A Multidimensional Scaling Model for Three-Way Data Analysis

This article proposes a model that facilitates the analysis of triadic relationships among three objects. Recently, interest in studies of three-way data models has increased, and many significant contributions have been made in this area. However, one-mode, three-way models have yet to be considered. This study focuses on a onemode, three-way model in which three-way distances are explained as the subtraction of the smallest squared distance among the three squared distances from the sum of these squared distances. This formulation is used to illustrate the idea that relationships with many differences carry more information than relationships with few differences. Moreover, the distance between two objects is weighted more heavily when two objects differ greatly, and this weight indicates the salience of their dyadic distance. Finally, the model and algorithm are applied to purchase data for convenience stores. The proposed model of multidimensional scaling clearly identifies differences among groups of objects.

     

运用多维尺度分析进行噪声品质的主观评价

引言 噪声声品质的研究是近些年环境声学中一个比较新的方向.此研究源于许多情况下,传统的噪声评价方法例如A声级、A声功率级以及三分之一倍频程不能描述人们对噪声的评价.     

Bayesian Nonmetric Successive Categories Multidimensional Scaling

A Bayesian nonmetric successive categories multidimensional scaling (MDS) method is proposed. The proposed method can be seen as a Bayesian alternative to the maximum likelihood multidimensional successive scaling method proposed by Takane (1981), or as a nonmetric extension of Bayesian metric MDS by Oh and Raftery (2001). The model has a graded-response type measurement model part and a latent metric MDS part. All the parameters are jointly estimated using a Markov chain Monte Carlo (MCMC) estimation technique. Moreover, WinBUGS/OpenBUGS code for the proposed methodology is also given to aid applied researchers. The proposed method is illustrated through the analysis of empirical two-mode three-way similarity data.

     

A Bayesian Approach to Asymmetric Multidimensional Scaling

Behaviormetrika - We propose a Bayesian approach to asymmetric multidimensional scaling (MDS), which incorporates an asymmetric data structure. The asymmetry is represented by the hill-climbing...     

Analysis of Perceptual Dimensions of Schematic Facial Expressions Via Three-Way Multidimensional Scaling

Behaviormetrika - In order to investigate perceptual dimensions of facial expressions, three-way multidimensional scaling methods were applied to the analysis of two types of judgment data. That...     

Asymmetric Triangulation Scaling: Asymmetric Multidimensional Scaling for Visualizing Inter-Item Dependency Structure

Behaviormetrika - In test data analysis, it is very important to clarify the underlying inter-item dependency structure. Once the structure is identified, we can reorder the units in the relevant...     

Multidimensional Scaling to Explore Complex Aspects in Dissimilarity Judgment

This paper proposes a model to analyze the structure and context effects involved in dissimilarity judgment. With some restrictions incorporated, the model is also interpreted as a kind of the distance-density model and further interpreted as a mixed distance and content model. Algorithms for multidimensional scaling based on the proposed model are implemented using nonlinear optimization methods. The algorithms are evaluated through a Monte Carlo study, and applications are demonstrated with real data. Problems regarding the model, the algorithms and possible applications are discussed.

     

Exploratory Approaches to Seriation by Asymmetric Multidimensional Scaling

Seriation and multidimensional scaling are two techniques aimed at exploring relationships in dominance or proximity data matrices. Rodgers and Thompson (1992) argued that the two approaches can profitably interact in the analysis of asymmetric proximity matrices, and proposed a method that uses seriation to define an empirical ordering of the stimuli, and symmetric multidimensional scaling to scale the two separate triangles of the proximity matrix defined by this ordering (an approach anticipated by Method 3 in Gower (1977)). Following a similar concept, this paper proposes some procedures to explore seriation through asymmetric multidimensional scaling. The paper focuses on skew-symmetric components of a particular class of asymmetric matrices (including e.g. tournament or paired comparison matrices). Two short examples of possible applications are provided to illustrate the procedures, both in the dichotomous and quantitative case.

     

多维度评定计量法在面部识别中的运用

研究采用多维度评定计量法(MultidimensionalScaling),让46名被试对成对人脸作相似性判断及对单个人脸作主观评价,以此来探索面部识别中的心理过程。结果表明:①男女被试对人脸相似性判断的标准有差异,女性被试判断维度是人脸的性别、种族和异常性,而男性被试的判断依据是人脸的年龄、种族和异常性;②人脸的社会意义在相似性判断中并未起作用,但是男女被试对同一人脸的主观评价上有差异。     

Multidimensional Scaling of Asymmetric Proximity: Model and Method

Behaviormetrika - This paper proposes a mutidimensional scaling method for asymmetric proximity data whose diagonal entries are not all equal. For a suggested model, necessary and sufficient...     

