[工學]第8章主成分分析-wenkub

　

【正文】 2) X3 (Variable 3) PCA – Bi Plots PC1 PC2 Samples Scores Plot By default, after doing PCA on The Unscrambler, it is present in the top left corner PC1 PC2 Loadings Plot By default, after doing PCA on The Unscrambler, it is present in the top right corner X1 (Variable 1) X2 (Variable 2) X3 (Variable 3) PCA – Bi Plots PC1 PC2 Samples Scores Plot By default, after doing PCA on The Unscrambler, it is present in the top left corner PC1 PC2 Loadings Plot By default, after doing PCA on The Unscrambler, it is present in the top right corner X1 (Variable 1) X2 (Variable 2) X3 (Variable 3) PC1 PC2 Variable 1 Variable 2 Variable 3 Bi Plot The Unscrambler can display both Samples and Variables in the same plot for easy interpretation + Principal Component Analysis (PCA) Interpretation of Plots The Viewer displays the PCA Overview. The PCA Overview contains 4 of the many predefined plots that are available. PCA Overview High levels of Redness and Colour indicate low levels of Thickness, and vice versa Correlation Loadings plot: positive and negative relationships (correlations) High levels of R. Smell and R. Flavour indicate low levels of OffFlavour, and vice versa Loadings Plot (top right plot) Correlation Loadings plot: variables with no relationship Colour and Raspberry properties are not correlated: they are fully independent of each other. A high redness does not indicate anything on the raspberry properties of the jam Loadings Plot (top right plot) 2101233 2 1 0 1 2 3 4 R E S U L T 3 , X e x p l : 5 8 % , 2 8 % C 1 _ H 1C 2 _ H 1C 3 _ H 1C 4 _ H 1C 1 _ H 3C 2 _ H 3C 3 _ H 3C 4 _ H 3C 1 _ H 2C 2 _ H 2C 3 _ H 2C 4 _ H 2P C 1P C 2 S co r e sThe Score plot shows which products are similar/dissimilar Products close together on the map are similar on the first 2 ponents Scores Plot (top left plot) 2101233 2 1 0 1 2 3 4 R E S U L T 3 , X e x p l : 5 8 % , 2 8 % C 1 _ H 1C 2 _ H 1C 3 _ H 1C 4 _ H 1C 1 _ H 3C 2 _ H 3C 3 _ H 3C 4 _ H 3C 1 _ H 2C 2 _ H 2C 3 _ H 2C 4 _ H 2P C 1P C 2 S co r e sThe Score plot shows which products are similar/dissimilar A sample close to the center is an average sample Scores Plot (top left plot) 1 . 0 0 . 500 . 51 . 0 0 . 8 0 . 6 0 . 4 0 . 2 0 0 . 2 0 . 4 0 . 6 0 . 8 1 . 0 R E S U L T 3 , X e x p l : 5 8 % , 2 8 % C 1 _ H 1C 2 _ H 1C 3 _ H 1C 4 _ H 1C 1 _ H 3C 2 _ H 3C 3 _ H 3C 4 _ H 3C 1 _ H 2C 2 _ H 2C 3 _ H 2C 4 _ H 2R E D N E S SC O L O U RS H I N I N E SR . S M E L LR . F L A VS W E E T N E SS O U R N E S SB I T T E R N EO F F F L A VJ U I C I N E ST H I C K N E SC H E W . R E SP C 1P C 2 B i p l o tThe Biplot relates the position of the samples to their characteristics These products have high levels of Redness, Colour and Off Flavour BiPlot Scores and Loadings on same plot What is Multivariate Analysis ? Multivariate analysis is the best way to summarize a data tables with many variables by creating a few new variables containing most of the information. These new variables are then used for problem solving and display, ., classification, relationships, control charts, and more. ? The new variables, the scores, denoted by t, are created as weighted linear binations of the original variables. Each observations has tvalues. ? PCA, the basic MV method, summarizes one data table. ? Plotting the scores (t’ s) gives an overview of the observations (objects) ? PLS summarizes simultaneously 2 data tables (X the predictor variables) and (Y the response variables) in order to develop a relationship between them ? PCA and PLS are called Projection methods What is a Projection? Reduction of dimensionality, model in latent variables ? Algebraically – Summarizes the information in the observations as a few new (latent) variables ? Geometrically – The swarm of points in a K dimensional space (K = number of variables) is approximated by a (hyper)plane and the points are projected on that plane. Notation Each obs has values of t (and u) – Each variable has values of p (and w and c) ? t: the X scores。 ?可以把第一和第二主成分的載荷點出一個二維圖以直觀地顯示它們如何解釋原來的變量的。 ? 比如 x1表示式中 y1的系數為 ， 這就是說第一主成分和數學變量的相關系數為 。 T o t a l V a r i a n c e E x p l a i n e d3 . 7 3 5 6 2 . 2 5 4 6 2 . 2 5 4 3 . 7 3 5 6 2 . 2 5 4 6 2 . 2 5 41 . 1 3 3 1 8 . 8 8 7 8 1 . 1 4 2 1 . 1 3 3 1 8 . 8 8 7 8 1 . 1 4 2. 4 5 7 7 . 6 1 9 8 8 . 7 6 1. 3 2 3 5 .