Immunology as a Metaphor for Computational ... - Napier University

Chapter 5. EA Based Model — COSDM 128Finally, the evolved radii of the hard locations are examined for each category ofdatasets; for all half-schema experiments, the average radius of the antibodies evolvedby COSDM is either 29 or 30, with no obvious trend with increasing N. The averageradii of all antibodies evolved for quarter-schemas for all values of N is 30, and foreighth-schema experiments, the evolved average radius varies (again with no obviouspattern) between 28 and 29. Therefore, there is a tendency in all experiments forthe radius to tend towards the maximum possible, as this allows more antigens to berecognised. This finding is confirmed by repeating the experiments but allowing 6bits to define the radius, giving a maximum possible radius of 2 6 1¥ 63. Forthe eighth-schema experiments, no change is observed, for all values of n, i.e. the£number of antigens in the dataset, the radius varies between 28 and 30, and the numberof unrecognised antigen follows the same pattern observed in figure 5.6. However,for the quarter-schema experiments, for values of n 350 the radius rises well abovethe theoretical maximum upto a value of 45 for n 500 — this is coupled howeverwith a corresponding decrease in the number of antigens that are not recognised by theevolved immune system for all n. Similarly, for half-schema, the evolved radii increasewith increasing n to reach a maximum of 47 at n 500, and in this case, no antigenare unrecognised, even at n 500.Recall that the mean recall accuracy quantity is an average over all antigens inthe dataset, and therefore antigens which are not recognised by the immune systemhave a recall accuracy of zero, and therefore have a large effect on the mean accuracy.Clearly this results in a trade-off between recognising as many antigens as possible vsthe accuracy with which antigens can be recalled. In the case of the eighth-schema experiments,increasing the number of antigens recognised does not lead to an increase inthe mean accuracy of recall, therefore the radii evolve towards the maximum predictedby the theory. For quarter-schema datasets however, increasing the number of antigensrecognised produces an increase in mean recall accuracy — even though the antigensare recalled less accurately than compared to the case when the maximum value radiusis set to 31, the fact that more antigens can be recognised and hence stored in the memorycompensates for this. The same arguments apply to the half-schema datasets inwhich of course a randomly generated string would match on average half of the bits