real-valued negative selection algorithms zhou ji 11-2-2005

Real-valued Real-valued negative negative selection selection

algorithmsalgorithmsZhou JiZhou Ji

11-2-200511-2-2005

outlineoutline

BackgroundBackground Variations of real-valued selection Variations of real-valued selection

algorithmsalgorithms More details through an example: More details through an example: V-V-

detectordetector DemonstrationDemonstration

3background

Background: AISBackground: AIS AIS (Artificial Immune Systems) – only AIS (Artificial Immune Systems) – only

about 10 years’ historyabout 10 years’ history Negative selection (development of T cells)Negative selection (development of T cells) Immune network theory (how B cells and Immune network theory (how B cells and

antibodies interact with each other)antibodies interact with each other) Clonal selection (how a pool of B cells, Clonal selection (how a pool of B cells,

especially, memory cells are developed)especially, memory cells are developed) New inspirations from immunology: danger New inspirations from immunology: danger

theory, germinal center, etc.theory, germinal center, etc. Negative selection algorithmsNegative selection algorithms

The earliest and most widely used AIS.The earliest and most widely used AIS.

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Biological metaphor of Biological metaphor of negative selectionnegative selection

How T cells mature in the thymus:How T cells mature in the thymus: The cell are diversified.The cell are diversified. Those that recognize self are eliminated.Those that recognize self are eliminated. The rest are used to recognize nonself.The rest are used to recognize nonself.

5background

The idea of negative The idea of negative selection algorithms (NSA)selection algorithms (NSA)

The problem to deal with: anomaly detection (or The problem to deal with: anomaly detection (or one-class classification)one-class classification)

Detector setDetector set random generation: maintain diversityrandom generation: maintain diversity censoring: eliminating those that match self samplescensoring: eliminating those that match self samples

The concept of feature space and detectors

6background

Outline of a typical NSAOutline of a typical NSA

Generation of detector setAnomaly detection:(classification of incoming data items)

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Family of NSAFamily of NSATypes of works about NSATypes of works about NSA Applications: solving real world problems by using a Applications: solving real world problems by using a

typical version or adapting for specific applications typical version or adapting for specific applications Improving NSA of new detector scheme and generation Improving NSA of new detector scheme and generation

method and analyzing existing methods. Works are data method and analyzing existing methods. Works are data representation specific, mostly binary representation.representation specific, mostly binary representation.

Establishment of framework for binary representation to Establishment of framework for binary representation to include various matching rules; discussion on uniqueness include various matching rules; discussion on uniqueness and usefulness of NSA; introduction of new concepts.and usefulness of NSA; introduction of new concepts.

What defines a negative selection algorithm?What defines a negative selection algorithm? Representation in negative spaceRepresentation in negative space One-class learningOne-class learning Usage of detector setUsage of detector set

Data representation in Data representation in NSANSA

Different representations vs. different Different representations vs. different searching spacesearching space

Various representations:Various representations: BinaryBinary String over finite alphabet: no fundamental String over finite alphabet: no fundamental

difference from binarydifference from binary Real-valued vectorReal-valued vector hybridhybrid

Different distance measureDifferent distance measure Data representation is not the only factor to make Data representation is not the only factor to make

a scheme differenta scheme different

Real-valued NSAReal-valued NSA

Why is real-valued NSA different from Why is real-valued NSA different from binary NSA?binary NSA? Hard to analyze: simple combinatorics would Hard to analyze: simple combinatorics would

not worknot work Necessary and proper for many real Necessary and proper for many real

applications: binary representation may applications: binary representation may decouple the relation between feature space decouple the relation between feature space and representationand representation

Is categorization based on data Is categorization based on data representation a good way to understand representation a good way to understand and develop NSA? and develop NSA?

