How Many Parachutists will be Needed to Find a Needle in a Pastoral?

Akira Imada

Brest State Technical University Moskowskaja 267 Brest 224017 Belarus akira@bstu.by

Abstract— This article is a consideration on computer network intrusion detection using artificial neural networks, or whatever else using machine learning techniques. We assume an intrusion to a network is like a needle in a haystack not like one family of iris flower, and we consider how an attack can be detected by an intelligent way, if any.

I. Introduction

The parachute drop went smoothly ... slithering down the chute and out into space ... Flick landed perfectly, with her knees bent and her arms tucked into her sides as she fell to the ground ... She folded her parachute into a neat bundle, then set out to find the other Jackdaws. – “Jackdaws” by Ken Follett.

Most banks nowadays facilitate their ATM (Automated Teller Machine) in which we may have a personal account to which we can access with PIN-code, usually four digits of decimal numerals. For security reason, if we failed to enter the PIN more than three times, then the PIN would loose its validity thereafter. Then what we are curious is, “How many trials would be needed for random challenges to reveal the secret PIN if an infinite number of trials were permitted?” Let’s formalize this problem.

Problem 1 (Breaking a PIN) Assuming p-bit of octal numeral is employed to construct a PIN, only one configuration out of those 8^{p} possible combinations is the secret PIN. No one except for the owner of the PIN knows it. Then question is, “How many average trials-and-errors will be needed to know the PIN under a specific strategy?”

This might be reminiscent of the famous problem called a needle in a haystack which was originally proposed by Hinton & Nowlan [1] in 1987. The needle in the proposal was exactly the one configuration of 20-bit of binary string, that is, the search space is made up of 2^{20} points and only one point is the needle to be searched for. No information such as how close is a currently searching point to the needle, or how likely is a searching point to be the needle. See Figure 1.

We assume that TCP connections to a computer network are represented with n-dimensional vectors and those represented by intrusions are such as needles among huge amount of normal transactions which might look like a haystack or pastoral.

II. Network Intrusion Detection

Those highly qualified hackers who provide security services to companies during the daytime and then go home at night to conduct totally illegal hacking are the ones who are the most dangerous. – by Enis Senerdem from Turkish Daily News on 29 March 2006.

When we are to design a network intrusion detection system, which is one of the hottest topics these days, by means of so called soft computings such as artificial immune system, fuzzy logic, evolutionary computations, neural networks, whatever it might be, we need a set of sample data to train the system and to test the system afterwards.

A. When a Family of Iris Flower is Normal Then are Others Abnormal? — Where is an Outlier?

The Spearman’s iris flower database^{1} is a frequently used dataset in pattern recognition/classification, data mining, etc. As such, there have been fair amount of studies in which this iris flower database is employed as a dataset to train and to test the intrusion detection system.

A total of 150 samples consists of three species: setosa, versicolor and virginica, each of which includes 50 samples. Each sample is a four-dimensional vector representing four attributes of the iris flower, that is, sepal length, sepal width, petal length, and petal width.

Let us take an example where this iris flower dataset was employed. Castellano et al. [2] assumed one family to be normal whilst the other two to be abnormal. The whole dataset was divided into 10 parts each of which has 15 samples uniformly drawn from the three classes. The system is trained by the remaining 135 samples. The originally picked up 15 samples are used to test the results. After this 10-fold cross validation, the authors concluded that

Fig. 1. A fictitious sketch of fitness landscape of a-needle-in-a-haystack. The haystack here is drawn as a two-dimensional flat plane of fitness zero.

1 University of California Urvine Machine Learning Repository. ics.uci.edu: pub/machine-learning-databases.

the abnormal detection rate is 96% while the false alarm rate is 0.6%. How nice, isn’t it? In reality, however, it is not so simple. It might not be difficult at all for a hacker to find an unlearned region which could work to invade the system.

We now look at the Figure 2 to see how the three spieces are distributed in the whole search space. This is depicted by the Sammon Mapping.

Sammon Mapping maps a set of points in a highdimensional space to the 2-dimensional space with the distance relation being preserved as much as possible, or equivalently, the distances in the n-dimensional space are approximated by distances in the 2-dimensional distance with a minimal error.

Just a brief look at the figure reveals us that there remains an enormously wide region of unlearned.

Fig. 2. A 2-D visualization of iris flower data by Sammon Mapping. Three different families of iris flower each contains 50 samples are represented in the figure with circles, triangles and squears.

B. Intrusion Might Look Like a Needle in a Hay! The other type of dataset, naturally more often employed in the context of network intrusion, is the KDD cup 1999 dataset which was prepared by MIT Lincoln Laboratory as a dataset for the 1998 DARPA intrusion detection evaluation [3]. This dataset has been, and still is going to be, a common benchmark for evaluation of intrusion detection techniques.

KDD dataset, beside normal data, covers four major categories of attacks: (i) Probing attacks which attack by proving a vulnerability of the network; (ii) Denial-of-Service (DoS) attacks which try an invasion by denying legitimate requests to a system; (iii) User-to-Root (U2R) attacks which tries an unauthorized access to local super-user or root; and (iv) Remote-to-Local (R2L) attacks which is an unauthorized local access from a remote machine. These four categories of attacks include a total of 32 different attack types.

The dataset consists of two sub-datasets. The one is provided as testing data and contains 4,898,430 records each of which is labeled as either normal, or as an attack indicating one specific attack type. The second is unlabeled and contains 311,029 records, which is provided as testing data.^{2}

What a huge dataset! In fact, the Sammon Mapping we had tried in the iris dataset above wouldn’t work any more. Therefore, many approaches have tried a many data reduction techniques.

Kuchimanchi et al. [4] used the principal component analysis, and suggested the first most important 19 attributes.^{3} However, still huge, is it not?.

Nevertheless, we have had a lot of successes reported so far. Let us name a few. Joshi et al. [5] wrote, “Exploiting only 5 out of 41 attributes^{4} the best results was 79% accuracy in correctly detecting attacks, and 21% is accounted for false positive^{5} rate plus false negative^{6} rate.”

Pan et al. [6] asserted, “Our model based on neural network and expert system finally achieves the average detection rate of 93.28% and false positive rate of 0.2% which were obtained for five typical types of attacks (neptune, portsweep, satan, buffer overflow, and guess passwd).” Pan et al. exploited three-layer (70-14-6) feed-forward neural network with a Sigmoid transfer function trained with back propagation using scaled conjugate gradient decent. Let’s see the result more in detail. Authors wrote, “The test result indicates that in total 99.6% of the normal examples were recognized correctly. For neptune, satan, portsweep, we can obtain the average detect rate of 96.6% and the false positive rate of 0.049%. Because all buffer overflow and guess passwd attacks fail to be classified by this back propagation neural network, we only obtain the average detect rate of 64.9% and the false positive rate of 26.7% for all the five kinds of attacks. However, these two kinds of attacks can be accurately detected by rule-based detector. Expert system can detect the R2L and U2R intrusions more accurately than neural network.” And then concluded, “The model improves the detection rate for all intrusions.”

Wow! We, however, would be rather more interested in why this neural network failed to be classified for buffer overflow and guess passwd attacks, rather than the performance improvement by using rule-based detector.

2 The labeled training dataset includes 972,780 Normals, 41,102 Probes, 3,883,370 DoSs, 52 U2Rs, and 1,126 R2Ls.

3 They are src bytes, dst bytes, duration, is guest login, is host login, srv diff host rate, diff srv rate, service, flag, protocol type, num root, hot, num compromised, dst host same srv rate, dst host count, rerror rate, srv count, and dst host srv diff host rate.

4 I.e., src bytes, dst bytes, duration, is host login, and is guest login. 5 I.e., recognizing attack as normal. 6 I.e., recognizing normal as attack.

Pan et al. reported another result in the different article [7]. With the same architecture of neural network and with the same target of five attacks, but using C4.5 instead of expert system, they reported that correctly predicted (normal, neptune, satan, portsweep, buffer overflow, guess passwd) was (73.3%, 99.2%, 94.6%, 94.2%, 0.0%, 0.0%), respectively. And conclude the back propagation network can’t detect the buffer overflow and guess passwd attacks. This sounds more realistic assertion.

