Multiblock Data Fusion in Statistics and Machine Learning. Tormod Næs. Читать онлайн. Newlib. NEWLIB.NET

Автор: Tormod Næs
Издательство: John Wiley & Sons Limited
Серия:
Жанр произведения: Химия
Год издания: 0
isbn: 9781119600992
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decompositions (ED) or maximising covariance or correlations (MC).

      The first item (A) is used to organise the different chapters. Some methods can deal with data of different measurements scales (heterogeneous data) and some methods can only handle homogeneous data. The difference between the simultaneous and sequential method is explained in more detail in Chapter 2. Some methods are defined by a clear model and some methods are based on an algorithm. The already discussed topic of common and distinct variation is also a distinguishing and important feature of the methods and the sections in some of the chapters are organised according to this principle. Finally, there are different ways of estimating the parameters (weights, scores, loadings, etc.) of the multiblock models. This is also explained in more detail in Chapter 2.

A B C D E F
Section U S C HOM HET SEQ SIM MOD ALG C CD CLD LS ML ED MC
ASCA 6.1
ASCA+ 6.1.3
LiMM-PCA 6.1.3
MSCA 6.2
PE-ASCA 6.3

      1.10 Notation and Terminology

xa scalar
xcolumn vector: bold lowercase
Xmatrix: bold uppercase
Xttranspose of X
X_three-way array: bold uppercase underlined
m = 1,…, Mindex for block
im = 1,…, Imindex for first way (e.g., sample) in block m (not shared first way)
i = 1,…, Iindex for first shared way of blocks
jm = 1,…, Jmindex for second way (e.g., variable) in block m (not shared second way)
j = 1,…, Jindex for second shared way of blocks
r = 1,…, Rindex for latent variables/principal components
Rmatrix used to compute scores for PLS
Xmblock m
xmii-th row of Xm (a column vector)
xmjj-th column of Xm (a column vector)
Wmatrix of weights
ILidentity matrix of size L×L
Tscore matrix
Ploading matrix
E,Fmatrices of residuals
1Lcolumn vector of ones of length L
diag(D)column vector containing the diagonal of D
Kronecker product
Khatri–Rao product (column-wise Kronecker product)
*Hadamard or element-wise product
Direct sum of spaces

      When