750 research outputs found
Diffeomorphic Image Registration with Neural Velocity Field
Diffeomorphic image registration, offering smooth transformation and topology
preservation, is required in many medical image analysis tasks.Traditional
methods impose certain modeling constraints on the space of admissible
transformations and use optimization to find the optimal transformation between
two images. Specifying the right space of admissible transformations is
challenging: the registration quality can be poor if the space is too
restrictive, while the optimization can be hard to solve if the space is too
general. Recent learning-based methods, utilizing deep neural networks to learn
the transformation directly, achieve fast inference, but face challenges in
accuracy due to the difficulties in capturing the small local deformations and
generalization ability. Here we propose a new optimization-based method named
DNVF (Diffeomorphic Image Registration with Neural Velocity Field) which
utilizes deep neural network to model the space of admissible transformations.
A multilayer perceptron (MLP) with sinusoidal activation function is used to
represent the continuous velocity field and assigns a velocity vector to every
point in space, providing the flexibility of modeling complex deformations as
well as the convenience of optimization. Moreover, we propose a cascaded image
registration framework (Cas-DNVF) by combining the benefits of both
optimization and learning based methods, where a fully convolutional neural
network (FCN) is trained to predict the initial deformation, followed by DNVF
for further refinement. Experiments on two large-scale 3D MR brain scan
datasets demonstrate that our proposed methods significantly outperform the
state-of-the-art registration methods.Comment: WACV 202
Pattern vectors from algebraic graph theory
Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs
Fault-tolerant computer study
A set of building block circuits is described which can be used with commercially available microprocessors and memories to implement fault tolerant distributed computer systems. Each building block circuit is intended for VLSI implementation as a single chip. Several building blocks and associated processor and memory chips form a self checking computer module with self contained input output and interfaces to redundant communications buses. Fault tolerance is achieved by connecting self checking computer modules into a redundant network in which backup buses and computer modules are provided to circumvent failures. The requirements and design methodology which led to the definition of the building block circuits are discussed
