Real-valued negative selection algorithms

1. Real-valued negative selection algorithms Zhou Ji 11-2-2005

2. outline • Background • Variations of real-valued selection algorithms • More details through an example: V-detector • Demonstration

3. Background: AIS • AIS (Artificial Immune Systems) – only about 10 years’ history • Negative selection (development of T cells) • Immune network theory (how B cells and antibodies interact with each other) • Clonal selection (how a pool of B cells, especially, memory cells are developed) • New inspirations from immunology: danger theory, germinal center, etc. • Negative selection algorithms • The earliest and most widely used AIS. background

4. Biological metaphor of negative selection How T cells mature in the thymus: • The cell are diversified. • Those that recognize self are eliminated. • The rest are used to recognize nonself.

5. The idea of negative selection algorithms (NSA) The concept of feature space and detectors • The problem to deal with: anomaly detection (or one-class classification) • Detector set • random generation: maintain diversity • censoring: eliminating those that match self samples background

6. Outline of a typical NSA Anomaly detection: (classification of incoming data items) Generation of detector set background

7. Family of NSA Types of works about NSA • Applications: solving real world problems by using a typical version or adapting for specific applications • Improving NSA of new detector scheme and generation method and analyzing existing methods. Works are data representation specific, mostly binary representation. • Establishment of framework for binary representation to include various matching rules; discussion on uniqueness and usefulness of NSA; introduction of new concepts. What defines a negative selection algorithm? • Representation in negative space • One-class learning • Usage of detector set background

8. Data representation in NSA • Different representations vs. different searching space • Various representations: • Binary • String over finite alphabet: no fundamental difference from binary • Real-valued vector • hybrid • Different distance measure • Data representation is not the only factor to make a scheme different

9. Real-valued NSA • Why is real-valued NSA different from binary NSA? • Hard to analyze: simple combinatorics would not work • Necessary and proper for many real applications: binary representation may decouple the relation between feature space and representation • Is categorization based on data representation a good way to understand and develop NSA?

10. Major issues in NSA • Number of detectors • Affecting the efficiency of generation and detection • Detector coverage • Affecting the accuracy detection • Generation mechanisms • Affecting the efficiency of generation and the quality of resulted detectors • Matching rules – generalization • How to interpret the training data • depending on the feature space and representation scheme • Issues that are not NSA specific • Difficulty of one-class classification • Curse of dimensionality

11. Variations of real-valued NSA • Rectangular detectors generated with GA • Circular detectors that move and change size • MILA (multilevel immune learning algorithm)

12. Rectangular detectors + GA • Rectangular detectors: “rules” of value range • Generated by a typical genetic algorithm By Gonzalez, Dasgupta

13. Circular detectors (hypersphere) • From constant size to variable size • Moving after initial generation: • Reduce overlap • “artificial annealing” By Dasgupta, KrishnaKumar et al By Dasgupta, Gonzalez

14. MILA • Multilevel – to capture local patterns and global patterns • Negative selection + positive selection • Euclidean 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.

15. V-detector • V-detector is a new negative selection algorithm. • It embraces a series of related works to develop a more efficient and more reliable algorithm. • It has its unique process to generate detectors and determine coverage.

16. V-detector’s major features • Variable-sized detectors • Statistical confidence in detector coverage • Boundary-aware algorithm • Extensibility

17. Match or not match? In real-valued representation, detector can be visualized as hyper-sphere. Candidate 1: thrown-away; candidate 2: made a detector.

18. Variable sized detectors in V-detector method are “maximized detector” • Unanswered question: what is the self space? V-detector: maximized size traditional detectors: constant size

19. Why is the idea of “variable sized detectors” novel? • The rational of constant size: a uniform matching threshold • Detectors of variable size exist in some negative selection algorithms as a different mechanism • Allowing multiple or evolving size to optimize the coverage – limited by the concern of overlap • Variable size as part of random property of detectors/candidates • V-detector uses variable sized detectors to maximize the coverage with limited number of detectors • Size is decided on by the training data • Large nonself region is covered easily • Small detectors cover ‘holes’ • Overlap is not an issue in V-detector

20. Statistical estimate of detector coverage • Exiting works: estimate necessary number of detectors – no direct relationship between the estimate and the actual detector set obtained. • Novelty of V-detector: • Evaluate the coverage of the actual detector set • Statistical inference is used as an integrated components of the detector generation algorithm, not to estimate coverage of finished detector set.

