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1.
Rotation in Correspondence Analysis 总被引:1,自引:1,他引:0
In correspondence analysis rows and columns of a nonnegative data matrix are
depicted as points in a, usually, two-dimensional plot. Although such a two-dimensional
plot often provides a reasonable approximation, the situation can occur that an approximation
of higher dimensionality is required. This is especially the case when the data
matrix is large. In such instances it may become difficult to interpret the solution. Similar
to what is done in principal component analysis and factor analysis the correspondence
analysis solution can be rotated to increase the interpretability. However, due to the various
scaling options encountered in correspondence analysis, there are several alternative
options for rotating the solutions. In this paper we consider two options for rotation in
correspondence analysis. An example is provided so that the benefits of rotation become
apparent. 相似文献
2.
A common approach to deal with missing values in multivariate exploratory data analysis consists in minimizing the loss function
over all non-missing elements, which can be achieved by EM-type algorithms where an iterative imputation of the missing values
is performed during the estimation of the axes and components. This paper proposes such an algorithm, named iterative multiple
correspondence analysis, to handle missing values in multiple correspondence analysis (MCA). The algorithm, based on an iterative
PCA algorithm, is described and its properties are studied. We point out the overfitting problem and propose a regularized
version of the algorithm to overcome this major issue. Finally, performances of the regularized iterative MCA algorithm (implemented in the R-package named missMDA) are assessed from both simulations and a real dataset. Results are
promising with respect to other methods such as the missing-data passive modified margin method, an adaptation of the missing passive method used in Gifi’s Homogeneity analysis framework. 相似文献
3.
Non-symmetrical correspondence analysis (NSCA) is a very practical statistical technique for the identification of the structure
of association between asymmetrically related categorical variables forming a contingency table. This paper considers some
tools that can be used to numerically and graphically explore in detail the association between these variables and include
the use of confidence regions, the establishment of the link between NSCA and the analysis of variance of categorical variables,
and the effect of imposing linear constraints on a variable.
The authors would like to thank the anonymous referees for their comments and suggestions during the preparation of this paper. 相似文献
4.
Within the non-iterative procedures for performing a correspondence analysis with linear constraints, a strategy is proposed
to impose linear constraints in analyzing a contingency table with one or two ordered sets of categories. At the heart of
the approach is the partition of the Pearson chi-squared statistics which involves terms that summarize the association between
the nominal/ordinal variables using bivariate moments based on orthogonal polynomials. Linear constraints are then included
directly in suitable matrices reflecting the most important components, overcoming also the problem of imposing linear constraints
based on subjective decisions. 相似文献
5.
对海峡两岸科技名词对照中常见的简繁对应字,以及音义同而形不同繁体字和异体字等问题进行了归类整理,以便交流和规范使用。 相似文献
6.
塔斯基的语义真理论常被当作符合论.通过区分塔斯基式真定义的普遍特征和具体的定义形式,并对不同语言构造具有不同语义特征的定义实例,揭示出塔斯基所持的是一种语义工具论.塔斯基的真理论并不是符合论. 相似文献
7.
从符合论的观点看逻辑真理 总被引:4,自引:0,他引:4
从真理符合论的观点看,逻辑真理与一般的事实真理有本质的不同.我们认为,逻辑真理不应看作是真理,而只是一类逻辑有效式,它们与逻辑推理的普遍有效式是一致的.逻辑学的任务就是探寻逻辑真理. 相似文献
8.
对应规则在科学哲学中是为了解决理论术语的经验意义问题而引发出来的。在逻辑经验主义的双语言模型中,对应规则赋予理论词汇以经验内容。在理论的还原解释中,对应规则起限制性条件、双向条件语句或恒等陈述作用。在科学实践中,从不同的角度可以将对应规则分为不同的类型。 相似文献
9.
We present an alternative approach to Multiple Correspondence Analysis (MCA) that is appropriate when the data consist of
ordered categorical variables. MCA displays objects (individuals, units) and variables as individual points and sets of category
points in a low-dimensional space. We propose a hybrid decomposition on the basis of the classical indicator super-matrix,
using the singular value decomposition, and the bivariate moment decomposition by orthogonal polynomials. When compared to
standard MCA, the hybrid decomposition will give the same representation of the categories of the variables, but additionally,
we obtain a clear association interpretation among the categories in terms of linear, quadratic and higher order components.
Moreover, the graphical display of the individual units will show an automatic clustering. 相似文献
10.
Fionn Murtagh 《Journal of Classification》1998,15(2):161-183
We discuss the use of orthogonal wavelet transforms in preprocessing multivariate data for subsequent analysis, e.g., by
clustering the dimensionality reduction. Wavelet transforms allow us to introduce multiresolution approximation, and multiscale
nonparametric regression or smoothing, in a natural and integrated way into the data analysis. As will be explained in the
first part of the paper, this approach is of greatest interest for multivariate data analysis when we use (i) datasets with
ordered variables, e.g., time series, and (ii) object dimensionalities which are not too small, e.g., 16 and upwards. In
the second part of the paper, a different type of wavelet decomposition is used. Applications illustrate the powerfulness
of this new perspective on data analysis. 相似文献
11.
We consider two fundamental properties in the analysis of two-way tables of positive data: the principle of distributional
equivalence, one of the cornerstones of correspondence analysis of contingency tables, and the principle of subcompositional
coherence, which forms the basis of compositional data analysis. For an analysis to be subcompositionally coherent, it suffices
to analyze the ratios of the data values. A common approach to dimension reduction in compositional data analysis is to perform
principal component analysis on the logarithms of ratios, but this method does not obey the principle of distributional equivalence.