Reconfigurable middleware architectures for large scale sensor networks
Wireless sensor networks, in an effort to be energy efficient, typically lack the high-level abstractions of advanced programming languages. Though strong, the dichotomy between these two paradigms can be overcome. The SENSIX software framework, described in this dissertation, uniquely integrates constraint-dominated wireless sensor networks with the flexibility of object-oriented programming models, without violating the principles of either. Though these two computing paradigms are contradictory in many ways, SENSIX bridges them to yield a dynamic middleware abstraction unifying low-level resource-aware task reconfiguration and high-level object recomposition. Through the layered approach of SENSIX, the software developer creates a domain-specific sensing architecture by defining a customized task specification and utilizing object inheritance. In addition, SENSIX performs better at large scales (on the order of 1000 nodes or more) than other sensor network middleware which do not include such unified facilities for vertical integration
Understanding Visualization: A formal approach using category theory and semiotics
This article combines the vocabulary of semiotics and category theory to provide a formal analysis of visualization. It shows how familiar processes of visualization fit the semiotic frameworks of both Saussure and Peirce, and extends these structures using the tools of category theory to provide a general framework for understanding visualization in practice, including: relationships between systems, data collected from those systems, renderings of those data in the form of representations, the reading of those representations to create visualizations, and the use of those visualizations to create knowledge and understanding of the system under inspection. The resulting framework is validated by demonstrating how familiar information visualization concepts (such as literalness, sensitivity, redundancy, ambiguity, generalizability, and chart junk) arise naturally from it and can be defined formally and precisely. This article generalizes previous work on the formal characterization of visualization by, inter alia, Ziemkiewicz and Kosara and allows us to formally distinguish properties of the visualization process that previous work does not
Federated and Transfer Learning: A Survey on Adversaries and Defense Mechanisms
The advent of federated learning has facilitated large-scale data exchange