21. Basic idea leading to the new estimation mechanism • Random points are taken as detector candidates. The probability that a random point falls on covered region (some exiting detectors) reflects the portion that is covered -- similar to the idea of Monte Carlo integral. • Proportion of covered nonself space = probability of a sample point to be a covered point. (the points on self region not counted) • When more nonself space has been covered, it becomes less likely that a sample point to be an uncovered one. In other words, we need try more random point to find a uncovered one - one that can be used to make a detector.

22. Statistics involved • Central limit theory: sample statistic follows normal distribution • Using sample statistic to population parameter • In our application, use proportion of covered random points to estimate the actual proportion of covered area proportion 0 1

23. Statistic inference • Point estimate versus confidence interval • Estimate with confidence interval versus hypothesis testing • Proportion that is close to 100% will make the assumption of central limit theory invalid – not normal distribution. • Purpose of terminating the detector generation

24. Hypothesis testing • Identifying null hypothesis/alternative hypothesis. • Type I error: falsely reject null hypothesis • Type II error: falsely accept null hypothesis • The null hypothesis is the statement that we’d rather take as true if there is not strong enough evidence showing otherwise. In other words, we consider type I error more costly. • In term of coverage estimate, we consider falsely inadequate coverage is more costly. So the null hypothesis is: the current coverage is below the target coverage. • Choose significant level: maximum probability we are willing to accept in making Type I Error. • Collect sample and compute its statistic, in this case, the proportion. • Calculate z score from proportion an compare with za • If z is larger, we can reject null hypothesis and claim adequate coverage with confidence

25. Boundary-aware algorithm versus point-wise interpretation • A new concept in negative selection algorithm • Previous works of NSA • Matching threshold is used as mechanism to control the extent of generalization • However, each self sample is used individually. The continuous area represented by a group of sample is not captured. (point-wise interpretation) Desired interpretation: The area represented by The group of points More specificity Relatively more aggressive to detect anomaly More generalization The real boundary is Extended.

26. Boundary–aware: using the training points as a collection • Boundary-aware algorithm • A ‘clustering’ mechanism though represented in negative space • The training data are used as a collection instead individually. • Positive selection cannot do the same thing

27. V-detector is more than a real-valued negative selection algorithm • V-detector can be implemented for any data representation and distance measure. • Usually negative selection algorithms were designed with specific data representation and distance measure. • The features we just introduced are not limited by representation scheme or generation mechanism. (as long as we have a distance measure and a threshold to decide matching)

28. V-detector algorithm with confidence in detector coverage contribution

29. V-detector algorithm with confidence in detector coverage contribution

30. V-detector algorithm with confidence in detector coverage contribution

31. V-detector’s advantages • Efficiency: • fewer detectors • fast generation • Coverage confidence • Extensibility, simplicity

32. Experiments • A large pool of synthetic data (2-D real space) are experimented to understand V-detector’s behavior • More detail analysis of the influence of various parameters is planned as ‘work to do’ • Real world data • Confirm it works well enough to detect real world “anomaly” • Compare with methods dealing with similar problems • Demonstration • How actual training data and detector look like • Basic UI and visualization of V-detector implementation

33. Parameters to evaluate its performance • Detection rate • False alarm rate • Number of detectors

34. Control parameters and algorithm variations • Self radius – key parameter • Target coverage • Significant level (of hypothesis testing) • Boundary-aware versus point-wise • Hypothesis testing versus naïve estimate • Reuse random points versus minimum detector set (to be implemented)

35. Data’s influence on performance • Specific shape • Intuitively, “corners” will affect the results. • Number of training points • Major influence

36. Experiments on 2-D synthetic data Training points (1000) Test data (1000 points) and the ‘real shape’ we try to learn

37. Detector sets generated Trained with 1000 points Trained with 100 points

38. Synthetic data (‘intersection’ and pentagram): compare naïve estimate and hypothesis testing ‘intersection’ shape pentagram

39. Synthetic data : results for different shapes of self region

40. Synthetic data (ring): compare boundary-aware and point-wise False alarm rate Detection rate

41. Synthetic data (cross-shaped self): balance of errors

42. Real world data • Biomedical data • Pollution data • Ball bearing – preprocessed time series data • Others: Iris data, gene data, India Telugu

43. Results of biomedical data

44. Results of air pollution data Detection rate and false alarm rate Number of detectors

45. Ball bearing’s structure and damage Damaged cage

46. Ball bearing data Example of raw data (new bearings, first 1000 points) • raw data: time series of acceleration measurements • Preprocessing (from time domain to representation space for detection) • FFT (Fast Fourier Transform) with Hanning windowing: window size 32 • Statistical moments: up to 5th order

47. Ball bearing data: results Preprocessed with FFT Preprocessed with statistical moments

48. Ball bearing experiments with two different preprocessing techniques contribution

49. Results of Iris data

50. Iris data: number of detectors