Thus far, such more careful conclusions appear in the recent literatures. For example Stibor et al. [8] wrote, “The real-valued negative selection with variable-sized detectors has poor classification performance on the highdimensional KDD dataset.”

When this detector was proposed by Ji et al. [9], the result of applying it to the iris dataset was that the correct detection rate of (setosa, versicolor, virginica) was (99.98%, 85.95%, 81.87%) respectively, while false alarm rates were all zero!

As yet another example of implicit report of failure, Dam et al. [10] claimed, “While by the traditional evolutionary classifier system, each of the detection rate for (normal, DoS, Probe, U2R, and R2L) was (57.2%, 0.0%, 0.0%, 0.2%, and 63.7%),” and went on to write as the result of their improvement of the classifier system, they proudly claimed, “Each of the detection rate of (normal, DoS, Probe, U2R, R2L) was (95.7%, 49.1%, 93.0%, 8.5%, 3.9%).”

We don’t think the result is very satisfactory. But again we are rather interested in why detection rate is so low for U2R and R2L.

Finnaly, it would be interesting to take a look what Sabhnani et al. [11] reported. See Table 1 to have a bird’s eye view of those results above.

Table 1. Detection rate for 4 attack types each with 9 different machine learning technique. From Sabhnani et al. [11]

PROBE DoS U2R R2L
Multilayer Perceptron  88.7  97.2 13.2 5.6
Gaussian Classifier  90.2  82.4 22.8 9.6
K-mean Clustering  87.6  97.3 29.8 6.4
Nearest Cluster Algorithm  88.8  97.1 2.2  3.4
Radial Basis Function  93.2  73.0 6.1  5.9
Leader Algorithm  83.8  97.2 6.6  1.0
Hypersphere Algorithm  84.8  97.2 8.3  1.0
Fuzzy Art Map  77.2  97.0 6.1  3.7
C4.5 Decision Tree  80.8  97.0 1.8  4.6

Note that KDD cup 1999 winner’s Detection rate for (PROBE, DoS, U2R, and R2L) was (83.3%, 97.1%, 13.2%, 8.4%).

Our Conjecture Here, we, conjecture that those sometimes observed poor results is because some of the attack data are like needles in a haystack of huge amount of normal data. If we could fully visualize such large size of normal and a few samples picked up from abnormal samples, the latter might look like a needle in a hay stack of the former, like in Figure 3. Though we are not yet ready, we plan to show it elsewhere.

Fig. 3. We conjecture that some attack data are like needles in a hay of normal data.

To summerize the problem here, we ask the readers,

Problem 2 (A Challenge in KDD-cup-99 dataset) Design an intrusion detection system which has 41 inputs corresponding to attributes from KDD-cup-1999 dataset, and 5 YES/NO outputs indicating that the input is either of normal, PROBE, DoS, U2R, or R2L. The question is, “Such design is possible or not?”

Also see Figure 4 below.

Fig. 4. A simple architecture of neural network we desire to classify KDD cup 99 dataset.

III. Experiments

Flick remembered the legend of the Jackdaw of Rheims, the bird that stole the bishop’s ring. The monks couldn’t figure out who had taken it, so the bishop cursed the unknown thief. Next thing they knew, the jackdaw appeared all bedraggled, and they realized he was suffering from the effects of curse, and must be the culprit. Sure enough they found the ring in his nest. – “Jackdaws” by Ken Follett.

Assuming our conjecture that real attack sample is like a needle in a haystack of normal samples, we now look at how easy or difficult to find it? Let’s start with a random search. Note that some proposed algorithms which were reported as success actually were not good as asserted, and sometimes found to be worse than a random search.

A. Random Fall of Parachutists Algorithm 1 (Random Fall) (1) Create a p-bit octal PIN at random. (2) Create randomly 3p-bit of binary string. (3) Translate the string into p-bit octal code.

(4) Check if the translated code matches the PIN. (5) If matches end the run. Otherwise go back to (2).