amongst machine learning models while maintaining privacy. Despite its brief
history, federated learning is rapidly evolving to make wider use more
practical. One of the most significant advancements in this domain is the
incorporation of transfer learning into federated learning, which overcomes
fundamental constraints of primary federated learning, particularly in terms of
security. This chapter performs a comprehensive survey on the intersection of
federated and transfer learning from a security point of view. The main goal of
this study is to uncover potential vulnerabilities and defense mechanisms that
might compromise the privacy and performance of systems that use federated and
transfer learning.Comment: Accepted for publication in edited book titled "Federated and
Transfer Learning", Springer, Cha
Efficient Computation and FPGA implementation of Fully Homomorphic Encryption with Cloud Computing Significance
Homomorphic Encryption provides unique security solution for cloud computing. It ensures not only that data in cloud have confidentiality but also that data processing by cloud server does not compromise data privacy. The Fully Homomorphic Encryption (FHE) scheme proposed by Lopez-Alt, Tromer, and Vaikuntanathan (LTV), also known as NTRU(Nth degree truncated polynomial ring) based method, is considered one of the most important FHE methods suitable for practical implementation. In this thesis, an efficient algorithm and architecture for LTV Fully Homomorphic Encryption is proposed. Conventional linear feedback shift register (LFSR) structure is expanded and modified for performing the truncated polynomial ring multiplication in LTV scheme in parallel. Novel and efficient modular multiplier, modular adder and modular subtractor are proposed to support high speed processing of LFSR operations. In addition, a family of special moduli are selected for high speed computation of modular operations. Though the area keeps the complexity of O(Nn^2) with no advantage in circuit level. The proposed architecture effectively reduces the time complexity from O(N log N) to linear time, O(N), compared to the best existing works. An FPGA implementation of the proposed architecture for LTV FHE is achieved and demonstrated. An elaborate comparison of the existing methods and the proposed work is presented, which shows the proposed work gains significant speed up over existing works
METTLE: a METamorphic testing approach to assessing and validating unsupervised machine LEarning systems
