Krishnamoorthy Sivakumar

Random-data perturbation techniques and privacy-preserving data mining

Privacy is becoming an increasingly important issue in many data-mining applications. This has triggered the development of many privacy-preserving data-mining techniques. A large fraction of them use randomized data-distortion techniques to mask the data for preserving the privacy of sensitive data. This methodology attempts to hide the sensitive data by randomly modifying the data values often using additive noise. This paper questions the utility of the random-value distortion technique in privacy preservation. The paper first notes that random matrices have predictable structures in the spectral domain and then it develops a random matrix-based spectral-filtering technique to retrieve original data from the dataset distorted by adding random values. The proposed method works by comparing the spectrum generated from the observed data with that of random matrices. This paper presents the theoretical foundation and extensive experimental results to demonstrate that, in many cases, random-data distortion preserves very little data privacy. The analytical framework presented in this paper also points out several possible avenues for the development of new privacy-preserving data-mining techniques. Examples include algorithms that explicitly guard against privacy breaches through linear transformations, exploiting multiplicative and colored noise for preserving privacy in data mining applications.

Distributed clustering using collective principal component analysis

Abstract. This paper considers distributed clustering of high-dimensional heterogeneous data using a distributed principal component analysis (PCA) technique called the collective PCA. It presents the collective PCA technique, which can be used independent of the clustering application. It shows a way to integrate the Collective PCA with a given off-the-shelf clustering algorithm in order to develop a distributed clustering technique. It also presents experimental results using different test data sets including an application for web mining.

Morphological operators for image sequences

This paper presents a unifying approach to the problem of morphologically processing image sequences (or, equivalently, vector-valued images) by means of lattice theory, thus providing a mathematical foundation for vector morphology. Lattice theory is an abstract algebraic tool that has been extensively used as a theoretical framework for scalar morphology (i.e., mathematical morphology applied on single images). Two approaches to vector morphology are discussed. According to the first approach, vector morphology is viewed as a natural extension of the well-known scalar morphology. This approach formalizes and generalizes Wilsons matrix morphology and shows that the latter is a direct consequence of marginal vector ordering. The derivation of the second approach is more delicate and requires careful treatment. This approach is a direct consequence of a vector transformation followed by marginal ordering. When the vector transformation is the identity transformation, the two approaches are equivalent. A number of examples demonstrate the applicability of the proposed theory in a number of image processing and analysis problems.

Collective Mining of Bayesian Networks from Distributed Heterogeneous Data

We present a collective approach to learning a Bayesian network from distributed heterogeneous data. In this approach, we first learn a local Bayesian network at each site using the local data. Then each site identifies the observations that are most likely to be evidence of coupling between local and non-local variables and transmits a subset of these observations to a central site. Another Bayesian network is learnt at the central site using the data transmitted from the local site. The local and central Bayesian networks are combined to obtain a collective Bayesian network, which models the entire data. Experimental results and theoretical justification that demonstrate the feasibility of our approach are presented.

Row-Column Soft-Decision Feedback Algorithm for Two-Dimensional Intersymbol Interference

We present a novel iterative row-column soft decision feedback algorithm (IRCSDFA) for detection of binary images corrupted by 2-D intersymbol interference and additive white Gaussian noise. The algorithm exchanges weighted soft information between row and column maximum a posteriori (MAP) detectors. Each MAP detector exploits soft-decision feedback from previously processed rows or columns. The new algorithm gains about 0.3 dB over the previously best published results for the 2times2 averaging mask. For a non-separable 3times3 mask, the IRCSDFA gains 0.8 dB over a previous soft-input/soft-output iterative algorithm which decomposes the 2-D convolution into 1-D row and column operations.

Morphologically constrained GRFs: applications to texture synthesis and analysis

A new class of Gibbs random fields (GRFs) is proposed capable of modeling geometrical constraints in images by means of mathematical morphology. The proposed approach, known as morphologically constrained GRFs, models images by means of their size density. Since the size density is a multiresolution statistical summary, morphologically constrained GRFs explicitly incorporate multiresolution information into image modeling. Important properties are studied and their implication to texture synthesis and analysis is discussed. Statistical inference can be easily implemented by means of mathematical morphology. This allows the design of a computationally simple morphological Bayes classifier which produces excellent results in classifying natural textures.

Discrete morphological size distributions and densities: estimation techniques and applications

Morphological size distributions and densities are frequently used as descriptors of granularity or texture within an image. They have been successfully employed in a number of image processing and analysis tasks, including shape analysis, multiscale shape representation, texture classification, and noise filtering. In most cases however it is not possible to analytically compute these quantities. In this paper, we study the problem of estimating the (discrete) morphological size distribution and density of random images, by means of empirical as well as Monte Carlo estimators. Theoretical and experimental results demonstrate clear superiority of the Monte Carlo estimation approach. Examples illustrate the usefulness of the proposed estimators in traditional image processing and analysis problems.

Privacy-sensitive Bayesian network parameter learning

This paper considers the problem of learning the parameters of a Bayesian network, assuming the structure of the network is given, from a privacy-sensitive dataset that is distributed between multiple parties. For a binary-valued dataset, we show that the count information required to estimate the conditional probabilities in a Bayesian network can be obtained as a solution to a set of linear equations involving some inner product between the relevant different feature vectors. We consider a random projection-based method that was proposed elsewhere to securely compute the inner product (with a modified implementation of that method).

Distributed Web mining using Bayesian networks from multiple data streams

We present a collective approach to mining Bayesian networks from distributed heterogenous Web-log data streams. In this approach we first learn a local Bayesian network at each site using the local data. Then each site identifies the observations that are most likely to be evidence of coupling between local and non-local variables and transmits a subset of these observations to a central site. Another Bayesian network is learnt at the central site using the data transmitted from the local site. The local and central Bayesian networks are combined to obtain a collective Bayesian network that models the entire data. We applied this technique to mining multiple data streams, where data centralization is difficult because of large response time and scalability issues. Experimental results and theoretical justification that demonstrate the feasibility of our approach are presented.

Collective Principal Component Analysis from Distributed, Heterogeneous Data

Principal component analysis (PCA) is a statistical technique to identify the dependency structure of multivariate stochastic observations. PCA is frequently used in data mining applications. This paper considers PCA in the context of the emerging network-based computing environments. It offers a technique to perform PCA from distributed and heterogeneous data sets with relatively small communication overhead. The technique is evaluated against different data sets, including a data set for a web mining application. This approach is likely to facilitate the development of distributed clustering, associative link analysis, and other heterogeneous data mining applications that frequently use PCA.