Let us allow to use a metaphor here. We now assume only one needle in a pastoral, and parachutists fall from the airplane to the pastoral one by one, then how would it be likely for a parachutist to fall just on the needle. This might be taken as a random search, and will be our criterion of comparison hereafter.

Note that one parachutist is represented our genotypes of a 3p-digit binary strings. Let’s take an example of p = 4:

((100)(111)(000)(010))

maps into its phenotype (4 7 0 2).

First, one p-bit octal PIN is created which we assume no one knows a priori. With p being increasing from 2, we count the number of randomly created genotypes until its phenotype strictly matches to the hidden PIN. The average number, during 1024 runs, of parachutists needed to firstly find the needle for p = 2, 3, 4, 5, 6, 7 were, respectively,

(66, 512, 3951, 32154, 254673, 2058527).  (1)

See Figure 5.

B. What if Parachutists are Allowed to Walk after Fall? Algorithm 2 (Random Fall) (1) Create a p-bit octal PIN at random. (2) Create randomly 3p-bit of binary string. (3) Translate the string into p-bit octal code.

(4) Check if the translated code matches the PIN. (5) If matches end the run. Otherwise give a mutation by flipping a bit chosen at random with a probability of 1/3p until the translation matches the PIN or number of steps exceeds 1000. (6) If still hasn’t been matched, then repeat from (2).

What will happen if the fallen parachutist allows to explore, say, 1000 random steps, around the falling spot? This might remind readers of the seminal experiment once made by Hinton & Nowlan [1] who reffered it to “lifetime learning — Baldwin Effect” though our parachutist in this paper ends her life without creating a next generation. The results, again over the average of 1024 runs, for p = 4, 5, 6, 7, 8 were, respectively,

(5, 36, 308, 2436, 23087).  (2)

The results are also shown in Figure 5 with the result of our random parachutists in the previous subsection. In both cases, we can see complexity is an exponential order. But look! How impressive an exploration-after-fall improves the performance!

As you have probably noticed already, however, it’s not fair just to compare the number of parachutists. The total number of points searched by those walking parachutists are plotted as a function of p in Figure 6. We can see that the result is rather worse than our random parachutists.

Fig. 5. (a) Number of random creations of candidate until the PIN is matched (filled circles), and (b) The number when created candidate is allowed random walks of 1000 steps (empty circles). Both are the average of 1024 runs.

Fig. 6. Average number of points searched by all the randomly created candidates who are allowed further random walks of 1000 steps until the needle is found. Average are taken among 1024 runs.

C. Neutral Mutation

Algorithm 3 (Walk by Neutral Mutations) (1) Create a PIN at random. (2) Create one genotype at random.

(3) Try point-wise mutation on the genotype so that the result maps into the same phenotype as the one before mutation. (4) Assess each single-mutation-neighbor of the new genotype to determine whether any new phenotypes were discovered. (5) Step 3 to 4 are repeated untill the phenotype matches the PIN, or untill a pre-fixed number of steps is reached.

This is a paraphrase of the algorithm proposed by Shipman et al. [12] who called the step 3 a neutral mutation (mutation in step 4 is a standard one). Its efficiency was studied in their paper by applying it to a random Boolean network and telecommunication networks. But why not more simple example can be explored, if it is to work universally?

To apply this in our problem of searching for the needle, that is, octal p-bit PIN, we design our genotype as 15p-bit binary string such that the number-of-1 (mod 8) in each of 15-digit blocks in the string maps into one bit of the corresponding octal code.^{7} For example

((100011000000100)(111111111111111)(111110001101010))

maps into (4 7 1).

The average number, during 1024 runs, of parachutists needed to firstly finds the needle for p = 2, 3, 4, 5, 6 were, respectively,

(71728, 583593, 4930624, 36592634, 314817878). (3)

Much worse than a random search.