Unsupervised machine learning is the training of an artificial intelligence
system using information that is neither classified nor labeled, with a view to
modeling the underlying structure or distribution in a dataset. Since
unsupervised machine learning systems are widely used in many real-world
applications, assessing the appropriateness of these systems and validating
their implementations with respect to individual users' requirements and
specific application scenarioscontexts are indisputably two important
tasks. Such assessment and validation tasks, however, are fairly challenging
due to the absence of a priori knowledge of the data. In view of this
challenge, we develop a amorphic esting approach to
assessing and validating unsupervised machine arning systems,
abbreviated as METTLE. Our approach provides a new way to unveil the (possibly
latent) characteristics of various machine learning systems, by explicitly
considering the specific expectations and requirements of these systems from
individual users' perspectives. To support METTLE, we have further formulated
11 generic metamorphic relations (MRs), covering users' generally expected
characteristics that should be possessed by machine learning systems. To
demonstrate the viability and effectiveness of METTLE we have performed an
experiment involving six commonly used clustering systems. Our experiment has
shown that, guided by user-defined MR-based adequacy criteria, end users are
able to assess, validate, and select appropriate clustering systems in
accordance with their own specific needs. Our investigation has also yielded
insightful understanding and interpretation of the behavior of the machine
learning systems from an end-user software engineering's perspective, rather
than a designer's or implementor's perspective, who normally adopts a
theoretical approach
๋ฏผ๊ฐํ ์ ๋ณด๋ฅผ ๋ณดํธํ ์ ์๋ ํ๋ผ์ด๋ฒ์ ๋ณด์กด ๊ธฐ๊ณํ์ต ๊ธฐ์ ๊ฐ๋ฐ
ํ์๋
ผ๋ฌธ(๋ฐ์ฌ) -- ์์ธ๋ํ๊ต๋ํ์ : ๊ณต๊ณผ๋ํ ์ฐ์
๊ณตํ๊ณผ, 2022. 8. ์ด์ฌ์ฑ.์ต๊ทผ ์ธ๊ณต์ง๋ฅ์ ์ฑ๊ณต์๋ ์ฌ๋ฌ ๊ฐ์ง ์์ธ์ด ์์ผ๋, ์๋ก์ด ์๊ณ ๋ฆฌ์ฆ์ ๊ฐ๋ฐ๊ณผ ์ ์ ๋ ๋ฐ์ดํฐ ์์ ๊ธฐํ๊ธ์์ ์ธ ์ฆ๊ฐ๋ก ์ธํ ์ํฅ์ด ํฌ๋ค. ๋ฐ๋ผ์ ๊ธฐ๊ณํ์ต ๋ชจ๋ธ๊ณผ ๋ฐ์ดํฐ๋ ์ค์ฌ์ ๊ฐ์น๋ฅผ ๊ฐ์ง๊ฒ ๋๋ฉฐ, ํ์ค ์ธ๊ณ์์ ๊ฐ์ธ ๋๋ ๊ธฐ์
์ ํ์ต๋ ๋ชจ๋ธ ๋๋ ํ์ต์ ์ฌ์ฉํ ๋ฐ์ดํฐ๋ฅผ ์ ๊ณตํจ์ผ๋ก์จ ์ด์ต์ ์ป์ ์ ์๋ค. ๊ทธ๋ฌ๋, ๋ฐ์ดํฐ ๋๋ ๋ชจ๋ธ์ ๊ณต์ ๋ ๊ฐ์ธ์ ๋ฏผ๊ฐ ์ ๋ณด๋ฅผ ์ ์ถํจ์ผ๋ก์จ ํ๋ผ์ด๋ฒ์์ ์นจํด๋ก ์ด์ด์ง ์ ์๋ค๋ ์ฌ์ค์ด ๋ฐํ์ง๊ณ ์๋ค.
๋ณธ ๋
