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A Novel Similarity Measure for Intrusion Detection using Gaussian Function
Authors:
Gunupudi Rajesh Kumar,
N Mangathayaru,
G Narsimha
Abstract:
In this paper the major objective is to design and analyze the suitability of Gaussian similarity measure for intrusion detection. The objective is to use this as a distance measure to find the distance between any two data samples of training set such as DARPA Data Set, KDD Data Set. This major objective is to use this measure as a distance metric when applying k- means algorithm. The novelty of…
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In this paper the major objective is to design and analyze the suitability of Gaussian similarity measure for intrusion detection. The objective is to use this as a distance measure to find the distance between any two data samples of training set such as DARPA Data Set, KDD Data Set. This major objective is to use this measure as a distance metric when applying k- means algorithm. The novelty of this approach is making use of the proposed distance function as part of k-means algorithm so as to obtain disjoint clusters. This is followed by a case study, which demonstrates the process of Intrusion Detection. The proposed similarity has fixed upper and lower bounds. The proposed similarity measure satisfies all properties of a typical similarity measure.
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Submitted 26 April, 2016;
originally announced April 2016.
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Exact Common Information
Authors:
Gowtham Ramani Kumar,
Cheuk Ting Li,
Abbas El Gamal
Abstract:
This paper introduces the notion of exact common information, which is the minimum description length of the common randomness needed for the exact distributed generation of two correlated random variables $(X,Y)$. We introduce the quantity $G(X;Y)=\min_{X\to W \to Y} H(W)$ as a natural bound on the exact common information and study its properties and computation. We then introduce the exact comm…
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This paper introduces the notion of exact common information, which is the minimum description length of the common randomness needed for the exact distributed generation of two correlated random variables $(X,Y)$. We introduce the quantity $G(X;Y)=\min_{X\to W \to Y} H(W)$ as a natural bound on the exact common information and study its properties and computation. We then introduce the exact common information rate, which is the minimum description rate of the common randomness for the exact generation of a 2-DMS $(X,Y)$. We give a multiletter characterization for it as the limit $\bar{G}(X;Y)=\lim_{n\to \infty}(1/n)G(X^n;Y^n)$. While in general $\bar{G}(X;Y)$ is greater than or equal to the Wyner common information, we show that they are equal for the Symmetric Binary Erasure Source. We do not know, however, if the exact common information rate has a single letter characterization in general.
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Submitted 1 February, 2014;
originally announced February 2014.
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Which Boolean Functions are Most Informative?
Authors:
Gowtham R. Kumar,
Thomas A. Courtade
Abstract:
We introduce a simply stated conjecture regarding the maximum mutual information a Boolean function can reveal about noisy inputs. Specifically, let $X^n$ be i.i.d. Bernoulli(1/2), and let $Y^n$ be the result of passing $X^n$ through a memoryless binary symmetric channel with crossover probability $α$. For any Boolean function $b:\{0,1\}^n\rightarrow \{0,1\}$, we conjecture that…
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We introduce a simply stated conjecture regarding the maximum mutual information a Boolean function can reveal about noisy inputs. Specifically, let $X^n$ be i.i.d. Bernoulli(1/2), and let $Y^n$ be the result of passing $X^n$ through a memoryless binary symmetric channel with crossover probability $α$. For any Boolean function $b:\{0,1\}^n\rightarrow \{0,1\}$, we conjecture that $I(b(X^n);Y^n)\leq 1-H(α)$. While the conjecture remains open, we provide substantial evidence supporting its validity.
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Submitted 15 July, 2013; v1 submitted 11 February, 2013;
originally announced February 2013.