Asymmetric Multidimensional Scaling of Brand Switching Among Margarine Brands

Behaviormetrika - Brand switching data among 12 margarine brands were analyzed by the asymmetric multidimensional scaling based on the singular value decomposition. A two-dimensional result was...     

On The Relations Among Four Methods of Multidimensional Scaling

Behaviormetrika - Some intriguing relationships among four methods of metric and nonmetric multidimensional scaling (MDS) are explicated. It is shown that all four methods of MDS considered here...     

基于融合鲁棒特征与多维尺度变换的紧凑图像哈希算法

目的为了增强哈希序列对任意旋转角度的鲁棒性与识别能力,提出一种基于融合鲁棒特征与多维尺度变换的紧凑图像哈希算法。方法首先,利用双线性插值来固定图像的哈希序列长度,获取规则尺寸的图像;借助高斯低通滤波对规则图像完成过滤操作,消除噪声污染和插值误差对哈希生成的影响;将滤波图像转换到YCbCr颜色空间,提取亮度Y分量,增强哈希对亮度调整的鲁棒性;利用极坐标变换LPT方法处理亮度Y分量,输出二次图像;引入SVD机制来分解二次图像,获取其抗旋转的鲁棒特征;同时,根据Fourier变换与残差机制,获取Y分量的局部显著特征;随后,将这2种特征组合,形成融合鲁棒特征,将其视为中间哈希序列;引入多维尺度变换,对中间哈希序列完成压缩,获取紧凑哈希;基于Logistic映射,完成紧凑哈希序列的加密,形成目标哈希;通过计算真实图像与待认证图像之间哈希序列对应的Hamming距离,根据预设阈值,完成图像识别。结果测试数据表明,较已有的哈希方案而言,所提方案拥有更高的鲁棒性和更紧凑的哈希长度,呈现出更为理想的ROC曲线,在多种攻击下,其稳定的正确识别率保持在96%以上。结论所提哈希方案拥有良好的鲁棒性与敏感性,在包装图标检索、信息水印等行业具备较好的应用价值。     

Contributions to eij-Type Quantification and Development of a New Method of Multidimensional Scaling

Behaviormetrika - This paper is concerned with a methodological study of Hayashi’s eej-type quantification method (EQ) and development of a new method (PAMSE) of multidimensional scaling...     

Multidimensional Analysis of Trends in Patent Activity

Only multidimensional analyses can provide overviews of complex relationships among many variables. We have previously illustrated the use of Correspondence Factor Analysis (CFA) in the analysis of publication profiles. In this article, we retrace our activity in patent analysis from the late 1970s to the present day and show how CFA is a particularly useful tool not only for describing the correlations between countries and technological fields but also for highlighting non-linear patenting time trends.     

环境设计的方法及其多维分析

目的以信息可视化的方式考察环境设计方法,从设计方法的视角反思环境设计的内涵。方法首先,运用文献法,梳理了从“环境艺术”、“环境艺术设计”到“环境设计”的发展脉络,基于对不同时期中外学者的定义的比较,揭示出了环境设计的内涵。其次,采集并筛选了一百一十八种与环境设计相关的设计方法,从方法属性、设计流程、设计对象三个维度进行方法分类。然后,通过信息可视化和比较法,对上述方法分别进行了一维方法分析、二维关联分析和三维综合分析。结论从“环境艺术”到“环境艺术设计”再到“环境设计”的概念更迭,不仅是我国不同发展阶段对环境设计的认知的差异,而且更加反映出了时代背景、现实需求的变化,也必然带来相应设计方法的变化。当前,环境设计正在从关注环境中物质对象的设计,转向关注环境中人和人、人和物、物和物的关系等非物质对象的设计。     

Non-Parametric Sensitivity Analysis in Linear Programming

A linear programming problem subject to uncertainty in the requirements vector is solved deterministically, then sensitivity analysis is performed to determine the effect of the random variation on this solution. Since there could be an appreciable cost of modifying a solution once implemented, the probability of the random components perturbing a solution is considered. Unlike existing methods of linear programming under uncertainty, this article assumes no knowledge of the distributions of the random variables. Rather, the notion of non-parametric tolerance limits is employed to establish a criterion for changing basic solutions.