ผ๋ฌธ์ ๋ชฉํ๋ ๋ฏผ๊ฐ ์ ๋ณด๋ฅผ ๋ณดํธํ ์ ์๋ ํ๋ผ์ด๋ฒ์ ๋ณด์กด ๊ธฐ๊ณํ์ต ๋ฐฉ๋ฒ๋ก ์ ๊ฐ๋ฐํ๋ ๊ฒ์ด๋ค. ์ด๋ฅผ ์ํด ์ต๊ทผ ํ๋ฐํ ์ฐ๊ตฌ๋๊ณ ์๋ ๋ ๊ฐ์ง ํ๋ผ์ด๋ฒ์ ๋ณด์กด ๊ธฐ์ , ์ฆ ๋ํ ์ํธ์ ์ฐจ๋ถ ํ๋ผ์ด๋ฒ์๋ฅผ ์ฌ์ฉํ๋ค. ๋จผ์ , ๋ํ ์ํธ๋ ์ํธํ๋ ๋ฐ์ดํฐ์ ๋ํด ๊ธฐ๊ณํ์ต ์๊ณ ๋ฆฌ์ฆ์ ์ ์ฉ ๊ฐ๋ฅํ๊ฒ ํจ์ผ๋ก์จ ๋ฐ์ดํฐ์ ํ๋ผ์ด๋ฒ์๋ฅผ ๋ณดํธํ ์ ์๋ค. ๊ทธ๋ฌ๋ ๋ํ ์ํธ๋ฅผ ํ์ฉํ ์ฐ์ฐ์ ๊ธฐ์กด์ ์ฐ์ฐ์ ๋นํด ๋งค์ฐ ํฐ ์ฐ์ฐ ์๊ฐ์ ์๊ตฌํ๋ฏ๋ก ํจ์จ์ ์ธ ์๊ณ ๋ฆฌ์ฆ์ ๊ตฌ์ฑํ๋ ๊ฒ์ด ์ค์ํ๋ค. ํจ์จ์ ์ธ ์ฐ์ฐ์ ์ํด ์ฐ๋ฆฌ๋ ๋ ๊ฐ์ง ์ ๊ทผ๋ฒ์ ์ฌ์ฉํ๋ค. ์ฒซ ๋ฒ์งธ๋ ํ์ต ๋จ๊ณ์์์ ์ฐ์ฐ๋์ ์ค์ด๋ ๊ฒ์ด๋ค. ํ์ต ๋จ๊ณ์์๋ถํฐ ๋ํ ์ํธ๋ฅผ ์ ์ฉํ๋ฉด ํ์ต ๋ฐ์ดํฐ์ ํ๋ผ์ด๋ฒ์๋ฅผ ํจ๊ป ๋ณดํธํ ์ ์์ผ๋ฏ๋ก ์ถ๋ก ๋จ๊ณ์์๋ง ๋ํ ์ํธ๋ฅผ ์ ์ฉํ๋ ๊ฒ์ ๋นํด ํ๋ผ์ด๋ฒ์์ ๋ฒ์๊ฐ ๋์ด์ง์ง๋ง, ๊ทธ๋งํผ ์ฐ์ฐ๋์ด ๋์ด๋๋ค. ๋ณธ ๋
ผ๋ฌธ์์๋ ์ผ๋ถ ๊ฐ์ฅ ์ค์ํ ์ ๋ณด๋ง์ ์ํธํํจ์ผ๋ก์จ ํ์ต ๋จ๊ณ๋ฅผ ํจ์จ์ ์ผ๋ก ํ๋ ๋ฐฉ๋ฒ๋ก ์ ์ ์ํ๋ค. ๊ตฌ์ฒด์ ์ผ๋ก, ์ผ๋ถ ๋ฏผ๊ฐ ๋ณ์๊ฐ ์ํธํ๋์ด ์์ ๋ ์ฐ์ฐ๋์ ๋งค์ฐ ์ค์ผ ์ ์๋ ๋ฆฟ์ง ํ๊ท ์๊ณ ๋ฆฌ์ฆ์ ๊ฐ๋ฐํ๋ค. ๋ํ ๊ฐ๋ฐ๋ ์๊ณ ๋ฆฌ์ฆ์ ํ์ฅ์์ผ ๋ํ ์ํธ ์นํ์ ์ด์ง ์์ ํ๋ผ๋ฏธํฐ ํ์ ๊ณผ์ ์ ์ต๋ํ ์ ๊ฑฐํ ์ ์๋ ์๋ก์ด ๋ก์ง์คํฑ ํ๊ท ์๊ณ ๋ฆฌ์ฆ์ ํจ๊ป ์ ์ํ๋ค.
ํจ์จ์ ์ธ ์ฐ์ฐ์ ์ํ ๋ ๋ฒ์งธ ์ ๊ทผ๋ฒ์ ๋ํ ์ํธ๋ฅผ ๊ธฐ๊ณํ์ต์ ์ถ๋ก ๋จ๊ณ์์๋ง ์ฌ์ฉํ๋ ๊ฒ์ด๋ค. ์ด๋ฅผ ํตํด ์ํ ๋ฐ์ดํฐ์ ์ง์ ์ ์ธ ๋
ธ์ถ์ ๋ง์ ์ ์๋ค. ๋ณธ ๋
ผ๋ฌธ์์๋ ์ํฌํธ ๋ฒกํฐ ๊ตฐ์งํ ๋ชจ๋ธ์ ๋ํ ๋ํ ์ํธ ์นํ์ ์ถ๋ก ๋ฐฉ๋ฒ์ ์ ์ํ๋ค.
๋ํ ์ํธ๋ ์ฌ๋ฌ ๊ฐ์ง ์ํ์ ๋ํด์ ๋ฐ์ดํฐ์ ๋ชจ๋ธ ์ ๋ณด๋ฅผ ๋ณดํธํ ์ ์์ผ๋, ํ์ต๋ ๋ชจ๋ธ์ ํตํด ์๋ก์ด ๋ฐ์ดํฐ์ ๋ํ ์ถ๋ก ์๋น์ค๋ฅผ ์ ๊ณตํ ๋ ์ถ๋ก ๊ฒฐ๊ณผ๋ก๋ถํฐ ๋ชจ๋ธ๊ณผ ํ์ต ๋ฐ์ดํฐ๋ฅผ ๋ณดํธํ์ง ๋ชปํ๋ค. ์ฐ๊ตฌ๋ฅผ ํตํด ๊ณต๊ฒฉ์๊ฐ ์์ ์ด ๊ฐ์ง ๋ฐ์ดํฐ์ ๊ทธ ๋ฐ์ดํฐ์ ๋ํ ์ถ๋ก ๊ฒฐ๊ณผ๋ง์ ์ด์ฉํ์ฌ ์ด์ฉํ์ฌ ๋ชจ๋ธ๊ณผ ํ์ต ๋ฐ์ดํฐ์ ๋ํ ์ ๋ณด๋ฅผ ์ถ์ถํ ์ ์์์ด ๋ฐํ์ง๊ณ ์๋ค. ์๋ฅผ ๋ค์ด, ๊ณต๊ฒฉ์๋ ํน์ ๋ฐ์ดํฐ๊ฐ ํ์ต ๋ฐ์ดํฐ์ ํฌํจ๋์ด ์๋์ง ์๋์ง๋ฅผ ์ถ๋ก ํ ์ ์๋ค. ์ฐจ๋ถ ํ๋ผ์ด๋ฒ์๋ ํ์ต๋ ๋ชจ๋ธ์ ๋ํ ํน์ ๋ฐ์ดํฐ ์ํ์ ์ํฅ์ ์ค์์ผ๋ก์จ ์ด๋ฌํ ๊ณต๊ฒฉ์ ๋ํ ๋ฐฉ์ด๋ฅผ ๋ณด์ฅํ๋ ํ๋ผ์ด๋ฒ์ ๊ธฐ์ ์ด๋ค. ์ฐจ๋ถ ํ๋ผ์ด๋ฒ์๋ ํ๋ผ์ด๋ฒ์์ ์์ค์ ์ ๋์ ์ผ๋ก ํํํจ์ผ๋ก์จ ์ํ๋ ๋งํผ์ ํ๋ผ์ด๋ฒ์๋ฅผ ์ถฉ์กฑ์ํฌ ์ ์์ง๋ง, ํ๋ผ์ด๋ฒ์๋ฅผ ์ถฉ์กฑ์ํค๊ธฐ ์ํด์๋ ์๊ณ ๋ฆฌ์ฆ์ ๊ทธ๋งํผ์ ๋ฌด์์์ฑ์ ๋ํด์ผ ํ๋ฏ๋ก ๋ชจ๋ธ์ ์ฑ๋ฅ์ ๋จ์ด๋จ๋ฆฐ๋ค. ๋ฐ๋ผ์, ๋ณธ๋ฌธ์์๋ ๋ชจ์ค ์ด๋ก ์ ์ด์ฉํ์ฌ ์ฐจ๋ถ ํ๋ผ์ด๋ฒ์ ๊ตฐ์งํ ๋ฐฉ๋ฒ๋ก ์ ํ๋ผ์ด๋ฒ์๋ฅผ ์ ์งํ๋ฉด์๋ ๊ทธ ์ฑ๋ฅ์ ๋์ด์ฌ๋ฆฌ๋ ์๋ก์ด ๋ฐฉ๋ฒ๋ก ์ ์ ์ํ๋ค.
๋ณธ ๋
ผ๋ฌธ์์ ๊ฐ๋ฐํ๋ ํ๋ผ์ด๋ฒ์ ๋ณด์กด ๊ธฐ๊ณํ์ต ๋ฐฉ๋ฒ๋ก ์ ๊ฐ๊ธฐ ๋ค๋ฅธ ์์ค์์ ํ๋ผ์ด๋ฒ์๋ฅผ ๋ณดํธํ๋ฉฐ, ๋ฐ๋ผ์ ์ํธ ๋ณด์์ ์ด๋ค. ์ ์๋ ๋ฐฉ๋ฒ๋ก ๋ค์ ํ๋์ ํตํฉ ์์คํ
์ ๊ตฌ์ถํ์ฌ ๊ธฐ๊ณํ์ต์ด ๊ฐ์ธ์ ๋ฏผ๊ฐ ์ ๋ณด๋กค ๋ณดํธํด์ผ ํ๋ ์ฌ๋ฌ ๋ถ์ผ์์ ๋์ฑ ๋๋ฆฌ ์ฌ์ฉ๋ ์ ์๋๋ก ํ๋ ๊ธฐ๋ ํจ๊ณผ๋ฅผ ๊ฐ์ง๋ค.Recent development of artificial intelligence systems has been driven by various factors such as the development of new algorithms and the the explosive increase in the amount of available data. In the real-world scenarios, individuals or corporations benefit by providing data for training a machine learning model or the trained model. However, it has been revealed that sharing of data or the model can lead to invasion of personal privacy by leaking personal sensitive information.
