen neural network results

Here we visualize the Kohonen neural network results with parallel coordinates (demonstrated previously). This visualization tool provides two important interactive capabilities: dynamic brushing (displayed here) and dynamic queries.

	Figure 4. Display of the Cluster newC Defined on the Kohonen Map. This image presents one result from the parallel coordinate visualization. Here the new cluster newC is brushed by the color blue to highlight those genes of interest and their expression profiles. The lines colored by red indicate all the other genes from the source data that are not contained in the new cluster newC. It is of interest here that this new cluster newC completely covers the original cluster C (that newC contains all the genes from the DeRisi et al defined cluster C). This is the only cluster with such a perfect matching.

	Figure 5. Display of the Cluster newB Defined on the Kohonen Map. This is another example image presenting the results from the parallel coordinate visualizaiton. Here the new cluster newB is brushed by the color blue to highlight those genes of interest and their expression profiles. As stated above, the lines colored by read indicate all the other genes from the source data that are not contained in the new cluster newB. Note here, that one gene from the original DeRisi et al defined cluster B is not present in this new cluster newB. This is an area that requires further analysis as the initial Kohonen training could require some parameter changes else this gene may have been miss classified in the original DeRisi et al clustering.

The results of applying the parallel coordinate visualization technique to the output of the Kohonen neural network has defined some very interesting questions concerning the generation of the original clusters defined by the DeRisi et al Paper and our results generated from the Kohonen map. With further training and analyses and the application of our various other data mining and visualization software tools AnVil Informatics has in-house we should obtain some very useful information pertaining to the generalization of gene functions based on their expression profiles.


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