Download IDS definition and classification

Anomaly Detection Systems
Contents
• Statistical methods
– parametric
– non-parametric (clustering)
• Systems with learning
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Anomaly detection
• Establishes profiles of normal
user/network behaviour
• Compares actual behaviour to those
profiles
• Alerts if deviations from the normal are
detected.
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Anomaly detection
• Profiles are defined as sets of metrics measures of particular aspects of
user/network behaviour.
• Each metric is associated a threshold or
permitted range of values.
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Anomaly detection
• Anomaly detection depends on an
assumption that users/networks exhibit
predictable, consistent patterns of system
usage.
• Adaptations to changes in behaviour over
time are possible.
• The problem with anomaly detection
– No set of metrics is rich enough to express all
anomalous behaviour.
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Statistical methods
• Statistical methods of anomaly detection
are categorized as
– Parametric methods
• Assumptions are made about the underlying
distribution of the data being analyzed.
– Non-parametric methods
• Involve nonparametric data classification
techniques - cluster analysis.
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Parametric methods
• The usual assumption is that the
distributions of usage patterns are
Gaussian:
1
f x  
e
 2

x  x0 2

2 2
x0 – mean
 - standard deviation
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Parametric methods
• The Denning’s model (the IDES model for
intrusion).
– Four statistical models may be included in the
system:
•
•
•
•
Operational model
Mean and standard deviation model
Multivariate model
Markov process model.
– Each model is suitable for a particular type of
system metric.
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Parametric methods
• Operational model
– This model applies to metrics such as event
counters for the number of password failures
in a particular time interval.
– The model compares the metric to a set
threshold, triggering an anomaly when the
metric exceeds the threshold value.
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Parametric methods
• Mean and standard deviation model (1)
– A classical mean and standard deviation
characterization of data.
– The assumption is that all the analyzer knows
about system behaviour metrics are the mean
and standard deviations.
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Parametric methods
• Mean and standard deviation model (2)
– A new behaviour observation is defined to be
abnormal if it falls outside a confidence
interval.
– This confidence interval is defined as ±d
standard deviations from the mean for some
parameter d (usually d =3).
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Parametric methods
• Mean and standard deviation model (3)
– This characterization is applicable to event
counters, interval timers, and resource
measures (memory, CPU, etc.)
– It is possible to assign weights to these
computations, such that, for example, more
recent data are assigned greater weights.
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Parametric methods
• Multivariate model (1)
– This is an extension to the mean and
standard deviation model.
– It is based on performing correlations among
two or more metrics.
– Instead of basing the detection of an anomaly
strictly on one measure, one might base it on
the correlation of that measure with another
measure.
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Parametric methods
• Multivariate model (2)
– Example:
• Instead of detecting an anomaly based solely on
the observed length of a session, one might base it
on the correlation of the length of the session with
the number of CPU cycles utilized.
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Parametric methods
• Markov process model (1)
– Under this model, the system considers each
different type of audit event as a state variable
and uses a state transition matrix to
characterize the transition frequencies
between states (not the frequencies of the
individual states/audit records).
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Parametric methods
• Markov process model (2)
– A new observation is defined as anomalous if
its probability, as determined by the previous
state and value in the state transition matrix,
is too low/high.
– This allows the system to detect unusual
command or event sequences, not just single
events.
– This introduces the concept of performing
stateful analysis of event sequences (frequent
episodes, etc.)
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Parametric methods
• Example - NIDES (Next-generation
Intrusion Detection Expert System) (1)
– Developed by SRI (Stanford Research
Institute) in the 1990s.
– Measures various activity levels.
– Combines these into a single “normality”
measure and checks it against a threshold.
– If the measure is above the threshold, the
activity is considered abnormal.
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Parametric methods
• Example - NIDES (2)
– NIDES measures (1)
• Intensity measures
– An example would be the number of audit records (log