D. Does Neutral Mutation on Intron Enhance Efficiency

of Search? Algorithm 4 (Neutral Network) (1) Create a PIN at random. (2) Create randomly an initial individual which is considered to be the winner to the next generation. (3) Carry out point-wise mutation on the winning parent to generate 4 offspring; (4) Construct a new generation with the winner and its offspring; (5) Select a winner from the current population using the following rules: (i) If any offspring has a better fitness than the parent, the one with highest fitness becomes the winner. (ii) If fitness of all offspring have the same fitness as the parents, one offspring is randomly selected and if the parent-offspring pair has a Hamming distance within the permitted range the offspring becomes the winner, otherwise, the parent remains as the winner. (5) Back to step 2 unless the maximum number of generations reaches or a solution is found.

We had an interesting discussion between Yu & Miller’s paper “Finding Needles in Haystacks is Not Hard with Neutrality” (2002) [13] vs. Collin’s “Finding Needles in Haystacks is Harder with Neutrality” (2005). [14]

What Yu and Miller attacked as a type of a needle in a haystack problem was to make a Genetic Algorithm construct a even-n-parity logic circuit by employing only XOR and EQ, not AND and OR and so on, which shows a peculiar fitness landscape. The even-n-parity logic has n-bit binary inputs and if and only if the number of 1 is even, it returns 1 and otherwise returns 0. Hence, we can evaluate the fitness value of any one candidate of the solution, by giving all the possible configurations of 0 and 1 and counting how many correct outputs. Thus, from a combinatorial

7 A brief consideration might give us 7-bit binary for each octal is enough, however, we implement in this way so that each octal from 0 to 7 are created uniformly at random.

point of view we have 2^{n} cases of fitness values. In reality, however, we have, only three different values. That is, 2^{n}, 2^{(n−1)} and 0, namely, the output is all correct, half correct, or no correct at all. For example, candidates of even-3-parity constructed only by XOR and EQ returns either 8, 4 or 0 correct outputs for the eight possible inputs (000), (001), (010), (011), ..., (111).

Though Yu & Miller claimed in the case of random creation of 4,000,000 candidates of even-12-parity, the solution (fitness 4096) was never emerged, while even-10-parity 100,000 random creations of candidate yielded 540 solutions (fitness 1024). On the other hand, when neutral mutation is applied, to the candidates of even-12-parity, the 48 out of 100 runs reached solution(s) with each run being only within 10,000 iterations.

Collins argued back concluding, “Reported success is due to a bias of the selection” [14]. In the other of Collin’s work [15], it was analytically shown that the number of possible candidate of even-12-parity is 1.315 × 10^{139} in which number of real solutions is 2.568 × 10^{132}, claiming “Yu & Miller’s result is, therefore, worse than a possible random search.”

Again what we want to emphasize is, if the assertion is universally true, it would work in yet more principally simple examples. Before going to proceed, let’s see what is intron that Yu & Miller assumed to play an important role in their evolution. For example, take a look at a genotype representing a even-3-parity,

((EQ, A, B)(EQ, C, D)(XOR, 1, E)(EQ, F, G)(EQ, 3, H))

where each gene which corresponds to one unit constructs triples: with the 1st being which logic to be used (EQ or XOR); and with the 2nd and 3rd being connections to either one of the inputs or the outputs of a previous unit. Note that the 2nd and 4th genes in the above example do not contribute to construct the phenotype since those two genes will not be connected to any other unit, and hence are called intron as a biological metophore. Any mutation on an intron has no effect on phenotype, and as such, they are called neutral. The above genotype can be interpreted as the phenotype shown in Figure 6.

Fig. 7. An example of phenotype of even-3-parity constrcted only by EQ and XOR.

Now we try to apply this to our finding PIN problem. This time we use 4-digit binary, instead of 3-digit as above, to represent one octal numeral in the candidate of PIN. Then translation is into decimal instead of octal, and when the translated decimal is larger than seven we consider it an intron. For example

((0001)(1100)(0101)(0010)(0111))

is translated into (1, 5, 2, 7) since the second gene is translated into 12 and supposed to be an intron.

The average number, during 1024 runs, of parachutists needed to firstly find the needle for p = 2, 3, 4, 5 were, respectively,

(65, 488, 3751, 33710).  (4)

Alas, if we compare it with (1) we will see that the result is almost the same as our random parachutists.