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Major issues in Major issues in NSANSA

Number of detectorsNumber of detectors Affecting the efficiency of generation and detectionAffecting the efficiency of generation and detection

Detector coverageDetector coverage Affecting the accuracy detectionAffecting the accuracy detection

Generation mechanismsGeneration mechanisms Affecting the efficiency of generation and the quality of resulted Affecting the efficiency of generation and the quality of resulted

detectorsdetectors

Matching rules – generalizationMatching rules – generalization How to interpret the training dataHow to interpret the training data depending on the feature space and representation schemedepending on the feature space and representation scheme

Issues that are not NSA specificIssues that are not NSA specific Difficulty of one-class classificationDifficulty of one-class classification Curse of dimensionalityCurse of dimensionality

Variations of real-valued Variations of real-valued NSANSA

Rectangular detectors generated Rectangular detectors generated with GAwith GA

Circular detectors that move and Circular detectors that move and change sizechange size

MILA (multilevel immune learning MILA (multilevel immune learning algorithm)algorithm)

Rectangular detectors + Rectangular detectors + GAGA

Rectangular detectors: “rules” of value Rectangular detectors: “rules” of value rangerange

Generated by a typical genetic algorithmGenerated by a typical genetic algorithm

By Gonzalez, Dasgupta

Circular detectors Circular detectors (hypersphere)(hypersphere)

From constant size to variable sizeFrom constant size to variable size Moving after initial generation:Moving after initial generation:

Reduce overlapReduce overlap ““artificial annealing”artificial annealing”

By Dasgupta, KrishnaKumar et al

By Dasgupta, Gonzalez

MILAMILA Multilevel – to capture local patterns Multilevel – to capture local patterns

and global patternsand global patterns Negative selection + positive Negative selection + positive

selectionselection Euclidean distance on sub-spaceEuclidean distance on sub-space

For example, suppose that a self string is <s1, s2, …, sL> and the window size is chosen as 3, then the self peptide strings can be <s1, s3, sL>, < s2, s4, s9 >, < s5, s7, s8 > and so on by randomly picking up the attribute at some positions.

V-detectorV-detector

V-detector is a new negative V-detector is a new negative selection algorithm.selection algorithm.

It embraces a series of related works It embraces a series of related works to develop a more efficient and more to develop a more efficient and more reliable algorithm.reliable algorithm.

It has its unique process to generate It has its unique process to generate detectors and determine coverage.detectors and determine coverage.

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V-detector’s major V-detector’s major featuresfeatures

Variable-sized detectorsVariable-sized detectors Statistical confidence in detector Statistical confidence in detector

coveragecoverage Boundary-aware algorithmBoundary-aware algorithm ExtensibilityExtensibility

In real-valued representation, detector can be visualized as hyper-sphere.Candidate 1: thrown-away; candidate 2: made a detector.

Match or not match?

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Variable sized detectors in V-detector Variable sized detectors in V-detector method method

are “maximized detector”are “maximized detector”

Unanswered question: what is the self space?Unanswered question: what is the self space?

traditional detectors: constant size V-detector: maximized size

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Why is the idea of “variable sized Why is the idea of “variable sized detectors” novel?detectors” novel?

The rational of constant size: a uniform matching The rational of constant size: a uniform matching thresholdthreshold

Detectors of variable size exist in some negative Detectors of variable size exist in some negative selection algorithms as a different mechanismselection algorithms as a different mechanism Allowing multiple or evolving size to optimize the coverage Allowing multiple or evolving size to optimize the coverage

– limited by the concern of overlap– limited by the concern of overlap Variable size as part of random property of Variable size as part of random property of

detectors/candidatesdetectors/candidates V-detector uses variable sized detectors to maximize V-detector uses variable sized detectors to maximize

the coverage with limited number of detectors the coverage with limited number of detectors Size is decided on by the training dataSize is decided on by the training data Large nonself region is covered easilyLarge nonself region is covered easily Small detectors cover ‘holes’Small detectors cover ‘holes’ Overlap is not an issue in V-detectorOverlap is not an issue in V-detector

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Statistical estimate of detector Statistical estimate of detector coveragecoverage

Exiting works: estimate necessary number Exiting works: estimate necessary number of detectors – no direct relationship of detectors – no direct relationship between the estimate and the actual between the estimate and the actual detector set obtained.detector set obtained.

Novelty of Novelty of V-detectorV-detector:: Evaluate the coverage of the actual detector Evaluate the coverage of the actual detector

setset Statistical inference is used as an integrated Statistical inference is used as an integrated

components of the detector generation components of the detector generation algorithm, not to estimate coverage of finished algorithm, not to estimate coverage of finished detector set.detector set.