entries) generated within a set time interval.
– Several different time intervals are used in order to track
short-, medium-, and long-term behaviour.
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Parametric methods
• Example - NIDES (3)
– NIDES measures (2)
• Distribution measures
– The overall distribution of the various audit records (log
file entries) is tracked via histograms.
– A difference measure is defined to determine how close
a given short-term histogram is to “normal” behaviour.
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Parametric methods
• Example - NIDES (4)
– NIDES measures (3)
• Categorical data
– The names of files accessed or the names of remote
computers accessed are examples of categorical data
used.
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Parametric methods
• Example - NIDES (5)
– NIDES measures (4)
• Counting measures
– These are numerical values that measure parameters
such as the number of seconds of CPU time used.
– They are generally taken over a fixed amount of time or
over a specific event, such as a single login.
– Thus, they are similar in character to intensity measures,
although they measure a different kind of activity.
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Parametric methods
• Example - NIDES (6)
– The different measurements each define a
statistic Sj .
– These measurements are assumed
(designed to be) appropriate (this includes
normalization), and are combined to produce
a 2-like statistic:
n
1
T 2   S 2j
n j 1
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Parametric methods
• Example - NIDES (7)
– A more complicated measure would include
the correlation between the events (as was
done with IDES):
IS  S1 , , S n C 1 S1 , , S n 
T
– Here, C is the correlation matrix between Si
and Sj for all i and j. IS is called the IDES
score.
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Parametric methods
• Example - NIDES (8)
– NIDES compares recent activity with past
activity, using a methodology that amounts to
a sliding window on the past.
– Thus it is designed to detect changes in
activity and to adapt to new activity levels.
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Parametric methods
• Example - NIDES (9)
– NIDES intensity measures are counts of audit
records per time unit etc.
– This provides an overall activity level for the
system.
– These are updated continuously rather than
recomputed at each time interval.
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Parametric methods
• Example - NIDES (10)
– Possible elements that can be monitored:
•
•
•
•
Average system load.
Number of active processes.
Number of E-mails received.
Different types of audit records (can be tracked
separately).
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Parametric methods
• Example - NIDES (11)
– The obvious extension of the intensity
measures idea is to track the different types of
audit records.
– This leads to a distribution (histogram) for the
audit records.
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Parametric methods
• Example - NIDES (12)
– Similarly, one could track the sizes of E-mail
messages received, or the types of files
accessed.
– These can be updated continuously.
– Distributions are then compared by means of
a squared error metric.
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Parametric methods
• Example - NIDES (13)
– Categorical measures can be for example the
names of files accessed.
– They are treated just like distributional
measures.
– Now each bin corresponds to a categorical,
while with distributional measures the bin can
correspond to a range of values.
– The updates are still performed continuously.
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Parametric methods
• Example - NIDES (14)
– All the measures are combined in the T 2
statistic.
– The value is compared with a threshold to
determine if the activity is “abnormal”.
– The threshold is usually set empirically, based
on the observed network behaviour in some
period of time.
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Parametric methods
• Example - NIDES (15)
– NIDES produces a single, overall measure of
“normality”, which could allow further
investigation into the components that make
up the statistic upon an alert.
– The problem with this is that an unusually low
value for one statistic can mask a high one for
another – multifaceted measures are more
useful.
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Parametric methods
• Advantages of parametric approach (1)
– Statistical anomaly detection using parametric
approach could reveal interesting, sometimes
suspicious, activities that could lead to
discoveries of security breaches.
– Parametric statistical systems do not require
the constant updates and maintenance that
misuse detection systems do.
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Parametric methods
• Advantages of parametric approach (2)
– However, metrics must be well chosen,
adequate for good discrimination, and welladapted to changes in behaviour (that is,
changes in behaviour must produce a
consistent, noticeable change in the
corresponding metrics).
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Parametric methods
• Disadvantages of parametric approach (1)
