Principal component analysis of binary data by iterated singular value decomposition

Leeuw, Jan de

doi:10.1016/j.csda.2004.07.010

Cited by 86 publications

(67 citation statements)

References 20 publications

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“…Although its linear convergence rate is necessarily slower than the golden standard of the Newton method, it has many applications in large scale optimization and is useful when high precision is not needed. Besides the MDS applications reviewed in this paper, majorization has been used in many other statistical techniques, such as, for example, support vector machines (Groenen, Nalbantov, Bioch, and C 2008) and logistic regression (De Leeuw 2006). It is our expectation that a decade from now majorization will be included in many nonlinear optimization textbooks.…”

Section: Discussionmentioning

confidence: 99%

Multidimensional Scaling by Majorization: A Review

Groenen¹,

Velden²

2016

J. Stat. Soft.

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A major breakthrough in the visualization of dissimilarities between pairs of objects was the formulation of the least-squares multidimensional scaling (MDS) model as defined by the Stress function. This function is quite flexible in that it allows possibly nonlinear transformations of the dissimilarities to be represented by distances between points in a low dimensional space. To obtain the visualization, the Stress function should be minimized over the coordinates of the points and the over the transformation. In a series of papers, Jan de Leeuw has made a significant contribution to majorization methods for the minimization of Stress in least-squares MDS. In this paper, we present a review of the majorization algorithm for MDS as implemented in the smacof package and related approaches. We present several illustrative examples and special cases.

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Section: Discussionmentioning

confidence: 99%

Multidimensional Scaling by Majorization: A Review

Groenen¹,

Velden²

2016

J. Stat. Soft.

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“…and the equality holds when x ¼ y [36,37]. This equation provides quadratic upper bounds for the first term of (3.5) at the tangent point y.…”

Section: Optimization Algorithmmentioning

confidence: 99%

Clustering of multivariate binary data with dimension reduction via L1-regularized likelihood maximization

Yamamoto

Hayashi

2015

Pattern Recognition

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a b s t r a c tClustering methods with dimension reduction have been receiving considerable wide interest in statistics lately and a lot of methods to simultaneously perform clustering and dimension reduction have been proposed. This work presents a novel procedure for simultaneously determining the optimal cluster structure for multivariate binary data and the subspace to represent that cluster structure. The method is based on a finite mixture model of multivariate Bernoulli distributions, and each component is assumed to have a low-dimensional representation of the cluster structure. This method can be considered as an extension of the traditional latent class analysis. Sparsity is introduced to the loading values, which produces the low-dimensional subspace, for enhanced interpretability and more stable extraction of the subspace. An EM-based algorithm is developed to efficiently solve the proposed optimization problem. We demonstrate the effectiveness of the proposed method by applying it to a simulation study and real datasets.

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“…where U and V are the orthogonal matrix, UAR m Â m , VAR n Â n , D is the diagonal matrix, D=[diag (s 1 , s 2 , y, s q ), O] or its transposition, and this is decided by m on or m Zn, DAR m Â n , O is the zero matrix, q=min(m, n), s 1 Zs 2 ZyZ s q 40. s i (i=1, 2, y, q) are called the singular values of matrix A. SVD method has been widely applied to many fields in recent years, such as data compression [1,2], system recognition [3], adaptive filter [4,5], principal component analysis (PCA) [6,7], noise reduction [8][9][10], faint signal extraction [11,12], machine condition monitoring [13] and so on. For example, Ahmed et al utilize SVD to compress the electrocardiogram (ECG) signal, their main idea is to transform the ECG signals to a rectangular matrix, compute its SVD, then discard the signals represented by the small singular values and only those signals represented by some big singular values are reserved so that ECG signal can be greatly compressed [1].…”

Section: Introductionmentioning

confidence: 99%