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Basic idea leading to the new Basic idea leading to the new estimation mechanismestimation mechanism

Random points are taken as detector Random points are taken as detector candidates. The probability that a candidates. The probability that a random point falls on covered region random point falls on covered region (some exiting detectors) reflects the (some exiting detectors) reflects the portion that is covered -- similar to portion that is covered -- similar to the idea of Monte Carlo integral.the idea of Monte Carlo integral. Proportion of covered nonself space Proportion of covered nonself space

= probability of a sample point to be = probability of a sample point to be a covered point. (the points on self a covered point. (the points on self region not counted)region not counted)

When more nonself space has been When more nonself space has been covered, it becomes less likely that a covered, it becomes less likely that a sample point to be an uncovered sample point to be an uncovered one. In other words, we need try one. In other words, we need try more random point to find a more random point to find a uncovered one - one that can be uncovered one - one that can be used to make a detector.used to make a detector.

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Statistics involvedStatistics involved

Central limit theory: sample statistic follows normal Central limit theory: sample statistic follows normal distributiondistribution Using sample statistic to population parameterUsing sample statistic to population parameter In our application, use proportion of covered random points to In our application, use proportion of covered random points to

estimate the actual proportion of covered areaestimate the actual proportion of covered area

proportion0 1

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Statistic inferenceStatistic inference

Point estimate versus confidence intervalPoint estimate versus confidence interval

Estimate with confidence interval versus Estimate with confidence interval versus hypothesis testinghypothesis testing Proportion that is close to 100% will make the Proportion that is close to 100% will make the

assumption of central limit theory invalid – assumption of central limit theory invalid – not normal distribution.not normal distribution.

Purpose of terminating the detector Purpose of terminating the detector generationgeneration

Hypothesis testingHypothesis testing Identifying null hypothesis/alternative hypothesis.Identifying null hypothesis/alternative hypothesis.

Type I error: falsely reject null hypothesis Type I error: falsely reject null hypothesis Type II error: falsely accept null hypothesisType II error: falsely accept null hypothesis The null hypothesis is the statement that we’d rather take as The null hypothesis is the statement that we’d rather take as

true if there is not strong enough evidence showing true if there is not strong enough evidence showing otherwise. In other words, we consider type I error more otherwise. In other words, we consider type I error more costly.costly.

In term of coverage estimate, we consider falsely inadequate In term of coverage estimate, we consider falsely inadequate coverage is more costly. So the null hypothesis is: the current coverage is more costly. So the null hypothesis is: the current coverage is below the target coverage.coverage is below the target coverage.

Choose significant level: maximum probability we are Choose significant level: maximum probability we are willing to accept in making Type I Error.willing to accept in making Type I Error.

Collect sample and compute its statistic, in this case, the Collect sample and compute its statistic, in this case, the proportion.proportion.

Calculate Calculate zz score from proportion an compare with score from proportion an compare with zz If If zz is larger, we can reject null hypothesis and claim is larger, we can reject null hypothesis and claim

adequate coverage with confidenceadequate coverage with confidence

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Boundary-aware algorithm Boundary-aware algorithm versus point-wise versus point-wise

interpretationinterpretation A new concept in negative selection algorithmA new concept in negative selection algorithm Previous works of NSAPrevious works of NSA

Matching threshold is used as mechanism to control the Matching threshold is used as mechanism to control the extent of generalizationextent of generalization

However, each self sample is used individually. The However, each self sample is used individually. The continuous area represented by a group of sample is continuous area represented by a group of sample is not captured. (point-wise interpretation)not captured. (point-wise interpretation)

More specificityRelatively more aggressive to detect anomaly

More generalizationThe real boundary isExtended.

Desired interpretation: The area represented byThe group of points

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Boundary–aware: using the training Boundary–aware: using the training points as a collectionpoints as a collection

• Boundary-aware algorithmA ‘clustering’ mechanism though represented in negative space• The training data are used as a collection instead individually.• Positive selection cannot do the same thing

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V-detector is more than a V-detector is more than a real-valued negative real-valued negative selection algorithmselection algorithm

V-detector can be implemented for any V-detector can be implemented for any data representation and distance measure.data representation and distance measure. Usually negative selection algorithms were Usually negative selection algorithms were

designed with specific data representation and designed with specific data representation and distance measure.distance measure.