– Batch mode processing of audit records,
which eliminates the capability to perform
automated responses to block damage.
– The memory and processing loads involved in
using and maintaining the user/network profile
knowledge base usually cause the system to
lag behind audit record generation.
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Parametric methods
• Disadvantages of parametric approach (2)
– The nature of statistical analysis reduces the
capability of taking into account the sequential
relationships between events.
– The exact order of the occurrence of events is
not provided as an attribute in most of these
systems.
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Parametric methods
• Disadvantages of parametric approach (3)
– Since many anomalies indicating attack
depend on such sequential event
relationships, this situation represents a
serious limitation to the approach.
– In cases when quantitative methods
(Denning's operational model) are utilized, it is
also difficult to select appropriate values for
thresholds and ranges.
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Parametric methods
• Disadvantages of parametric approach (4)
– The false positive rates associated with
statistical analysis systems are high, which
sometimes leads to users ignoring or
disabling the systems.
– The false negative rates are also difficult to
reduce in these systems.
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Non-parametric methods
• One of the problems of parametric
methods is that error rates are high when
the assumptions about the distribution are
incorrect.
• When researchers began collecting
information about system usage patterns
that included attributes such as system
resource usage, the distributions were
discovered not to be Gaussian.
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Non-parametric methods
• Then, including Gaussian distribution
assumption into the measures led to high
error rates.
• A way of overcoming these problems is to
utilize non-parametric techniques for
performing anomaly detection.
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Non-parametric methods
• Non-parametric approach
– provides the capability of analyzing users with
less predictable usage patterns
– allows the system to take into account system
measures that are not easily analyzed by
parametric schemes.
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Non-parametric methods
• The non-parametric approach involves
non-parametric data classification
techniques, specifically cluster analysis.
• In cluster analysis, large quantities of
historical data are collected (a sample set)
and organized into clusters according to
some evaluation criteria.
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Non-parametric methods
• Pre-processing is performed in which
features associated with a particular event
stream (often mapped to a specific user)
are converted into a vector representation
(for example, Xi = [f1, f2, ..., fn ] in an
n-dimensional state).
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Non-parametric methods
• A clustering algorithm is used to group
vectors into classes by behaviours
– members of each class are as close as
possible to each other
– different classes are as far apart as possible.
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Non-parametric methods
• In non-parametric statistical anomaly
detection, the premise is that activity data,
as expressed in terms of the features, fall
into two distinct clusters:
– a cluster indicating anomalous activity
– a cluster indicating normal activity.
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Non-parametric methods
• Clustering algorithms
– algorithms that use simple distance measures
to determine whether an object falls into a
cluster
– concept-based algorithms (more complex)
• an object is "scored“ according to a set of
conditions and that score is used to determine
membership in a particular cluster.
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Non-parametric methods
• The advantages of non-parametric
approaches include the capability of
performing reliable reduction of event data
(in the transformation of raw event data to
vectors).
• This effect may reach as high as two
orders of magnitude compared to the
classical approach that does not include
vectors.
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Non-parametric methods
• Other benefits are improvement in the
speed of detection and improvement in
accuracy over parametric statistical
analysis.
• Disadvantages involve concerns that
expanding features beyond resource
usage would reduce the efficiency and the
accuracy of the analysis.
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Clustering in anomaly detection
• Formal definition:
– Let P be a set of vectors, whose cardinality
is m, and whose elements are p1,…,pm , of
dimensions n1,…,nm , respectively.
– The task: partition, optimizing a partition
criterion, the set P into k subsets P1,…,Pk ,
such that the following holds:
P1  P2    Pk  P
Pi  Pj  , i, j  1,2,  , k , i  j
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Clustering in anomaly detection
Incoming
traffic/logs
Data pre-processor
Activity data
Detection
model(s)
Detection algorithm
Clustering!
Alerts
