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[object Object],[object Object],[object Object],[object Object],Applying Support Vector Machines for Intrusion Detection on Virtual Machines Lecture 6
Outline ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Slides adapted from presentation by Fatemeh Azmandian (http://www.ece.neu.edu/~fazmandi)
Background ,[object Object],[object Object],[object Object],[object Object],[object Object]
Background (cont’d) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Background (cont’d) ,[object Object],[object Object],[object Object],[object Object],[object Object]
Financial Impact of Virus Attacks
Intrusion Detection Approaches ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Intrusion Detection Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Intrusion Detection Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Intrusion Detection Systems ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
VMM-IDS Overview
Support Vector Machines (SVMs) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Linear Classifiers Slide Source: Andrew W. Moore f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data?
Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
Classifier Margin f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) Slide Source: Andrew W. Moore Define the margin of a linear classifier as the width that the boundary could be increased by before hitting a datapoint
Maximum Margin x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) Slide Source: Andrew W. Moore The maximum margin linear classifier is the linear classifier with the maximum margin. This is the simplest kind of SVM (Called an LSVM) Linear SVM f
Maximum Margin x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) Slide Source: Andrew W. Moore The maximum margin linear classifier is the linear classifier with the maximum margin. This is the simplest kind of SVM (Called an LSVM) Linear SVM f Support Vectors are those datapoints that the margin pushes up against
Suppose 1-dimension What would SVMs do with this data? x=0
Suppose 1-dimension Not a big surprise Positive “plane” Negative “plane” x=0
Harder 1-dimensional dataset What can be done about this? x=0
Harder 1-dimensional dataset Use a kernel function to project the data onto higher dimensional space x=0
Harder 1-dimensional dataset x=0 Use a kernel function to project the data onto higher dimensional space
Non-linear SVMs: Feature spaces Φ : x -> φ ( x ) Input space Feature space
Non-linear SVMs: Feature spaces ,[object Object], (.)  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( )  ( ) Feature space Input space
Non-linear SVMs:Kernel Functions ,[object Object],[object Object],[object Object],[object Object],[object Object]
Dataset ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Constructing Features
Features
Two-Class SVM Results Experiment Workload Train on Abn1 Test on Abn2 Train on Abn2 Test on Abn1 Mixed Features SQL 0.90 0.96 Asterisk 0.81 0.81 Rate Features SQL 0.91 0.95 Asterisk 0.82 0.76 Correlation Features SQL 0.91 0.95 Asterisk 0.85 0.73
SQL Train on Abn1 and Test on Abn2: Time Series Plot
SQL Train : Train on Abn1 and Test on Abn2: (ROC Curve)
SQL Train on Abn2 and Test on Abn1: Time Series Plot
SQL Train on Abn2 and Test on Abn1: ROC Curve
Conclusions ,[object Object],[object Object]
References ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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PPT

  • 1.
  • 2.
  • 3.
  • 4.
  • 5.
  • 6. Financial Impact of Virus Attacks
  • 7.
  • 8.
  • 9.
  • 10.
  • 12.
  • 13. Linear Classifiers Slide Source: Andrew W. Moore f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data?
  • 14. Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
  • 15. Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
  • 16. Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
  • 17. Linear Classifiers f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) How would you classify this data? Slide Source: Andrew W. Moore
  • 18. Classifier Margin f x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) Slide Source: Andrew W. Moore Define the margin of a linear classifier as the width that the boundary could be increased by before hitting a datapoint
  • 19. Maximum Margin x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) Slide Source: Andrew W. Moore The maximum margin linear classifier is the linear classifier with the maximum margin. This is the simplest kind of SVM (Called an LSVM) Linear SVM f
  • 20. Maximum Margin x  y est denotes +1 denotes -1 f ( x , w ,b ) = sign( w . x - b ) Slide Source: Andrew W. Moore The maximum margin linear classifier is the linear classifier with the maximum margin. This is the simplest kind of SVM (Called an LSVM) Linear SVM f Support Vectors are those datapoints that the margin pushes up against
  • 21. Suppose 1-dimension What would SVMs do with this data? x=0
  • 22. Suppose 1-dimension Not a big surprise Positive “plane” Negative “plane” x=0
  • 23. Harder 1-dimensional dataset What can be done about this? x=0
  • 24. Harder 1-dimensional dataset Use a kernel function to project the data onto higher dimensional space x=0
  • 25. Harder 1-dimensional dataset x=0 Use a kernel function to project the data onto higher dimensional space
  • 26. Non-linear SVMs: Feature spaces Φ : x -> φ ( x ) Input space Feature space
  • 27.
  • 28.
  • 29.
  • 32. Two-Class SVM Results Experiment Workload Train on Abn1 Test on Abn2 Train on Abn2 Test on Abn1 Mixed Features SQL 0.90 0.96 Asterisk 0.81 0.81 Rate Features SQL 0.91 0.95 Asterisk 0.82 0.76 Correlation Features SQL 0.91 0.95 Asterisk 0.85 0.73
  • 33. SQL Train on Abn1 and Test on Abn2: Time Series Plot
  • 34. SQL Train : Train on Abn1 and Test on Abn2: (ROC Curve)
  • 35. SQL Train on Abn2 and Test on Abn1: Time Series Plot
  • 36. SQL Train on Abn2 and Test on Abn1: ROC Curve
  • 37.
  • 38.

Notes de l'éditeur

  1. Reasons for decrease from 2004 to 2005: Anti-virus and anti-spyware companies improved their products. A lot of companies starting coming to the realization that they needed to have a strong IDS in place.
  2. Reasons for decrease from 2004 to 2005: Anti-virus and anti-spyware companies improved their products. A lot of companies starting coming to the realization that they needed to have a strong IDS in place.
  3. During training for OCSVMs, the data from the first class is transformed onto a feature space such that it is far away from the origin. Then during testing, the origin and data points that are close to it, and hence far away from points from the first class, are considered part of the second class.
  4. General idea : the original feature space can always be mapped to some higher-dimensional feature space where the training set is separable: