APL functions for interactive data analysis: Principal components analysis
نویسندگان
چکیده
منابع مشابه
Persian Handwriting Analysis Using Functional Principal Components
Principal components analysis is a well-known statistical method in dealing with large dependent data sets. It is also used in functional data for both purposes of data reduction as well as variation representation. On the other hand "handwriting" is one of the objects, studied in various statistical fields like pattern recognition and shape analysis. Considering time as the argument,...
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Principal component analysis (PCA) is a popular dimension reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-b...
متن کاملOnline Principal Components Analysis
We consider the online version of the well known Principal Component Analysis (PCA) problem. In standard PCA, the input to the problem is a set of ddimensional vectors X = [x1, . . . ,xn] and a target dimension k < d; the output is a set of k-dimensional vectors Y = [y1, . . . ,yn] that minimize the reconstruction error: minΦ ∑ i ‖xi − Φyi‖2. Here, Φ ∈ Rd×k is restricted to being isometric. The...
متن کاملPrincipal Components Analysis
Derivation of PCA I: For a set of d-dimensional data vectors {x}i=1, the principal axes {e}qj=1 are those orthonormal axes onto which the retained variance under projection is maximal. It can be shown that the vectors ej are given by the q dominant eigenvectors of the sample covariance matrix S, such that Sej = λjej . The q principal components of the observed vector xi are given by the vector ...
متن کاملPrincipal Components Analysis
Let X be an n× p matrix whose rows are iid random vectors Xi· with mean μ ∈ R and covariance Σ ∈ Sp+— for example, they might be (Xi·) iid ∼ No(μ,Σ). For many problems (such as multivariate regression of some Y on X) we might wish to reduce the dimension p of these rows. For example, if we have a vector of p = 1000 possible explanatory variables about each individual, we may hope that a small s...
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ژورنال
عنوان ژورنال: Behavior Research Methods & Instrumentation
سال: 1981
ISSN: 1554-351X,1554-3528
DOI: 10.3758/bf03202083