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1.
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
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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
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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
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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
6.
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
7.
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
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Optimal Variable Weighting for Ultrametric and Additive Trees and K-means Partitioning: Methods and Software 总被引:1,自引:0,他引:1
K -means partitioning. We also describe some new features and improvements to the algorithm proposed by De Soete. Monte Carlo simulations have been conducted using different error conditions. In all cases (i.e., ultrametric or additive trees, or K-means partitioning), the simulation results indicate that the optimal weighting procedure should be used for analyzing data containing noisy variables that do not contribute relevant information to the classification structure. However, if the data involve error-perturbed variables that are relevant to the classification or outliers, it seems better to cluster or partition the entities by using variables with equal weights. A new computer program, OVW, which is available to researchers as freeware, implements improved algorithms for optimal variable weighting for ultrametric and additive tree clustering, and includes a new algorithm for optimal variable weighting for K-means partitioning. 相似文献
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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.
Let G = (V,E,w) be a graph with vertex and edge sets V and E, respectively, and w:E → R + a function which assigns a positive weight or length to each edge of G. G is called a realization of a finite metric space
(M,d), with M = { 1,...,n} if and only if { 1,...,n} ⫅ V and d(i,j) is equal to the length of the shortest chain linking i
and j in G ∀ i,j = 1,...,n. A realization G of (M,d), is said optimal if the sum of its weights is minimal among all the realizations
of (M,d). Consider a partition of M into two nonempty subsets K and L, and let e be an edge in a realization G of (M,d); we
say that e is a bridge linking K with L if e belongs to all chains in G linking a vertex of K with a vertex of L. The Metric
Bridge Partition Problem is to determine if the elements of a finite metric space (M,d) can be partitioned into two nonempty
subsets K and L such that all optimal realizations of (M,d) contain a bridge linking K with L. We prove in this paper that
this problem is polynomially solvable. We also describe an algorithm that constructs an optimal realization of (M,d) from
optimal realizations of (K,d|K) and (L,d|L). 相似文献
16.
李俨致严敦杰信1941年敦杰先生大鉴:读一月二十三日大示及徐树勋刊<圜锥曲线>(内卷一缺末一页,请设法抄副见示,以便订成全帙)及二十日来电并收及. 相似文献
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李俨致严敦杰信1940年敦杰先生惠鉴: 二星期来未接来示,甚以为念. 兹阅及道光二十年<俄罗斯进呈书籍目录>有算书数种,兹抄上,请于参考完毕原纸见掷为荷. 此间日来阴雨,甚平静.兄处如何? 尊稿祖暅别传,因两星期来到外段勘工,未及抄出.一俟抄出,再行呈寄不误. 相似文献
18.
李俨、严敦杰往来书信(1940—1941年)(一) 总被引:1,自引:0,他引:1
科学史研究在中国已有近百年的历史,从学术史的角度回顾这段历史也日渐成为迫切的研究课题,为此目的,本刊特开辟史家通信专栏,希冀通过对史料的发掘和整理,推动对中国科学史学科史的研究。 相似文献
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本文从世界军事发展的必然趋势入手,深入分析我军当前科技人才匮乏、素质亟待提高,科技练兵科技含量不足和军事科研活动滞缓的机制及其文化成因,并提出管窥之见。 相似文献