We show that by introducing weights for the rows and columns, the method achieves this desirable property and can be applied
to a wider class of methods. This weighted log-ratio analysis is theoretically equivalent to “spectral mapping”, a multivariate
method developed almost 30 years ago for displaying ratio-scale data from biological activity spectra. The close relationship
between spectral mapping and correspondence analysis is also explained, as well as their connection with association modeling.
The weighted log-ratio methodology is used here to visualize frequency data in linguistics and chemical compositional data
in archeology.
The first author acknowledges research support from the Fundación BBVA in Madrid as well as partial support by the Spanish
Ministry of Education and Science, grant MEC-SEJ2006-14098. The constructive comments of the referees, who also brought additional
relevant literature to our attention, significantly improved our article. 相似文献
12.
Separability of clusters is an issue that arises in many different areas, and is often used in a rather vague and subjective
manner. We introduce a combinatorial notion of interiority to derive a global view on separability of a set of entities. We
develop this approach further to evaluate the overall separability of a partition in the context of cluster analysis. Our
approach captures combinatorial and geometrical aspects of data and provides, in addition to numerical evaluations, graphical
representations particularly useful when data are not easily visualized. We illustrate the methodology on some real and simulated
datasets. 相似文献
13.
科技术语翻译是科技信息的沟通,也是文化元素的传递。术语概念形成机制和语言表达式都要受到文化认知的制约和影响。从等值传递专业概念的目标出发,术语翻译应当从文化认知原理、文化对应性等方面深入理解,通过对比分析,探讨术语翻译的实用方法和技巧。 相似文献
14.
In this paper, we present empirical and theoretical results on classification trees for randomized response data. We considered
a dichotomous sensitive response variable with the true status intentionally misclassified by the respondents using rules
prescribed by a randomized response method. We assumed that classification trees are grown using the Pearson chi-square test
as a splitting criterion, and that the randomized response data are analyzed using classification trees as if they were not
perturbed. We proved that classification trees analyzing observed randomized response data and estimated true data have a
one-to-one correspondence in terms of ranking the splitting variables. This is illustrated using two real data sets. 相似文献
15.
We construct a weighted Euclidean distance that approximates any distance or dissimilarity measure between individuals that is based on a rectangular cases-by-variables data matrix. In contrast to regular multidimensional scaling methods for dissimilarity data, our approach leads to biplots of individuals and variables while preserving all the good properties of dimension-reduction methods that are based on the singular-value decomposition. The main benefits are the decomposition of variance into components along principal axes, which provide the numerical diagnostics known as contributions, and the estimation of nonnegative weights for each variable. The idea is inspired by the distance functions used in correspondence analysis and in principal component analysis of standardized data, where the normalizations inherent in the distances can be considered as differential weighting of the variables. In weighted Euclidean biplots, we allow these weights to be unknown parameters, which are estimated from the data to maximize the fit to the chosen distances or dissimilarities. These weights are estimated using a majorization algorithm. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing the matrix and displaying its rows and columns in biplots. 相似文献
16.
17.
Functional Cluster Analysis via Orthonormalized Gaussian Basis Expansions and Its Application 总被引:1,自引:1,他引:0
We propose functional cluster analysis (FCA) for multidimensional functional data sets, utilizing orthonormalized Gaussian
basis functions. An essential point in FCA is the use of orthonormal bases that yield the identity matrix for the integral
of the product of any two bases. We construct orthonormalized Gaussian basis functions using Cholesky decomposition and derive
a property of Cholesky decomposition with respect to Gram-Schmidt orthonormalization. The advantages of the functional clustering
are that it can be applied to the data observed at different time points for each subject, and the functional structure behind
the data can be captured by removing the measurement errors. Numerical experiments are conducted to investigate the effectiveness
of the proposed method, as compared to conventional discrete cluster analysis. The proposed method is applied to three-dimensional
(3D) protein structural data that determine the 3D arrangement of amino acids in individual protein. 相似文献
18.
19.
Kajsa Br?ting 《Foundations of Science》2012,17(4):301-320
In this paper we consider the major development of mathematical analysis during the mid-nineteenth century. On the basis of Jahnke’s (Hist Math 20(3):265–284, 1993) distinction between considering mathematics as an empirical science based on time and space and considering mathematics as a purely conceptual science we discuss the Swedish nineteenth century mathematician E.G. Bj?rling’s general view of real- and complexvalued functions. We argue that Bj?rling had a tendency to sometimes consider mathematical objects in a naturalistic way. One example is how Bj?rling interprets Cauchy’s definition of the logarithm function with respect to complex variables, which is investigated in the paper. Furthermore, in view of an article written by Bj?rling (Kongl Vetens Akad F?rh Stockholm 166–228, 1852) we consider Cauchy’s theorem on power series expansions of complex valued functions. We investigate Bj?rling’s, Cauchy’s and the Belgian mathematician Lamarle’s different conditions for expanding a complex function of a complex variable in a power series. We argue that one reason why Cauchy’s theorem was controversial could be the ambiguities of fundamental concepts in analysis that existed during the mid-nineteenth century. This problem is demonstrated with examples from Bj?rling, Cauchy and Lamarle. 相似文献
20.
符号片面化是术语翻译构建术语理据的重要手段,译者通过符号对应建立起概念对应,用意义简写式引发认知主体对概念意义的感知,进而构建出术语理据。意义简写式既要凸显概念的本质特征,还需兼顾概念的系统性。在实践中还需避免符号的虚假对应问题。 相似文献