The Memory Cells

The B cells necessarily differentiate into extended lived memory cells which are able of producing high affinity antibodies, for the adaptive production control system.  Memory cells present the predicted value of outputs also. Mostly, memory cells contain the affinity that stands for the mean flow time like the performance measure.

All the antibodies are linked and have a weight. An input signal is shifted during the proliferation and an output signal is shifted or transferred to the memory cells or plasma cells by the upstream B cells or clones. The signal is passing after crossing its weighted value to the exact threshold value. This IS or immune system is trained via back-propagation algorithm which is described below. Assume that "i" shows the index of antibodies secreted by B cells and Xⁱ is the input value shown by this antibody and "j" shows the index of antibody from T cells. Suppose that the weight of the antibody which concerns links the antibody "i" and along with antibody as from T cells "j" is "W_ij" and "t" is the threshold value. Suppose On is the output value of neuron "i". The activation function of neuron "j" is:

                                                         On =1/1 + exp ((W_ij * X_i)- t ).......................Eqn1

                                                                                ΔE = O_n - O_a....................Eqn2

                                                              W_ijnew = W_ijold + ΔW_ij....................Eqn3

Here, O_a = Actual output value, and

 ΔE = error.

The value of "W_ij" and "t" is determined by the past behaviour of the system such is learned via Back-Propagation algorithm. The above-mentioned functioning of AIS or artificial immune systems can be visualized through following figure.

                                                                                Figure: AIS for Attribute Selection

The system attribute must be considered extreme carefully since the removal of a strong signal of system attribute or considering a system's weak signal attribute might affect the presentation of an artificial immune system.

In addition to the features of artificial immune system mentioned above, given measures should to be considered in attribute selection modules. One of the measures depends upon the signal weights merely. The mathematical formula is described below:

Here

i = index of antibody from B cells,

j = index of antibody from T cells,

k = index of antibody form output containing cells like memory or plasma cells,

W_ij = weight from antibody i to antibody j, and

W_jk = weight from antibody j to antibody as from output containing cells k.

On the basis of the above measure, we can compute the attribute selection score or ASS, the mathematical formula for i^th input is described below:

As per to the Eq..(5), the input, that has the highest score, is the most significant attribute. For selecting the attributes, a threshold value is set via:

                                                                           Tv= 1/n..........................Eqn(6)

Here TV = Threshold value, and

N = Number of attributes.

For deleting the insignificant attributes the attribute selection score is computed whether this is less than the threshold value, delete this else this is selected.

On the above equation's basis, this algorithm has the given steps :

(a) For all presentation criteria an immune system is created.

(b) Train the IS or immune system on the basis of back-propagation algorithm and remain the enhanced weights separately.

(c) Computed the measure for all immune system employing the Eq. (4).

(d) Computed the attribute selection score for all system by employing the Eq. (5).

(e) Verify this score by the threshold value by employing the Eq. (6).

As per to, this selects the attributes.