Can a negative selection detect unique non-self cell in an infinitely large number of self cells?

Akira Imada

Brest State Technical University

Republic of Belarus

(PRIP-2005 – at Minsk, Belarus) 2

“Can a negative selection detect unique non-self cell

in an infinitely large number of self cells?” ⇓ Our Goal is

to search for only one ABNORMAL(no-self) pattern

hidden in

an enormous amount of NORMAL (self) patterns

by

NEGATIVE SELECTION of Artificial Immune System

We came accross

an extremely difficult

PEAK to be searched for

in a

FITNESS LANDSCAPE

explored by an

EVOLUTIONARY COMPUTATION

(PRIP-2005 – at Minsk, Belarus) 4

To realize an ASSOCIATIVE MEMORY

we use SPIKING NEURONS whose learning is by

EVOLUTIONARY COMPUTATIONS.

□ Fitness Landscape on all possible configuration of weights

• Traditional Hopfield Model ⇒ Everywhere rugged and many peaks.

• Spiking Neurons ⇒ unique peak and everywhere else is flatland of fitness 0.

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□ A fictitious plot of fitness landscape

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□ A Needle in a Haystack

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□ A tiny-flat-island-in-a-huge-lake

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□ What can we do?

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□ How difficult?

• Random Search

2^{20} = 1, 048, 576

• Lifetime Learning – Baldwin Effect (Hinton & Nowlan 1995?)

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□ Random Search vs Baldwin Effect

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They say

“Why don’t you use Artifitial Immune System? It’ll be easy?”

Is it really true?

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1. An immune approach — Sphere Detectors

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What if top area shrinks?

2. A Fuzzy approach

⇓
(MMMMMM ⋯ M)
⇓

IF x_{1} is Middle, and ⋯, and x_{20} is Middle THEN no-self.

3. Negative Selection

Algorithm 1 (Exhaustive Detector Generating Algorithm)

1. Create N_{s} samples of self cells at random.

2. Create a population of candidate detectors at random;

3. Discard it if it matches self, otherwise take it as a detector,

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3. Negative Selection – II

Algorithm 2 (Greedy Detector Generating Algorithm)

“perfect matching” ⇓ “r-contiguous matching”

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any 2-contiguous matching, e.g. (11*) works when

(110), (111), (010), (011) ⇒ SELF (000), (001), (100), (101) ⇒ NO-SELF

no 2-contiguous matching, e.g. (11*) works when

(110), (100), (011), (001) ⇒ SELF (101), (111), (000), (010) ⇒ NO-SELF

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Still not easy if it might not be impossible. However, our original interst on “SEARCH for WEIGHTS”

is now on “INTRUSION DETECTION”

1) Train the system with only but huge NORMAL sample. Needle/Island ⇒ intrusion

5.1 3.5 1.4 0.2 setosa
4.9 3.0 1.4 0.2 setosa
· · · · · · · · · · · ·  ⋯
7.0 3.2 4.7 1.4 versicolor
6.4 3.2 4.5 1.5 versicolor
· · · · · · · · · · · ·  ⋯
6.3 3.3 6.0 2.5 virginica
5.8 2.7 5.1 1.9 virginica
· · · · · · · · · · · ·  ⋯

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□ Let’s visualize the Iris Dataset of 4D — Sammon Mapping

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□ An evolution — maintaining distance relation as much as possible.

□ Final location in 2D space mapped.

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