The features we just introduced are not The features we just introduced are not limited by representation scheme or limited by representation scheme or generation mechanism. (as long as we have generation mechanism. (as long as we have a distance measure and a threshold to a distance measure and a threshold to decide matching)decide matching)

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V-detector algorithm withconfidence in detector coverage

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V-detector’s advantagesV-detector’s advantages

Efficiency: Efficiency: fewer detectorsfewer detectors fast generationfast generation

Coverage confidenceCoverage confidence Extensibility, simplicityExtensibility, simplicity

ExperimentsExperiments A large pool of A large pool of synthetic data synthetic data (2-D real space) (2-D real space)

are experimented to understand V-detector’s are experimented to understand V-detector’s behaviorbehavior More detail analysis of the influence of various More detail analysis of the influence of various

parameters is planned as ‘work to do’parameters is planned as ‘work to do’ Real world dataReal world data

Confirm it works well enough to detect real world Confirm it works well enough to detect real world “anomaly”“anomaly”

Compare with methods dealing with similar Compare with methods dealing with similar problemsproblems

DemonstrationDemonstration How actual training data and detector look likeHow actual training data and detector look like Basic UI and visualization of V-detector Basic UI and visualization of V-detector

implementationimplementation

Parameters to evaluate its Parameters to evaluate its performanceperformance

Detection rateDetection rate False alarm rateFalse alarm rate Number of detectorsNumber of detectors

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Control parameters and Control parameters and algorithm variationsalgorithm variations

Self radius – key parameterSelf radius – key parameter Target coverageTarget coverage Significant level (of hypothesis testing)Significant level (of hypothesis testing) Boundary-aware versus point-wiseBoundary-aware versus point-wise Hypothesis testing versus naïve estimateHypothesis testing versus naïve estimate Reuse random points versus minimum Reuse random points versus minimum

detector set (to be implemented)detector set (to be implemented)

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Data’s influence on Data’s influence on performanceperformance

Specific shape Specific shape Intuitively, “corners” will affect the Intuitively, “corners” will affect the

results.results. Number of training pointsNumber of training points

Major influenceMajor influence

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Experiments on 2-D Experiments on 2-D synthetic datasynthetic data

Training points (1000) Test data (1000 points) and the ‘real shape’ we try to learn

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Detector sets generatedDetector sets generated

Trained with 1000 points Trained with 100 points

Synthetic data (‘intersection’ and pentagram): Synthetic data (‘intersection’ and pentagram):

compare naïve estimate and hypothesis testingcompare naïve estimate and hypothesis testing

‘intersection’ shape pentagram

Synthetic data : results for different shapes of Synthetic data : results for different shapes of self regionself region

Synthetic data (ring): compare boundary-Synthetic data (ring): compare boundary-aware and point-wiseaware and point-wise

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Real world dataReal world data

Biomedical dataBiomedical data Pollution dataPollution data Ball bearing – preprocessed time Ball bearing – preprocessed time

series dataseries data Others: Iris data, gene data, India Others: Iris data, gene data, India

TeluguTelugu

Results of biomedical Results of biomedical datadata

Training DataTraining Data AlgorithmAlgorithm Detection RateDetection Rate False Alarm rateFalse Alarm rate Number of DetectorsNumber of Detectors

MeanMean SDSD MeanMean SDSD MeanMean SDSD

100% training100% training MILAMILA 59.0759.07 3.853.85 00 00 10001000** 00

NSANSA 69.3669.36 2.672.67 00 00 10001000 00

r=0.1r=0.1 30.6130.61 3.043.04 00 00 21.5221.52 7.297.29

r=0.05r=0.05 40.5140.51 3.923.92 00 00 14.8414.84 5.145.14

50% training50% training MILAMILA 61.6161.61 3.823.82 2.432.43 0.430.43 10001000** 00

NSANSA 72.2972.29 2.632.63 2.942.94 0.210.21 10001000 00

r = 0.1r = 0.1 32.9232.92 2.352.35 0.610.61 0.310.31 15.51 15.51 4.854.85

r=0.05r=0.05 42.8942.89 3.833.83 1.071.07 0.490.49 12.2812.28 44

25% training25% training MILAMILA 80.4780.47 2.802.80 14.9314.93 2.082.08 10001000** 00

