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# DAL ToolBox
# version 1.0.777

source("https://raw.githubusercontent.com/cefet-rj-dal/daltoolbox/main/jupyter.R")

#loading DAL
load_library("daltoolbox") 

#for ploting
load_library("ggplot2")
load_library("dplyr")

Loading required package: daltoolbox

Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 


Attaching package: ‘daltoolbox’


The following object is masked from ‘package:base’:

    transform


Loading required package: ggplot2

Loading required package: dplyr


Attaching package: ‘dplyr’


The following objects are masked from ‘package:stats’:

    filter, lag


The following objects are masked from ‘package:base’:

    intersect, setdiff, setequal, union

In [2]:

wine <- get(load(url("https://raw.githubusercontent.com/cefet-rj-dal/daltoolbox/main/wine.RData")))
head(wine)

A data.frame: 6 × 14
	X1	X14.23	X1.71	X2.43	X15.6	X127	X2.8	X3.06	X.28	X2.29	X5.64	X1.04	X3.92	X1065
	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<int>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<dbl>	<int>
1	1	13.20	1.78	2.14	11.2	100	2.65	2.76	0.26	1.28	4.38	1.05	3.40	1050
2	1	13.16	2.36	2.67	18.6	101	2.80	3.24	0.30	2.81	5.68	1.03	3.17	1185
3	1	14.37	1.95	2.50	16.8	113	3.85	3.49	0.24	2.18	7.80	0.86	3.45	1480
4	1	13.24	2.59	2.87	21.0	118	2.80	2.69	0.39	1.82	4.32	1.04	2.93	735
5	1	14.20	1.76	2.45	15.2	112	3.27	3.39	0.34	1.97	6.75	1.05	2.85	1450
6	1	14.39	1.87	2.45	14.6	96	2.50	2.52	0.30	1.98	5.25	1.02	3.58	1290

Example: PCA components¶

Cummulative variance of PCA: First dimensions have high variance. However, adding more dimensions does not bring much benefit in terms of cummulative variance. The goal is to establish a trade-off.

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pca_res = prcomp(wine[,2:ncol(wine)], center=TRUE, scale.=TRUE)
y <- cumsum(pca_res$sdev^2/sum(pca_res$sdev^2))
x <- 1:length(y)

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dat <- data.frame(x, value = y, variable = "PCA")
dat$variable <- as.factor(dat$variable)
head(dat)

A data.frame: 6 × 3
	x	value	variable
	<int>	<dbl>	<fct>
1	1	0.3598307	PCA
2	2	0.5522435	PCA
3	3	0.6640381	PCA
4	4	0.7351492	PCA
5	5	0.8014366	PCA
6	6	0.8510403	PCA

In [5]:

grf <- plot_scatter(dat, label_x = "dimensions", label_y = "cumulative variance", colors="black") + 
    theme(text = element_text(size=16))
plot(grf)

Minimum curvature¶

If the curve is increasing, use minimum curvature analysis. It brings a trade-off between having lower x values (with not so high y values) and having higher x values (not having to much increase in y values).

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myfit <- fit_curvature_min()
res <- transform(myfit, y)
head(res)

A data.frame: 1 × 3
	x	y	yfit
	<int>	<dbl>	<dbl>
1	6	0.8510403	-1.819591e-08

In [7]:

plot(grf + geom_vline(xintercept = res$x, linetype="dashed", color = "red", size=0.5))

Warning message:
“Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
ℹ Please use `linewidth` instead.”

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