Possible Conclusion at this Moment Here We have no such algorithm that can more efficiently look for a needle in a haystack than a random search, if not the scale is small enough. No way to find needles in a pastoral.

IV. Discussion

As Laskov et al. [16] claimed in their paper, “Labels can be extremely difficult or impossible to obtain. Analysis of network traffic or audit logs is very time-consuming and usually only a small portion of the available data can be labeled. Furthermore, in certain cases, for example at a packet level, it may be impossible to unambiguously assign a label to a data instance.” Authors further writes, “In a real application, one can never be sure that a set of available labeled examples covers all possible attacks. If a new attack appears, examples of it may not have been seen in training data.” Then our next question is,

Problem 3 (Attacks by Mutants) Pick up a set of n normal samples from KDD cup 1999 dataset. All of those n samples are given a point wise mutation and taken as attack data. Train your intrusion detection system using half of the normal samples and half of the attack samples (the number of both is n/2), then test the system using the remaining samples. Can the system detect those mutants as intrusion?

Moreover, though we have not remarked so far, there remains further difficult issue, that is, “How the system can learn only from normal data to detect abnormal?” Because we usually have enormous amount of normal data but we have no information about coming attacks untill it’s too late.

Gomez et al. [17] claimed, “A new technique for generating a set of fuzzy rules that can characterize the non-self space (abnormal) using only self (normal) samples.” Their experiment employed 10% dataset, also given as a part of KDD cup 1999 dataset, which reduced the number of records into 10% of the original ones. Further, they removed categorical attributes and normalized these remaining 33 numerical attributes between 0 and 1 using the maximum and minimum values found. Then 80% of the normal samples were picked up at random for training while the remaining 20% along with the same number of abnormal samples were used for testing. Gomez et al. designed the detector with what they called a immuno-fuzzy approach and system they call evolving fuzzy rules detectors claiming, “It detects records labeled attack with the detection rate 98.30% and false alarm rate 2.0%.” Really satisfactory, if its really true.

The report didn’t mention about the categories of attacks, which implies the reported success is an average over all attack types. It seems to be too good if we consider the results of other not-so-happy reports mentioned above. More important thing to notice here is the system learned “only with normal data” to establish this success? It would be splendid if it was really true, but we are fishy more or less.

This issue is something like we require a wine-taster to recognize bootleg champagne by only providing him/her real champagne to learn. Though this training-only-with-normal is our ultimate goal, but not so simple to be realized.

“Artificial Immune System detects Computer Virus Invasion!” How fantastic it sounds for innocent people. We wish it would work. But we are afraid it might be just a fantasy. So we need a placebo experiment.

Problem 4 (A Placebo Experiment) (1) Prepare two sub-dataset from KDD cup 1999 dataset. One is made up of normal samples and called D_{normal}. The other is made up of attack samples and called D_{attack}. (2) Train your intrusion detection system with those two samples. (Here let’s put the training-with-only-normal issue on the shelf.)

(3) Further create an atack dataset, D_{random}, at random.

(4) Then test with both D_{attack} and D_{random}, avoiding any a priori prediction.

V. Concluding Remarks

KDD Cup 1999 intrusion detection dataset has approximately 5 million records in the labeled dataset, of which 75.6111% are normal, while 0.0048% are U2R, for example. A likely interpretation is the U2R attack patterns are like needles in hay of normal patterns, if we are not very lucky. Considering we have not had so satisfactoly results to detect U2R attacks, we do not seem to be so lucky.

In addition, considering a hacker is a person who is extremly good at finding a pattern which is very close to the normal traffic. The point that might be located by a hacker is not a randomly located point.

It is said that we have two kind of intrusion detection. One is called misuse detection which recognizes known attack patterns. The other is called anomaly detection which detects no-normal unknown patterns. We are not interested in the former. All we want is to detect unknown outliers. And an outlier usually lies not far from normal but very close to it. We could not be so optimistic.

Nevertheless, this article is not to negate the possibility, but we hope this is a challenge to intrusion detection community to emerge real innovative ideas.