NSANSA 86.9686.96 2.722.72 19.5019.50 2.052.05 10001000 00

r=0.1r=0.1 43.6843.68 4.254.25 1.241.24 0.50.5 12.24 12.24 3.973.97

r=0.05r=0.05 57.9757.97 5.865.86 2.632.63 0.770.77 8.94 8.94 2.572.57

Results of air pollution Results of air pollution datadata

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Detection rate and false alarm rate Number of detectors

Ball bearing’s structure Ball bearing’s structure and damageand damage

Damaged cage

Ball bearing dataBall bearing data

raw data: time series of acceleration raw data: time series of acceleration measurementsmeasurements

Preprocessing (from time domain to representation Preprocessing (from time domain to representation space for detection)space for detection)

1.1. FFT (Fast Fourier Transform) with Hanning windowing: FFT (Fast Fourier Transform) with Hanning windowing: window size 32window size 32

2.2. Statistical moments: up to 5Statistical moments: up to 5thth order order

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1 33 65 97 129 161 193 225 257 289 321 353 385 417 449 481 513 545 577 609 641 673 705 737 769 801 833 865 897 929 961 993Example of raw data (new bearings, first 1000 points)

Ball bearing data: resultsBall bearing data: resultsBall bearing conditionsBall bearing conditions Total number of data pointsTotal number of data points Number of detected Number of detected

anomaliesanomaliesPercentage detectedPercentage detected

New bearing (normal)New bearing (normal) 27392739 00 0%0%

Outer race completely brokenOuter race completely broken 22412241 21822182 97.37%97.37%

Broken cage with one loose elementBroken cage with one loose element 29882988 577577 19.31%19.31%

Damage cage, four loose elementsDamage cage, four loose elements 29882988 337337 11.28%11.28%

No evident damage; badly wornNo evident damage; badly worn 29882988 209209 6.99%6.99%

Ball bearing conditionsBall bearing conditions Total number of data pointsTotal number of data points Number of detectedNumber of detectedanomaliesanomalies

Percentage detectedPercentage detected

New bearing (normal)New bearing (normal) 26512651 00 0%0%

Outer race completely brokenOuter race completely broken 21692169 16741674 77.18%77.18%

Broken cage with one loose elementBroken cage with one loose element 28922892 1414 0.48%0.48%

Damage cage, four loose elementsDamage cage, four loose elements 28922892 00 0%0%

No evident damage; badly wornNo evident damage; badly worn 28922892 00 0%0%

Preprocessed with FFT

Preprocessed with statistical moments

48contribution

Ball bearing experiments with two different preprocessing techniques

Results of Iris dataResults of Iris dataDetection rateDetection rate False alarm rateFalse alarm rate

Setosa 100%Setosa 100% MILAMILA 95.1695.16 00

NSA (single level)NSA (single level) 100100 00

V-detectorV-detector 99.9899.98 00

Setosa 50%Setosa 50% MILAMILA 94.0294.02 8.428.42

NSA (single level)NSA (single level) 100100 11.1811.18

V-detectorV-detector 99.9799.97 1.321.32

Versicolor 100%Versicolor 100% MILAMILA 84.3784.37 00

NSA (single level)NSA (single level) 95.6795.67 00


Versicolor 50%Versicolor 50% MILAMILA 84.4684.46 19.619.6

NSA (single level)NSA (single level) 9696 22.222.2


Virginica 100%Virginica 100% MILAMILA 75.7575.75 00

NSA (single level)NSA (single level) 92.5192.51 00


Virginica 50%Virginica 50% MILAMILA 88.9688.96 24.9824.98

NSA (single level)NSA (single level) 97.1897.18 33.2633.26


Iris data:Iris data: number of detectors number of detectors

meanmean maxmax MinMin SDSD

Setosa 100%Setosa 100% 2020 4242 55 7.877.87

Setosa 50%Setosa 50% 16.4416.44 3333 55 5.635.63

Veriscolor 100%Veriscolor 100% 153.24 153.24 255255 7272 38.838.8

Versicolor 50%Versicolor 50% 110.08 110.08 184184 6060 22.6122.61

Virginica 100%Virginica 100% 218.36 218.36 443443 7878 66.1166.11

Virginica 50%Virginica 50% 108.12108.12 203203 4646 30.7430.74

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ConclusionsConclusions Real-valued NSA has unique advantages and Real-valued NSA has unique advantages and

difficulties.difficulties. Good NSA should not be limited by the Good NSA should not be limited by the

difference in data representationdifference in data representation ““Killer application” is needed to support the Killer application” is needed to support the

necessity of NSA as many other “soft necessity of NSA as many other “soft computation” paradigmcomputation” paradigm Compare with other methods. In case of NSA, Compare with other methods. In case of NSA,

other one-class classification, e.g. one-class SVMother one-class classification, e.g. one-class SVM Good representation scheme and distance Good representation scheme and distance

measure play a very important role in measure play a very important role in performance – more important than performance – more important than algorithm variations in many cases.algorithm variations in many cases.