Decision
criteria
Alert filter
Action/Report
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Clustering in anomaly detection
• Why should we do clustering instead of
learning?
– Labelling a large set of samples is often costly.
– Very large data sets – train the system with a
large amount of unlabelled data and then label
with supervision, i.e. learning.
– Track slow changes of patterns in time without
supervision – improves performances.
– Smart feature extraction.
– Initial exploratory data analysis.
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Clustering in anomaly detection
• Appropriate cluster analysis algorithms (1)
– Two main classes of clustering algorithms
• Hierarchical
• Non-hierarchical (partitional)
– Hierarchical
• Less efficient
• More biased results in general
– Non-hierarchical
• Results often depend on the initial partition.
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Clustering in anomaly detection
• Appropriate cluster analysis algorithms (2)
– A trade-off between correctness and
efficiency of the CA algorithm must be found
in order to achieve the real-time operation of
an IDS.
– K-means algorithm – could be a good
candidate for implementation in IDS.
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Clustering in anomaly detection
•
Appropriate cluster analysis algorithms (3)
–
An outline of the K-means algorithm
1. Initialization: Randomly choose K vectors from the
data set and make them initial cluster centers.
2. Assignment: Assign each vector to its closest
center.
3. Updating: Replace each center with the mean of its
members.
4. Iteration: Repeat steps 2 and 3 until there is no
more updating.
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Clustering in anomaly detection
•
K-means algorithm
–
–
–
A local optimization algorithm – hill climbing.
Clustering depends on initial centers, but
this can be overcome in several ways.
Time complexity linear in the number of
input vectors – a major advantage over e.g.
hierarchical methods.
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Clustering in anomaly detection
•
Problems to solve
–
–
Determine the number of clusters
Determine the appropriate distance measure
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Clustering in anomaly detection
•
Determine the number of clusters
–
–
–
2 clusters if we want only to tell “abnormal”
from “normal” behaviour.
More complex clustering evaluation
algorithms should be used to detect the
number of clusters at which the most
compact and separated clusters are
obtained.
Use hierarchical clustering + clustering
evaluation algorithms (inefficient).
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Clustering in anomaly detection
•
Determine the appropriate distance
measure (1)
–
It must be a metric:
•
•
•
•
a,b, d (a,b )  0
a,b, d (a,b ) = 0  a =b
a,b, d (a,b ) =d (b,a )
a,b,c, d (a,c )  d (a,b ) +d (b,c ), i.e. the triangle
inequality must hold.
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Clustering in anomaly detection
•
Determine the appropriate distance
measure (2)
–
Typical metrics:
•
•
For equal length input vectors – the Minkowski
metric.
For unequal length input vectors – the edit distance
(which is also a metric).
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Clustering in anomaly detection
•
The Minkowski metric
d X, Y   q
n
x y
i 1
•
•
i
q
i
q=1, Manhattan (city block) distance
q=2, Euclidean distance
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Clustering in anomaly detection
• Edit distance
– Elementary edit operations
• Deletions
• Insertions
• Substitutions
– Minimum number of elementary edit
operations needed to transform one vector
into another.
– Computed recursively, by filling the matrix of
partial edit distances – edit distance matrix.
– The definition can include constraints.
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Clustering in anomaly detection
• Labelling clusters
– Way to determine which cluster contains
normal instances and which contain attacks.
– 1st assumption
• Associate the label “normal” with the cluster of the
greatest cardinality.
• Fails with massive attacks, as for example the
Syn-flood attack.
• Fails with KDD cup data without filtering out the
attacks.
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Clustering in anomaly detection
• To label properly, we need to explore the
structure of the clusters.
• The clustering quality criteria are used,
combined with some characteristics of the
clusters:
–
–
–
–
Silhouette index
Davies - Bouldin index
Dunn’s index
Clusters’ diameters
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Clustering in anomaly detection
• Intra-cluster distance
– The measure of compactness of a cluster
(complete diameter, average diameter,
centroid diameter, ...)
• Inter-cluster distance
– The measure of separation between clusters
(single linkage, complete linkage, average
linkage, centroid linkage, ...).
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Example – Davies - Bouldin
• Data set for clustering
X  X1 , , X N 
• Clustering into L clusters
C  C1 , , C L 
• Distance between the vectors X k and X l
d X k , X l 
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Example – Davies - Bouldin
• Davies - Bouldin index:
 Ci    C j 
1
DBC    max 