References

[1] G. E. Hinton, and S. J. Nowlan (1987) “How Learning can Guide Evolution.” Complex Systems, 1, pp. 495– 502.

[2] G. Castellano, and A. M. Fanelli (2000) “Fuzzy Inference and Rule Extraction using a Neural Network.” Neural Network World Journal Vol. 3, pp. 361– 371.

[3] S. J. Stolfo, F. Wei, W Lee, A. Prodromidis, and P. K. Chan (1999) “KDD Cup knowledge discovery and data mining competition.”

http://kdd.ics.uci.edu/databases/kddcup99/kddcup99.html

[4] G. K. Kuchimanchi, V. V. Phoha, K. S. Balagani, and S. R. Gaddam (2004) “Dimension Reduction Using Feature Extraction Methods for Real-time Misuse Detection Systems.” Proceedings of Workshop on Information Assurance and Security, pp. 1555–1563.

[5] S. S. Joshi, and V. V. Phoha (2005) “Investigating Hidden Markov Models Capabilities in Anomaly Detection.” Proceedings of the 43rd ACM Southeast Conference, Vol. 1, pp. 99–103.

[6] Z. Pan, H. Lian, G. Hu, and G. Ni (2005) “An Integrated Model of Intrusion Detection Based on Neural Network and Expert System.” Proceedings of IEEE International Conference on Tools with Artificial Intelligence, pp. 671–672.

[7] Z. Pan, S. Chen, G. Hu, and D. Zhangn (2003) “Hybrid Neural Network and C4.5 for Misuse Detection.” Proceedings of International Conference on Machine Learning and Cybernetics, pp. 2463–2467.

[8] T. Stibor, J. Timmis, and C. Eckert (2005) “A comparative Study of Real-valued Negative Selection to Statistical Anomaly Detection Techniques.” Proceedings of International Conference on Artificial Immune Systems, Lecture Notes in Computer Science, vol. 3627. Springer, pp. 262–275.

[9] Z. Ji, and D. Dasgupta (2004) “Real-valued Negative Selection Algorithm with Variable-sized Detectors.” Proceedings of Genetic and Evolutionary Computation Conference, Lecture Notes in Computer Science Vol. 3102, Springer pp. 287–298.

[10] H. H. Dam, K. Shafi, and H. A. Abbass “Can Evolutionary Computation Handle Large Dataset?” Technical Report: The Artificial Life and Adaptive Robotics Laboratory TR-ALAR-200507011.

[11] M. Sabhnani, and G. Serpen (2003) “Application of Machine Learning Algorithms to KDD Intrusion Detection Dataset within Misuse Detection Context.” Proceedings of the International Conference on Machine Learning: Models, Technologies and Applications, pp. 209–215.

[12] R. Shipman, M. Shackleton, and I. Harvey (2000) “The use of neutral genotype-phenotype mappings for improved evolutionary search.” BT Technology Journal Vol. 18 No. 4, pp. 103–111.

[13] Tina Yu and J. Miller (2002) “Finding Needles in Haystacks is Not Hard with Neutrality.” Proceedings of EuroGP 2002, Lecture Notes in Computer Science Vol. 2278, Springer, pp. 13–25.

[14] M. Collins (2005) “Finding Needles in Haystacks is Harder with Neutrality.” Proceedings of Genetic and Evolutionary Computation Conference, pp. 1613– 1618.

[15] M. Collins (2004) “Counting Solutions in Reduced Boolean Parity.” CD-ROM of Workshop Proceedings in Genetic and Evolutionary Computation Conference,

[16] P. Laskov et al. (2005) ”Learning Intrusion Detection: Supervised or Unsupervised?” Proceedings of International Conference on Image Analysis and Processing Lecture Notes in Computer Science Vol. 3617, Springer, pp. 50–57.

[17] J. Gomez, F. Gonzalez, and D. Dasgupta (2003) ”An Immuno-Fuzzy Approach to Anomaly Detection.” Proceedings of the 12th IEEE International Conference on Fuzzy Systems, Vol. 2, pp. 1219-1224.