referencesreferences S Forrest, A. S. Perelson, L. Allen, and R. Cherukuri. Self-nonself discrimination in a computer. S Forrest, A. S. Perelson, L. Allen, and R. Cherukuri. Self-nonself discrimination in a computer.

In Proc. of the IEEE Symposium on Research in Security and Privacy, IEEE Computer Society In Proc. of the IEEE Symposium on Research in Security and Privacy, IEEE Computer Society Press, Los Alamitos, CA, pp. 202–212, 1994.Press, Los Alamitos, CA, pp. 202–212, 1994.

D. Dasgupta and F. Gonzalez, An Immunity-Based Technique to Characterize Intrusions in D. Dasgupta and F. Gonzalez, An Immunity-Based Technique to Characterize Intrusions in Computer Networks. In the Journal IEEE Transactions on Evolutionary Computation, Computer Networks. In the Journal IEEE Transactions on Evolutionary Computation, Volume:6, Issue:3,Page(s):281-291, June, 2002.Volume:6, Issue:3,Page(s):281-291, June, 2002.

F. Gonzalez, D. Dasgupta and L.F. Nino. A Randomized Real-Valued Negative Selection F. Gonzalez, D. Dasgupta and L.F. Nino. A Randomized Real-Valued Negative Selection Algorithm. In the proceedings of the 2nd International Conference on Artificial Immune Algorithm. In the proceedings of the 2nd International Conference on Artificial Immune Systems UK September 1-3, 2003.Systems UK September 1-3, 2003.

D.Dasgupta, S.Yu and N.S. Majumdar. MILA - Multilevel Immune Learning Algorithm. In the D.Dasgupta, S.Yu and N.S. Majumdar. MILA - Multilevel Immune Learning Algorithm. In the proceedings of the Genetic and Evolutionary Computation Conference(GECCO) Chicago, July proceedings of the Genetic and Evolutionary Computation Conference(GECCO) Chicago, July 12-16 2003.12-16 2003.

Dasgupta, Ji, Gonzalez, Artificial immune system (AIS) research in the last five years, CEC Dasgupta, Ji, Gonzalez, Artificial immune system (AIS) research in the last five years, CEC 20032003

Ji, Dasgupta, Augmented negative selection algorithm with variable-coverage detectors, CEC Ji, Dasgupta, Augmented negative selection algorithm with variable-coverage detectors, CEC 20042004

D.Dasgupta, K.KrishnaKumar, D.Wong, M.Berry Negative Selection Algorithm for Aircraft D.Dasgupta, K.KrishnaKumar, D.Wong, M.Berry Negative Selection Algorithm for Aircraft Fault Detection. 3rd International Conference on Artificial Immune Systems Catania, Sicily.Fault Detection. 3rd International Conference on Artificial Immune Systems Catania, Sicily.(Italy) September 13-16 2004.(Italy) September 13-16 2004.

Ji, Dasgupta, Real-valued negative selection algorithm with variable-sized detectors, GECCO Ji, Dasgupta, Real-valued negative selection algorithm with variable-sized detectors, GECCO 20042004

Simon M. Garrett. How do we evaluate artificial immune systems? Evolutionary Computation, Simon M. Garrett. How do we evaluate artificial immune systems? Evolutionary Computation, 13(2):145–178, 2005.13(2):145–178, 2005.

