A Survey of Multiplicative Perturbation for Privacy-Preserving Data Mining
---
paper_title: A random rotation perturbation approach to privacy preserving data classification

paper_content:

This paper presents a random rotation perturbation approach for privacy preserving data classification. Concretely, we identify the importance of classificationspecific information with respect to the loss of information factor, and present a random rotation perturbation framework for privacy preserving data classification. Our approach has two unique characteristics. First, we identify that many classification models utilize the geometric properties of datasets, which can be preserved by geometric rotation. We prove that the three types of classifiers will deliver the same performance over the rotation perturbed dataset as over the original dataset. Second, we propose a multi-column privacy model to address the problems of evaluating privacy quality for multidimensional perturbation. With this metric, we develop a local optimal algorithm to find the good rotation perturbation in terms of privacy guarantee. We also analyze both naive estimation and ICA-based reconstruction attacks with the privacy model. Our initial experiments show that the random rotation approach can provide high privacy guarantee while maintaining zero-loss of accuracy for the dis-
---
paper_title: Privacy-preserving data mining

paper_content:

A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models without access to precise information in individual data records? We consider the concrete case of building a decision-tree classifier from training data in which the values of individual records have been perturbed. The resulting data records look very different from the original records and the distribution of data values is also very different from the original distribution. While it is not possible to accurately estimate original values in individual data records, we propose a novel reconstruction procedure to accurately estimate the distribution of original data values. By using these reconstructed distributions, we are able to build classifiers whose accuracy is comparable to the accuracy of classifiers built with the original data.
---
paper_title: A condensation approach to privacy preserving data mining

paper_content:

In recent years, privacy preserving data mining has become an important problem because of the large amount of personal data which is tracked by many business applications. In many cases, users are unwilling to provide personal information unless the privacy of sensitive information is guaranteed. In this paper, we propose a new framework for privacy preserving data mining of multi-dimensional data. Previous work for privacy preserving data mining uses a perturbation approach which reconstructs data distributions in order to perform the mining. Such an approach treats each dimension independently and therefore ignores the correlations between the different dimensions. In addition, it requires the development of a new distribution based algorithm for each data mining problem, since it does not use the multi-dimensional records, but uses aggregate distributions of the data as input. This leads to a fundamental re-design of data mining algorithms. In this paper, we will develop a new and flexible approach for privacy preserving data mining which does not require new problem-specific algorithms, since it maps the original data set into a new anonymized data set. This anonymized data closely matches the characteristics of the original data including the correlations among the different dimensions. We present empirical results illustrating the effectiveness of the method.
---
paper_title: Random projection-based multiplicative data perturbation for privacy preserving distributed data mining

paper_content:

This paper explores the possibility of using multiplicative random projection matrices for privacy preserving distributed data mining. It specifically considers the problem of computing statistical aggregates like the inner product matrix, correlation coefficient matrix, and Euclidean distance matrix from distributed privacy sensitive data possibly owned by multiple parties. This class of problems is directly related to many other data-mining problems such as clustering, principal component analysis, and classification. This paper makes primary contributions on two different grounds. First, it explores independent component analysis as a possible tool for breaching privacy in deterministic multiplicative perturbation-based models such as random orthogonal transformation and random rotation. Then, it proposes an approximate random projection-based technique to improve the level of privacy protection while still preserving certain statistical characteristics of the data. The paper presents extensive theoretical analysis and experimental results. Experiments demonstrate that the proposed technique is effective and can be successfully used for different types of privacy-preserving data mining applications.
---
paper_title: Limiting privacy breaches in privacy preserving data mining

paper_content:

There has been increasing interest in the problem of building accurate data mining models over aggregate data, while protecting privacy at the level of individual records. One approach for this problem is to randomize the values in individual records, and only disclose the randomized values. The model is then built over the randomized data, after first compensating for the randomization (at the aggregate level). This approach is potentially vulnerable to privacy breaches: based on the distribution of the data, one may be able to learn with high confidence that some of the randomized records satisfy a specified property, even though privacy is preserved on average.In this paper, we present a new formulation of privacy breaches, together with a methodology, "amplification", for limiting them. Unlike earlier approaches, amplification makes it is possible to guarantee limits on privacy breaches without any knowledge of the distribution of the original data. We instantiate this methodology for the problem of mining association rules, and modify the algorithm from [9] to limit privacy breaches without knowledge of the data distribution. Next, we address the problem that the amount of randomization required to avoid privacy breaches (when mining association rules) results in very long transactions. By using pseudorandom generators and carefully choosing seeds such that the desired items from the original transaction are present in the randomized transaction, we can send just the seed instead of the transaction, resulting in a dramatic drop in communication and storage cost. Finally, we define new information measures that take privacy breaches into account when quantifying the amount of privacy preserved by randomization.
---
paper_title: Privacy-preserving data mining

paper_content:

A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models without access to precise information in individual data records? We consider the concrete case of building a decision-tree classifier from training data in which the values of individual records have been perturbed. The resulting data records look very different from the original records and the distribution of data values is also very different from the original distribution. While it is not possible to accurately estimate original values in individual data records, we propose a novel reconstruction procedure to accurately estimate the distribution of original data values. By using these reconstructed distributions, we are able to build classifiers whose accuracy is comparable to the accuracy of classifiers built with the original data.
---
paper_title: k-Anonymity: A Model for Protecting Privacy

paper_content:

Consider a data holder, such as a hospital or a bank, that has a privately held collection of person-specific, field structured data. Suppose the data holder wants to share a version of the data with researchers. How can a data holder release a version of its private data with scientific guarantees that the individuals who are the subjects of the data cannot be re-identified while the data remain practically useful? The solution provided in this paper includes a formal protection model named k-anonymity and a set of accompanying policies for deployment. A release provides k-anonymity protection if the information for each person contained in the release cannot be distinguished from at least k-1 individuals whose information also appears in the release. This paper also examines re-identification attacks that can be realized on releases that adhere to k- anonymity unless accompanying policies are respected. The k-anonymity protection model is important because it forms the basis on which the real-world systems known as Datafly, µ-Argus and k-Similar provide guarantees of privacy protection.
---
paper_title: On the privacy preserving properties of random data perturbation techniques

paper_content:

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. We question the utility of the random value distortion technique in privacy preservation. We note that random objects (particularly random matrices) have "predictable" structures in the spectral domain and it develops a random matrix-based spectral filtering technique to retrieve original data from the dataset distorted by adding random values. We present the theoretical foundation of this filtering method and extensive experimental results to demonstrate that in many cases random data distortion preserve very little data privacy. We also point out possible avenues for the development of new privacy-preserving data mining techniques like exploiting multiplicative and colored noise for preserving privacy in data mining applications.
---
paper_title: A random rotation perturbation approach to privacy preserving data classification

paper_content:

This paper presents a random rotation perturbation approach for privacy preserving data classification. Concretely, we identify the importance of classificationspecific information with respect to the loss of information factor, and present a random rotation perturbation framework for privacy preserving data classification. Our approach has two unique characteristics. First, we identify that many classification models utilize the geometric properties of datasets, which can be preserved by geometric rotation. We prove that the three types of classifiers will deliver the same performance over the rotation perturbed dataset as over the original dataset. Second, we propose a multi-column privacy model to address the problems of evaluating privacy quality for multidimensional perturbation. With this metric, we develop a local optimal algorithm to find the good rotation perturbation in terms of privacy guarantee. We also analyze both naive estimation and ICA-based reconstruction attacks with the privacy model. Our initial experiments show that the random rotation approach can provide high privacy guarantee while maintaining zero-loss of accuracy for the dis-
---
paper_title: The Efficient Generation of Random Orthogonal Matrices with an Application to Condition Estimators

paper_content:

This paper presents a method for generating pseudo-random orthogonal matrices from the Haar distribution for the group of orthogonal matrices. The random matrices are expressed as products of $n - 1$ Householder transformations, which can be computed in $O(n^2 )$ time. The technique is used in an empirical study of two methods for estimating the condition number of a matrix.
---
paper_title: Random projection-based multiplicative data perturbation for privacy preserving distributed data mining

paper_content:

This paper explores the possibility of using multiplicative random projection matrices for privacy preserving distributed data mining. It specifically considers the problem of computing statistical aggregates like the inner product matrix, correlation coefficient matrix, and Euclidean distance matrix from distributed privacy sensitive data possibly owned by multiple parties. This class of problems is directly related to many other data-mining problems such as clustering, principal component analysis, and classification. This paper makes primary contributions on two different grounds. First, it explores independent component analysis as a possible tool for breaching privacy in deterministic multiplicative perturbation-based models such as random orthogonal transformation and random rotation. Then, it proposes an approximate random projection-based technique to improve the level of privacy protection while still preserving certain statistical characteristics of the data. The paper presents extensive theoretical analysis and experimental results. Experiments demonstrate that the proposed technique is effective and can be successfully used for different types of privacy-preserving data mining applications.
---
paper_title: On Privacy-Preservation of Text and Sparse Binary Data with Sketches

paper_content:

In recent years, privacy preserving data mining has become very important because of the proliferation of large amounts of data on the internet. Many data sets are inherently high dimensional, which are challenging to different privacy preservation algorithms. However, some domains of such data sets also have some special properties which make the use of sketch based techniques particularly useful. In this paper, we present a new method for privacy preserving data mining of text and binary data with the use of a sketch based approach. The special properties of such data sets which are exploited are that of sparsity; according to this property, only a small percentage of the attributes have non-zero values. We formalize an anonymity model for the sketch based approach, and utilize it in order to construct sketch based privacy preserving representations of the original data. This representation allows accurate computation of a number of important data mining primitives such as the dot product. Therefore, it can be used for a variety of data mining algorithms such as clustering and classification. We illustrate the effectiveness of our approach on a number of real and synthetic data sets. We show that the accuracy of data mining algorithms is preserved by the transformation even in the presence of increasing data dimensionality.
---
paper_title: The space complexity of approximating the frequency moments

paper_content:

The frequency moments of a sequence containing mi elements of type i, for 1 i n, are the numbers Fk = P n=1 m k . We consider the space complexity of randomized algorithms that approximate the numbers Fk, when the elements of the sequence are given one by one and cannot be stored. Surprisingly, it turns out that the numbers F0;F1 and F2 can be approximated in logarithmic space, whereas the approximation of Fk for k 6 requires n (1) space. Applications to data bases are mentioned as well.
---
paper_title: On Privacy-Preservation of Text and Sparse Binary Data with Sketches

paper_content:

In recent years, privacy preserving data mining has become very important because of the proliferation of large amounts of data on the internet. Many data sets are inherently high dimensional, which are challenging to different privacy preservation algorithms. However, some domains of such data sets also have some special properties which make the use of sketch based techniques particularly useful. In this paper, we present a new method for privacy preserving data mining of text and binary data with the use of a sketch based approach. The special properties of such data sets which are exploited are that of sparsity; according to this property, only a small percentage of the attributes have non-zero values. We formalize an anonymity model for the sketch based approach, and utilize it in order to construct sketch based privacy preserving representations of the original data. This representation allows accurate computation of a number of important data mining primitives such as the dot product. Therefore, it can be used for a variety of data mining algorithms such as clustering and classification. We illustrate the effectiveness of our approach on a number of real and synthetic data sets. We show that the accuracy of data mining algorithms is preserved by the transformation even in the presence of increasing data dimensionality.
---
paper_title: Privacy-preserving data mining

paper_content:

A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models without access to precise information in individual data records? We consider the concrete case of building a decision-tree classifier from training data in which the values of individual records have been perturbed. The resulting data records look very different from the original records and the distribution of data values is also very different from the original distribution. While it is not possible to accurately estimate original values in individual data records, we propose a novel reconstruction procedure to accurately estimate the distribution of original data values. By using these reconstructed distributions, we are able to build classifiers whose accuracy is comparable to the accuracy of classifiers built with the original data.
---
paper_title: An Introduction to Support Vector Machines and Other Kernel-based Learning Methods

paper_content:

From the publisher: This is the first comprehensive introduction to Support Vector Machines (SVMs), a new generation learning system based on recent advances in statistical learning theory. SVMs deliver state-of-the-art performance in real-world applications such as text categorisation, hand-written character recognition, image classification, biosequences analysis, etc., and are now established as one of the standard tools for machine learning and data mining. Students will find the book both stimulating and accessible, while practitioners will be guided smoothly through the material required for a good grasp of the theory and its applications. The concepts are introduced gradually in accessible and self-contained stages, while the presentation is rigorous and thorough. Pointers to relevant literature and web sites containing software ensure that it forms an ideal starting point for further study. Equally, the book and its associated web site will guide practitioners to updated literature, new applications, and on-line software.
---
paper_title: An Efficient Approach to Clustering in Large Multimedia Databases with Noise

paper_content:

Several clustering algorithms can be applied to clustering in large multimedia databases. The effectiveness and efficiency of the existing algorithms, however, is somewhat limited, since clustering in multimedia databases requires clustering high-dimensional feature vectors and since multimedia databases often contain large amounts of noise. In this paper, we therefore introduce a new algorithm to clustering in large multimedia databases called DENCLUE (DENsity-based CLUstEring). The basic idea of our new approach is to model the overall point density analytically as the sum of influence functions of the data points. Clusters can then be identified by determining density-attractors and clusters of arbitrary shape can be easily described by a simple equation based on the overall density function. The advantages of our new approach are (1) it has a firm mathematical basis, (2) it has good clustering properties in data sets with large amounts of noise, (3) it allows a compact mathematical description of arbitrarily shaped clusters in high-dimensional data sets and (4) it is significantly faster than existing algorithms. To demonstrate the effectiveness and efficiency of DENCLUE, we perform a series of experiments on a number of different data sets from CAD and molecular biology. A comparison with DBSCAN shows the superiority of our new approach.
---
paper_title: OPTICS: ordering points to identify the clustering structure

paper_content:

Cluster analysis is a primary method for database mining. It is either used as a stand-alone tool to get insight into the distribution of a data set, e.g. to focus further analysis and data processing, or as a preprocessing step for other algorithms operating on the detected clusters. Almost all of the well-known clustering algorithms require input parameters which are hard to determine but have a significant influence on the clustering result. Furthermore, for many real-data sets there does not even exist a global parameter setting for which the result of the clustering algorithm describes the intrinsic clustering structure accurately. We introduce a new algorithm for the purpose of cluster analysis which does not produce a clustering of a data set explicitly; but instead creates an augmented ordering of the database representing its density-based clustering structure. This cluster-ordering contains information which is equivalent to the density-based clusterings corresponding to a broad range of parameter settings. It is a versatile basis for both automatic and interactive cluster analysis. We show how to automatically and efficiently extract not only 'traditional' clustering information (e.g. representative points, arbitrary shaped clusters), but also the intrinsic clustering structure. For medium sized data sets, the cluster-ordering can be represented graphically and for very large data sets, we introduce an appropriate visualization technique. Both are suitable for interactive exploration of the intrinsic clustering structure offering additional insights into the distribution and correlation of the data.
---
paper_title: A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise

paper_content:

Clustering algorithms are attractive for the task of class identification in spatial databases. However, the application to large spatial databases rises the following requirements for clustering algorithms: minimal requirements of domain knowledge to determine the input parameters, discovery of clusters with arbitrary shape and good efficiency on large databases. The well-known clustering algorithms offer no solution to the combination of these requirements. In this paper, we present the new clustering algorithm DBSCAN relying on a density-based notion of clusters which is designed to discover clusters of arbitrary shape. DBSCAN requires only one input parameter and supports the user in determining an appropriate value for it. We performed an experimental evaluation of the effectiveness and efficiency of DBSCAN using synthetic data and real data of the SEQUOIA 2000 benchmark. The results of our experiments demonstrate that (1) DBSCAN is significantly more effective in discovering clusters of arbitrary shape than the well-known algorithm CLAR-ANS, and that (2) DBSCAN outperforms CLARANS by a factor of more than 100 in terms of efficiency.
---
paper_title: Data clustering: a review

paper_content:

Clustering is the unsupervised classification of patterns (observations, data items, or feature vectors) into groups (clusters). The clustering problem has been addressed in many contexts and by researchers in many disciplines; this reflects its broad appeal and usefulness as one of the steps in exploratory data analysis. However, clustering is a difficult problem combinatorially, and differences in assumptions and contexts in different communities has made the transfer of useful generic concepts and methodologies slow to occur. This paper presents an overviewof pattern clustering methods from a statistical pattern recognition perspective, with a goal of providing useful advice and references to fundamental concepts accessible to the broad community of clustering practitioners. We present a taxonomy of clustering techniques, and identify cross-cutting themes and recent advances. We also describe some important applications of clustering algorithms such as image segmentation, object recognition, and information retrieval.
---
paper_title: Privacy-preserving data mining

paper_content:

A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models without access to precise information in individual data records? We consider the concrete case of building a decision-tree classifier from training data in which the values of individual records have been perturbed. The resulting data records look very different from the original records and the distribution of data values is also very different from the original distribution. While it is not possible to accurately estimate original values in individual data records, we propose a novel reconstruction procedure to accurately estimate the distribution of original data values. By using these reconstructed distributions, we are able to build classifiers whose accuracy is comparable to the accuracy of classifiers built with the original data.
---
paper_title: A condensation approach to privacy preserving data mining

paper_content:

In recent years, privacy preserving data mining has become an important problem because of the large amount of personal data which is tracked by many business applications. In many cases, users are unwilling to provide personal information unless the privacy of sensitive information is guaranteed. In this paper, we propose a new framework for privacy preserving data mining of multi-dimensional data. Previous work for privacy preserving data mining uses a perturbation approach which reconstructs data distributions in order to perform the mining. Such an approach treats each dimension independently and therefore ignores the correlations between the different dimensions. In addition, it requires the development of a new distribution based algorithm for each data mining problem, since it does not use the multi-dimensional records, but uses aggregate distributions of the data as input. This leads to a fundamental re-design of data mining algorithms. In this paper, we will develop a new and flexible approach for privacy preserving data mining which does not require new problem-specific algorithms, since it maps the original data set into a new anonymized data set. This anonymized data closely matches the characteristics of the original data including the correlations among the different dimensions. We present empirical results illustrating the effectiveness of the method.
---
paper_title: An Attacker’s View of Distance Preserving Maps for Privacy Preserving Data Mining

paper_content:

We examine the effectiveness of distance preserving transformations in privacy preserving data mining. These techniques are potentially very useful in that some important data mining algorithms can be efficiently applied to the transformed data and produce exactly the same results as if applied to the original data e.g. distance-based clustering, k-nearest neighbor classification. However, the issue of how well the original data is hidden has, to our knowledge, not been carefully studied. We take a step in this direction by assuming the role of an attacker armed with two types of prior information regarding the original data. We examine how well the attacker can recover the original data from the transformed data and prior information. Our results offer insight into the vulnerabilities of distance preserving transformations.
---
paper_title: Privacy-preserving data mining

paper_content:

A fruitful direction for future data mining research will be the development of techniques that incorporate privacy concerns. Specifically, we address the following question. Since the primary task in data mining is the development of models about aggregated data, can we develop accurate models without access to precise information in individual data records? We consider the concrete case of building a decision-tree classifier from training data in which the values of individual records have been perturbed. The resulting data records look very different from the original records and the distribution of data values is also very different from the original distribution. While it is not possible to accurately estimate original values in individual data records, we propose a novel reconstruction procedure to accurately estimate the distribution of original data values. By using these reconstructed distributions, we are able to build classifiers whose accuracy is comparable to the accuracy of classifiers built with the original data.
---
paper_title: Random projection-based multiplicative data perturbation for privacy preserving distributed data mining

paper_content:

This paper explores the possibility of using multiplicative random projection matrices for privacy preserving distributed data mining. It specifically considers the problem of computing statistical aggregates like the inner product matrix, correlation coefficient matrix, and Euclidean distance matrix from distributed privacy sensitive data possibly owned by multiple parties. This class of problems is directly related to many other data-mining problems such as clustering, principal component analysis, and classification. This paper makes primary contributions on two different grounds. First, it explores independent component analysis as a possible tool for breaching privacy in deterministic multiplicative perturbation-based models such as random orthogonal transformation and random rotation. Then, it proposes an approximate random projection-based technique to improve the level of privacy protection while still preserving certain statistical characteristics of the data. The paper presents extensive theoretical analysis and experimental results. Experiments demonstrate that the proposed technique is effective and can be successfully used for different types of privacy-preserving data mining applications.
---
paper_title: An Attacker’s View of Distance Preserving Maps for Privacy Preserving Data Mining

paper_content:

We examine the effectiveness of distance preserving transformations in privacy preserving data mining. These techniques are potentially very useful in that some important data mining algorithms can be efficiently applied to the transformed data and produce exactly the same results as if applied to the original data e.g. distance-based clustering, k-nearest neighbor classification. However, the issue of how well the original data is hidden has, to our knowledge, not been carefully studied. We take a step in this direction by assuming the role of an attacker armed with two types of prior information regarding the original data. We examine how well the attacker can recover the original data from the transformed data and prior information. Our results offer insight into the vulnerabilities of distance preserving transformations.
---
paper_title: Deriving private information from arbitrarily projected data

paper_content:

Distance-preserving projection based perturbation has gained much attention in privacy-preserving data mining in recent years since it mitigates the privacy/accuracy tradeoff by achieving perfect data mining accuracy. One apriori knowledge PCA based attack was recently investigated to show the vulnerabilities of this distance-preserving projected based perturbation approach when a sample dataset is available to attackers. As a result, non-distance-preserving projection was suggested to be applied since it is resilient to the PCA attack with the sacrifice of data mining accuracy to some extent. In this paper we investigate how to recover the original data from arbitrarily projected data and propose AKICA, an Independent Component Analysis based reconstruction method. Theoretical analysis and experimental results show that both distance-preserving and non-distance-preserving projection approaches are vulnerable to this attack. Our results offer insight into the vulnerabilities of projection based approach and suggest a careful scrutiny when it is applied in privacy-preserving data mining.
---
paper_title: An Attacker’s View of Distance Preserving Maps for Privacy Preserving Data Mining

paper_content:

We examine the effectiveness of distance preserving transformations in privacy preserving data mining. These techniques are potentially very useful in that some important data mining algorithms can be efficiently applied to the transformed data and produce exactly the same results as if applied to the original data e.g. distance-based clustering, k-nearest neighbor classification. However, the issue of how well the original data is hidden has, to our knowledge, not been carefully studied. We take a step in this direction by assuming the role of an attacker armed with two types of prior information regarding the original data. We examine how well the attacker can recover the original data from the transformed data and prior information. Our results offer insight into the vulnerabilities of distance preserving transformations.
---

Title: A Survey of Multiplicative Perturbation for Privacy-Preserving Data Mining
Section 1: Introduction
Description 1: Introduce the concept of data perturbation and its dual objectives of preserving data privacy and utility, focusing on the importance of multiplicative perturbation techniques.

Section 2: Data Privacy vs. Data Utility
Description 2: Discuss the metrics used to evaluate perturbation techniques, the balance between privacy and utility, and the principles guiding multiplicative data perturbations.

Section 3: Definition of Multiplicative Perturbation
Description 3: Define multiplicative perturbations and their categories: Rotation Perturbation, Projection Perturbation, and Geometric Perturbation. Explain the characteristics of each category.

Section 4: Rotation Perturbation
Description 4: Describe rotation perturbation, its key features, and its application methods.

Section 5: Projection Perturbation
Description 5: Define projection perturbation and explain its method and challenges related to preserving distance and model accuracy.

Section 6: Sketch-based Approach
Description 6: Introduce the sketch-based approach for perturbing high-dimensional sparse data and explain its statistical properties.

Section 7: Geometric Perturbation
Description 7: Discuss geometric perturbation as an enhancement to rotation perturbation and its additional components like translation perturbation and noise addition for improved robustness.

Section 8: Transformation Invariant Data Mining Models
Description 8: Define transformation-invariant models and explore their ability to use perturbed data without a loss in accuracy, covering examples in classification and clustering.

Section 9: Privacy Evaluation for Multiplicative Perturbation
Description 9: Outline the methods for evaluating the privacy guarantees provided by multiplicative perturbations, including a conceptual privacy model and column privacy metrics.

Section 10: Incorporating Attack Evaluation
Description 10: Discuss incorporating resilience to attack analysis into privacy evaluation and the importance of considering different types of potential attacks.

Section 11: Attack Resilient Multiplicative Perturbations
Description 11: Describe potential inference attacks to multiplicative perturbations based on varying levels of attack knowledge and discuss countermeasures.

Section 12: Naive Estimation to Rotation Perturbation
Description 12: Provide an analysis of the privacy guarantee provided by rotation perturbation against naive estimation attacks.

Section 13: ICA-Based Attacks
Description 13: Explain Independent Component Analysis (ICA)-based attacks and their effectiveness under different conditions.

Section 14: Distance-Inference Attacks
Description 14: Discuss distance-inference attacks, scenarios under which they are effective, and the countermeasures including noise addition.

Section 15: Attacks with More Prior Knowledge
Description 15: Consider extreme attack scenarios where the attacker has substantial prior knowledge and discuss the effectiveness and limitations of PCA-based and AK-ICA attacks.

Section 16: Finding Attack-Resilient Perturbations
Description 16: Present algorithms and methods to find optimal perturbations resilient to known attacks and preserve privacy.

Section 17: Conclusion
Description 17: Summarize the importance of multiplicative perturbation techniques in privacy-preserving data mining and their advantages over other methods.