In this dissertation, we focus on developing privacy-preserving machine learning methods which can protect sensitive information. Homomorphic encryption can protect the privacy of data and the models because machine learning algorithms can be applied to encrypted data, but requires much larger computation time than conventional operations. For efficient computation, we take two approaches. The first is to reduce the amount of computation in the training phase. We present an efficient training algorithm by encrypting only few important information. In specific, we develop a ridge regression algorithm that greatly reduces the amount of computation when one or two sensitive variables are encrypted. Furthermore, we extend the method to apply it to classification problems by developing a new logistic regression algorithm that can maximally exclude searching of hyper-parameters that are not suitable for machine learning with homomorphic encryption.
Another approach is to apply homomorphic encryption only when the trained model is used for inference, which prevents direct exposure of the test data and the model information. We propose a homomorphic-encryption-friendly algorithm for inference of support based clustering.
Though homomorphic encryption can prevent various threats to data and the model information, it cannot defend against secondary attacks through inference APIs. It has been reported that an adversary can extract information about the training data only with his or her input and the corresponding output of the model. For instance, the adversary can determine whether specific data is included in the training data or not. Differential privacy is a mathematical concept which guarantees defense against those attacks by reducing the impact of specific data samples on the trained model. Differential privacy has the advantage of being able to quantitatively express the degree of privacy, but it reduces the utility of the model by adding randomness to the algorithm. Therefore, we propose a novel method which can improve the utility while maintaining the privacy of differentially private clustering algorithms by utilizing Morse theory.
The privacy-preserving machine learning methods proposed in this paper can complement each other to prevent different levels of attacks. We expect that our methods can construct an integrated system and be applied to various domains where machine learning involves sensitive personal information.Chapter 1 Introduction 1
1.1 Motivation of the Dissertation 1
1.2 Aims of the Dissertation 7
1.3 Organization of the Dissertation 10
Chapter 2 Preliminaries 11
2.1 Homomorphic Encryption 11
2.2 Differential Privacy 14
Chapter 3 Efficient Homomorphic Encryption Framework for Ridge Regression 18
3.1 Problem Statement 18
3.2 Framework 22
3.3 Proposed Method 25
3.3.1 Regression with one Encrypted Sensitive Variable 25
3.3.2 Regression with two Encrypted Sensitive Variables 30
3.3.3 Adversarial Perturbation Against Attribute Inference Attack 35
3.3.4 Algorithm for Ridge Regression 36
3.3.5 Algorithm for Adversarial Perturbation 37
3.4 Experiments 40
3.4.1 Experimental Setting 40
3.4.2 Experimental Results 42
3.5 Chapter Summary 47
Chapter 4 Parameter-free Homomorphic-encryption-friendly Logistic Regression 53
4.1 Problem Statement 53
4.2 Proposed Method 56
4.2.1 Motivation 56
4.2.2 Framework 58
4.3 Theoretical Results 63
4.4 Experiments 68
4.4.1 Experimental Setting 68
4.4.2 Experimental Results 70
4.5 Chapter Summary 75
Chapter 5 Homomorphic-encryption-friendly Evaluation for Support Vector Clustering 76
5.1 Problem Statement 76
5.2 Background 78
5.2.1 CKKS scheme 78
5.2.2 SVC 80
5.3 Proposed Method 82
5.4 Experiments 86
5.4.1 Experimental Setting 86
5.4.2 Experimental Results 87
5.5 Chapter Summary 89
Chapter 6 Differentially Private Mixture of Gaussians Clustering with Morse Theory 95
6.1 Problem Statement 95
6.2 Background 98
6.2.1 Mixture of Gaussians 98
6.2.2 Morse Theory 99
6.2.3 Dynamical System Perspective 101
6.3 Proposed Method 104
6.3.1 Differentially private clustering 105
6.3.2 Transition equilibrium vectors and the weighted graph 108
6.3.3 Hierarchical merging of sub-clusters 111
6.4 Theoretical Results 112
6.5 Experiments 117
6.5.1 Experimental Setting 117
6.5.2 Experimental Results 119
6.6 Chapter Summary 122
Chapter 7 Conclusion 124
7.1 Conclusion 124
7.2 Future Direction 126
Bibliography 128
๊ตญ๋ฌธ์ด๋ก 154๋ฐ
- โฆ