Ji, Dasgupta, Estimating the detector coverage in a negative selection algorithm, GECCO 2005Ji, Dasgupta, Estimating the detector coverage in a negative selection algorithm, GECCO 2005 Ji, A boundary-aware negative selection algorithm, ASC 2005Ji, A boundary-aware negative selection algorithm, ASC 2005 Ji, Dasgupta, Revisiting negative selection algorithms, submitted to the Evolutionary Ji, Dasgupta, Revisiting negative selection algorithms, submitted to the Evolutionary

Computation JournalComputation Journal Ji, Dasgupta, An efficient negative selection algorithm of “probably adequate” coverage, Ji, Dasgupta, An efficient negative selection algorithm of “probably adequate” coverage,

submitted to SMCsubmitted to SMC

Questions?Questions?

Thank you!Thank you!

What is matching rule?What is matching rule?

When a sample and a detector are When a sample and a detector are considered matching.considered matching.

Matching rule plays an important Matching rule plays an important role in negative selection algorithm. role in negative selection algorithm. It largely depends on the data It largely depends on the data representation.representation.

Experiments and ResultsExperiments and Results Synthetic DataSynthetic Data

2D. Training data are randomly chosen from the normal 2D. Training data are randomly chosen from the normal region.region.

Fisher’s Iris DataFisher’s Iris Data One of the three types is considered as “normal”.One of the three types is considered as “normal”.

Biomedical DataBiomedical Data Abnormal data are the medical measures of disease Abnormal data are the medical measures of disease

carrier patients.carrier patients. Air Pollution DataAir Pollution Data

Abnormal data are made by artificially altering the Abnormal data are made by artificially altering the normal air measurementsnormal air measurements

Ball bearings: Ball bearings: Measurement: time series data with preprocessing - 30D Measurement: time series data with preprocessing - 30D

and 5D and 5D

Synthetic data - Synthetic data - Cross-shaped Cross-shaped

self spaceself space Shape of self region and Shape of self region and example detector coverageexample detector coverage

(a) Actual self space (b) self radius = 0.05 (c) self radius = 0.1

Synthetic data - Synthetic data - Cross-Cross-

shaped self spaceshaped self space ResultsResults

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Synthetic data - Synthetic data - Ring-shaped Ring-shaped

self spaceself space ResultsResults


Iris dataIris dataVirginica as normal, 50% points Virginica as normal, 50% points

used to trainused to train

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Biomedical dataBiomedical data

Blood measure for a group of 209 Blood measure for a group of 209 patientspatients

Each patient has four different types Each patient has four different types of measurementof measurement

75 patients are carriers of a rare 75 patients are carriers of a rare genetic disorder. Others are normal.genetic disorder. Others are normal.

Biomedical data Biomedical data

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Air pollution dataAir pollution data Totally 60 original records.Totally 60 original records. Each is 16 different measurements concerning air Each is 16 different measurements concerning air

pollution.pollution. All the real data are considered as normal.All the real data are considered as normal. More data are made artificially:More data are made artificially:

1.1. Decide the normal range of each of 16 measurementsDecide the normal range of each of 16 measurements2.2. Randomly choose a real recordRandomly choose a real record3.3. Change three randomly chosen measurements within Change three randomly chosen measurements within

a larger than normal rangea larger than normal range4.4. If some the changed measurements are out of range, If some the changed measurements are out of range,

the record is considered abnormal; otherwise they the record is considered abnormal; otherwise they are considered normalare considered normal

Totally 1000 records including the original 60 are Totally 1000 records including the original 60 are used as test data. The original 60 are used as used as test data. The original 60 are used as training data.training data.

Example of data (FFT of new Example of data (FFT of new bearings)bearings)

--- first 3 coefficients of the first --- first 3 coefficients of the first 100 points100 points

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coefficient 1 coefficient 2 coeffcient 3

Example of data (statistical Example of data (statistical moments of new bearings)moments of new bearings)

--- moments up to 3rd order of --- moments up to 3rd order of the first 100 pointsthe first 100 points

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1st order 2nd order 3rd order

How much one sample How much one sample tellstells

Samples may be on Samples may be on boundaryboundary

In term of detectorsIn term of detectors

Comparing three Comparing three methodsmethods

Constant-sized detectors V-detector New algorithm

Self radius = 0.05

Comparing three Comparing three methodsmethods

Constant-sized detectors V-detectors New algorithm

Self radius = 0.1

Back to the presentation

real-valued negative selection algorithms zhou ji 11-2-2005

Documents

binary nsa

binary representation

realvalued nsa different

nsa applications

negative space representation

data representation

nsa different representations

nsa of new detector