Kazuhisa Nakasho

Privacy-Preserving Integration of Medical Data

Medical data are often maintained by different organizations. However, detailed analyses sometimes require these datasets to be integrated without violating patient or commercial privacy. Multiparty Private Set Intersection (MPSI), which is an important privacy-preserving protocol, computes an intersection of multiple private datasets. This approach ensures that only designated parties can identify the intersection. In this paper, we propose a practical MPSI that satisfies the following requirements: The size of the datasets maintained by the different parties is independent of the others, and the computational complexity of the dataset held by each party is independent of the number of parties. Our MPSI is based on the use of an outsourcing provider, who has no knowledge of the data inputs or outputs. This reduces the computational complexity. The performance of the proposed MPSI is evaluated by implementing a prototype on a virtual private network to enable parallel computation in multiple threads. Our protocol is confirmed to be more efficient than comparable existing approaches.

Topological Properties of Real Normed Space

Summary In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences is also refered here. Then we argue the condition when real normed subspaces become Banach’s spaces. We also formalize quotient vector space. In the last session, we argue the properties of the closure of real normed space. These formalizations are based on [19](p.3-41), [2] and [34](p.3-67).

σ-ring and σ-algebra of Sets1

Summary In this article, semiring and semialgebra of sets are formalized so as to construct a measure of a given set in the next step. Although a semiring of sets has already been formalized in [13], that is, strictly speaking, a definition of a quasi semiring of sets suggested in the last few decades [15]. We adopt a classical definition of a semiring of sets here to avoid such a confusion. Ring of sets and algebra of sets have been formalized as non empty preboolean set [23] and field of subsets [18], respectively. In the second section, definitions of a ring and a σ-ring of sets, which are based on a semiring and a ring of sets respectively, are formalized and their related theorems are proved. In the third section, definitions of an algebra and a σ-algebra of sets, which are based on a semialgebra and an algebra of sets respectively, are formalized and their related theorems are proved. In the last section, mutual relationships between σ-ring and σ-algebra of sets are formalized and some related examples are given. The formalization is based on [15], and also referred to [9] and [16].

The Basic Existence Theorem of Riemann-Stieltjes Integral

Summary In this article, the basic existence theorem of Riemann-Stieltjes integral is formalized. This theorem states that if f is a continuous function and ρ is a function of bounded variation in a closed interval of real line, f is Riemann-Stieltjes integrable with respect to ρ. In the first section, basic properties of real finite sequences are formalized as preliminaries. In the second section, we formalized the existence theorem of the Riemann-Stieltjes integral. These formalizations are based on [15], [12], [10], and [11].

Riemann-Stieltjes Integral

Abstract In this article, the definitions and basic properties of Riemann-Stieltjes integral are formalized in Mizar [1]. In the first section, we showed the preliminary definition. We proved also some properties of finite sequences of real numbers. In Sec. 2, we defined variation. Using the definition, we also defined bounded variation and total variation, and proved theorems about related properties. In Sec. 3, we defined Riemann-Stieltjes integral. Referring to the way of the article [7], we described the definitions. In the last section, we proved theorems about linearity of Riemann-Stieltjes integral. Because there are two types of linearity in Riemann-Stieltjes integral, we proved linearity in two ways. We showed the proof of theorems based on the description of the article [7]. These formalizations are based on [8], [5], [3], and [4].

Definition and Properties of Direct Sum Decomposition of Groups1

Summary In this article, direct sum decomposition of group is mainly discussed. In the second section, support of element of direct product group is defined and its properties are formalized. It is formalized here that an element of direct product group belongs to its direct sum if and only if support of the element is finite. In the third section, product map and sum map are prepared. In the fourth section, internal and external direct sum are defined. In the last section, an equivalent form of internal direct sum is proved. We referred to [23], [22], [8] and [18] in the formalization.

Rank of Submodule, Linear Transformations and Linearly Independent Subsets of Z-module

Summary In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, and that there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts of linear transformations between two Z-modules. In this section, we define homomorphism between two Z-modules and deal with kernel and image of homomorphism. In the last section, we formally prove some basic facts about linearly independent subsets and linear combinations. These formalizations are based on [9](p.191-242), [23](p.117-172) and [2](p.17-35).

Isomorphisms of Direct Products of Cyclic Groups of Prime Power Order

Summary In this paper we formalized some theorems concerning the cyclic groups of prime power order. We formalize that every commutative cyclic group of prime power order is isomorphic to a direct product of family of cyclic groups [1], [18].

Context based semantic scene classification and recognition used for a vision-based mobile robot

This paper presents a novel method using accelerated KAZE (AKAZE) and Gist for a context-based semantic classification and recognition of indoor scenes used for a vision-based mobile robot. Our method represents spatial relations among categories for mapping neighborhood units on category maps using counter propagation networks (CPNs) while maintaining sequential information of labels generated from adaptive resonance theory 2 (ART-2) networks. We evaluated the performance and accuracy of semantic categories using KTH-IDOL benchmark datasets. Compared with the earlier described method using scale-invariant feature transform (SIFT), accuracies of classification, recognition, and F-measure were improved to 2.9%, 3.4%, and 3.3% of our method using AKAZE. For analyzing results, confusion matrixes show that incorrect images between corridors and rooms are decreased in our method compared with the former method. We consider that our proposed feature representation method based on context and category formation, combined with ART-2 and CPNs, is useful for indoor scene classification and recognition for robot vision.

Adaptive learning based driving episode description on category maps

This study was conducted to create driving episodes using machine-learning-based algorithms that address long-term memory (LTM) and topological mapping. This paper presents a novel episodic memory model for driving safety according to traffic scenes. The model incorporates three important features: adaptive resonance theory (ART), which learns time-series features incrementally while maintaining stability and plasticity for time-series data; self-organizing maps (SOMs), which represent input data as a map with topological relations using self-mapping characteristics; and counter propagation networks (CPNs), which label category maps using input features and counter signals. Category maps represent driving episode information that includes driving contexts and facial expressions. The bursting states of respective maps produce LTM, which is created on ART as episodic memory. Evaluation of the experimentally obtained results show the possibility of using recorded driving episodes with image datasets obtained using an event data recorder (EDR) with two cameras. Using category maps, we visualize driving features according to driving scenes on a public road and an expressway.