L i 1 i  j   Ci , C j  
L
• Inter-cluster distance
 Ci , C j


• Intra-cluster distance
Ci 
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Example – Davies - Bouldin
• Intra-cluster distance – Centroid diameter

  d X k , sCi
 X k Ci
Ci   2
Ci


1
sCi 
Ci
X
X k Ci
 



k
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Example – Davies - Bouldin
• Inter-cluster distance – Centroid linkage

 Ci , C j   d sC , sC
1
sCi 
Ci
X
X k Ci
i
k
j

sC j
1

Cj
X
X k C j
k
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Clustering in anomaly detection
• The clusters labelling algorithm (1)
– Uses a combination of the Davies - Bouldin
index of the clustering and the centroid
diameters of the clusters.
– Two clusters: “normal” and “abnormal”.
– Main idea (1)
• Attack vectors are often mutually very similar, if not
identical.
• Consequently, the attack cluster in the case of a
massive attack is very compact.
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Clustering in anomaly detection
• The clusters labelling algorithm (2)
– Main idea (2)
• The Davies - Bouldin index of such a clustering is
either zero (non-attack cluster is empty) or very
close to zero.
• The expected value of the centroid diameter of the
attack cluster is smaller than that of the non-attack
cluster.
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Clustering in anomaly detection
• The clusters labelling algorithm (3)
– Main idea (3)
• Small value of the Davies - Bouldin index indicates
the existence of a massive attack
• Small value of the centroid diameter indicates the
attack cluster.
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Clustering in anomaly detection
• The clusters labelling algorithm (4)
– Main idea (4)
• A higher value of the Davies - Bouldin index
indicates that no massive attack is taking place.
• Then the attack cluster is expected to be less
compact than the non-attack cluster, i.e. its
centroid diameter is greater than that of the nonattack cluster (because non-massive attack
vectors are very different in general).
• In this case, even the cluster cardinality can be
used for proper labelling.
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Clustering in anomaly detection
• The clusters labelling algorithm (5)
– Input:
• A clustering C of N vectors into 2 clusters, C1 and
C2; C1 is the “non-attack” cluster, labelled with “1”.
• The Davies - Bouldin index threshold, DB.
• The centroid diameters difference thresholds, CD1
and CD2.
– Output:
• The eventually relabelled input clustering, if
relabelling conditions are met.
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Clustering in anomaly detection
• The clusters labelling algorithm (6)
db = DaviesBouldingIndex(C) ;
cd1 = CentroidDiameter(C1) ;
cd2 = CentroidDiameter(C2) ;
if (db==0)&&(cd2==0)
Relabel(C) ;
else if (db>DeltaDB)&&(cd1>(cd2+DeltaCD1))
Relabel(C) ;
else if (db<DeltaDB)&&((cd1+DeltaCD2)<cd2)
Relabel(C);
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Example – KDD cup data base
• Sample size: N=1000
• Number of clusters: 2
Record
No.
DB
CD1
CD2
0-1000
1.13
32759.24 7108.57
Intrusion Good
labelling
(K- means)
Relabel
N
N
2
5000-6000 0.96
4344.63
14158.54 N
Y
0
7000-8000 0.14
69.6
7096.34
Y-376
N
3
8000-9000 0
25.19
0
Y-1000
N
1
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Systems with learning
• Two phases of system operation:
– The learning phase, in which the system is
taught what a normal behaviour is.
– The recognition phase, in which the system
classifies the input vectors according to the
knowledge acquired in the learning process.
– These systems also include a conversion of
raw data into feature vectors.
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Systems with learning
• Example: Neural networks (1)
– Neural networks use adaptive learning
techniques to characterize anomalous
behaviour.
– This analysis technique operates on historical
sets of training data, which are presumably
cleansed of any data indicating intrusions or
other undesirable user behaviour.
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Systems with learning
• Example: Neural networks (2)
– Neural networks consist of numerous simple
processing elements called neurons that
interact by using weighted connections.
– The knowledge of a neural network is
encoded in the structure of the net in terms of
connections between units and their weights.
– The actual learning process takes place by
changing weights and adding or removing
connections.
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Systems with learning
A neural network
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Systems with learning
• Example: Neural networks (3)
– Neural network processing involves two
stages.
• In the first stage, the network is populated by a
training set of historical or other sample data that
represent user behaviour.
• In the second stage, the network accepts event
data and compares them to historical behaviour
references, determining similarities and
differences.
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Systems with learning
• Example: Neural networks (4)
– The network indicates that an event is
abnormal by changing the state of the units,
changing the weights of connections, adding
connections, or removing them.
– The network also modifies its definition of
what constitutes a normal event by performing
stepwise corrections.
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Systems with learning
• Example: Neural networks (5)
– Neural networks don't make prior
assumptions on expected statistical
distribution of metrics,
– consequence: this method retains some of the
advantages over classical statistical analysis
associated with statistical nonparametric
techniques.
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Systems with learning
• Example: Neural networks (6)
– Among the problems associated with utilizing
neural networks for intrusion detection is a
tendency to form unstable configurations in
which the network fails to learn certain things
for no apparent reason.
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Systems with learning
• Example: Neural networks (7)
– The major drawback to utilizing neural
networks for intrusion detection is that neural
networks do not provide any explanation of
the anomalies they find.
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Systems with learning
• Example: Neural networks (8)
– This practice prevents the ability of users to
establish accountability or otherwise address
the roots of the security problems that allowed
the detected intrusion.
– This made neural networks poorly suited to
the needs of security managers.
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Systems with learning
• General problems related to all systems
with learning (1)
– The problem with all learning-based
approaches is in the fact that the
effectiveness of the approach depends on the
quality of the training data.
– In learning-based systems, the training data
must reflect normal activity for the users of the
system.
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Systems with learning
• General problems related to all systems
with learning (2)
– This approach may not be comprehensive
enough to reflect all possible normal user
behaviour patterns.
– This weakness produces a large false positive
error rate.
– The error rate is high because if an event
does not match the learned knowledge
completely, a false alarm is often generated,
although it does not always happen.
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