/
session2.html
353 lines (287 loc) · 8.98 KB
/
session2.html
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
<!DOCTYPE html>
<html lang="" xml:lang="">
<head>
<title>Training in ade4 in R - Module I: Basic methods</title>
<meta charset="utf-8" />
<meta name="author" content="Stéphane Dray" />
<meta name="date" content="2023-12-06" />
<script src="libs/header-attrs/header-attrs.js"></script>
<link rel="stylesheet" href="custom.css" type="text/css" />
<link rel="stylesheet" href="xaringan-themer.css" type="text/css" />
</head>
<body>
<textarea id="source">
class: center, middle, inverse, title-slide
.title[
# Training in ade4 in R - Module I: Basic methods
]
.subtitle[
## Principal component analysis
]
.author[
### Stéphane Dray
]
.date[
### 2023-12-06
]
---
$$
%center text/code
\newcommand{\bcenter}{\begin{center}}
\newcommand{\ecenter}{\end{center}}
$$
$$
\newcommand{\bm}[1]{\boldsymbol{\mathbf{#1}}}
\newcommand{\tr}{\hspace{-0.05cm}^{\top}\hspace{-0.05cm}}% transpose d'une matrice
\newcommand{\mb}[1]{\mathbf{#1}}
\newcommand{\pt}{\mathsmaller \bullet}% petit point pour les indices
$$
$$
\newcommand{\triplet}[3]{
% pour ecrire un triplet dans le texte
$\left ( #1, #2, #3 \right )$
}
$$
$$
\newcommand{\sqnorm}[2]{
%norme au carré
\lVert #1 \rVert^2_{#2}
}
$$
$$
\newcommand{\norm}[2]{
%norme
\lVert #1 \rVert_{#2}
}
$$
---
# Data
We will analyze the `doubs` data set (see `?doubs`)
```r
library(ade4)
library(adegraphics)
data(doubs)
names(doubs)
```
```
## [1] "env" "fish" "xy" "species"
```
```r
names(doubs$env)
```
```
## [1] "dfs" "alt" "slo" "flo" "pH" "har" "pho" "nit" "amm" "oxy" "bdo"
```
---
# Some general information
```r
env <- doubs$env
apply(env, 2, range)
```
```
## dfs alt slo flo pH har pho nit amm oxy bdo
## [1,] 3 172 1.099 84 77 40 1 15 0 41 13
## [2,] 4530 934 6.176 6900 86 110 422 620 180 124 167
```
---
# Display the data
```r
table.value(scale(env), symbol = "circle")
```
<img src="fig/unnamed-chunk-3-1.svg" style="display: block; margin: auto;" />
---
# Spatial information
```r
xy <- doubs$xy
sl1 <- s.label(xy, ppoints.cex = 0, plot = FALSE)
st1 <- s.traject(xy, ppoints.cex = 0, plabels.cex = 0,
plot = FALSE)
s1 <- superpose(st1, sl1, plot = TRUE)
```
<img src="fig/unnamed-chunk-4-1.svg" width="40%" style="display: block; margin: auto;" />
---
# Map one variable
```r
s.value(xy, doubs$env[, 1])
```
<img src="fig/unnamed-chunk-5-1.svg" style="display: block; margin: auto;" />
---
# Map the different variables
```r
mypal <- colorRampPalette(c("#EDF8FB", "#006D2C"))
s.value(xy, doubs$env, pgrid.draw = FALSE, porigin.draw = FALSE,
plegend.drawKey = FALSE, psub.cex = 2, method = "color",
symbol = "circle", ppalette.quanti = mypal, ppoints.cex = 0.5)
```
<img src="fig/unnamed-chunk-6-1.svg" style="display: block; margin: auto;" />
---
# Perform the PCA
Must we scale or not the data?
---
# How many axes?
Choosing the number of dimensions that can be interpreted is an open question. Several methods have been proposed in the literature. Using your eyes to detect breaks in eigenvalue decrease is probably the best method.
However, `ade4` proposes one method developed for the case of PCA on scaled data. You can try it:
```r
testdim(pca1)$nb.cor
```
```
## [1] 2
```
---
# Display eigenvalues
* Make a barplot of eigenvalues
* Compute the percentage of variation explained by each dimension
* Compare to the results obtained by the function `summary`
---
# Graphical representation of PCA results
* Plot the variable scores with a correlation circle
* Plot the site scores on a separate plot
* Interpret
---
# PCA scores on the geographical map
* Draw maps of PCA scores on the first two axes
* Interpret the maps to describe the environmental structure of the river
---
# A look to variables
* Compute the correlations between original variables and PCA axes
* In which element of PCA outputs are stored these values
---
# A look to variables
The generic function `score` provides an optimal representation of the maximized criteria
```r
score(pca1)
```
<img src="fig/unnamed-chunk-13-1.svg" style="display: block; margin: auto;" />
</textarea>
<style data-target="print-only">@media screen {.remark-slide-container{display:block;}.remark-slide-scaler{box-shadow:none;}}</style>
<script src="https://remarkjs.com/downloads/remark-latest.min.js"></script>
<script>var slideshow = remark.create({
"highlightStyle": "github",
"highlightLines": true,
"countIncrementalSlides": false
});
if (window.HTMLWidgets) slideshow.on('afterShowSlide', function (slide) {
window.dispatchEvent(new Event('resize'));
});
(function(d) {
var s = d.createElement("style"), r = d.querySelector(".remark-slide-scaler");
if (!r) return;
s.type = "text/css"; s.innerHTML = "@page {size: " + r.style.width + " " + r.style.height +"; }";
d.head.appendChild(s);
})(document);
(function(d) {
var el = d.getElementsByClassName("remark-slides-area");
if (!el) return;
var slide, slides = slideshow.getSlides(), els = el[0].children;
for (var i = 1; i < slides.length; i++) {
slide = slides[i];
if (slide.properties.continued === "true" || slide.properties.count === "false") {
els[i - 1].className += ' has-continuation';
}
}
var s = d.createElement("style");
s.type = "text/css"; s.innerHTML = "@media print { .has-continuation { display: none; } }";
d.head.appendChild(s);
})(document);
// delete the temporary CSS (for displaying all slides initially) when the user
// starts to view slides
(function() {
var deleted = false;
slideshow.on('beforeShowSlide', function(slide) {
if (deleted) return;
var sheets = document.styleSheets, node;
for (var i = 0; i < sheets.length; i++) {
node = sheets[i].ownerNode;
if (node.dataset["target"] !== "print-only") continue;
node.parentNode.removeChild(node);
}
deleted = true;
});
})();
// add `data-at-shortcutkeys` attribute to <body> to resolve conflicts with JAWS
// screen reader (see PR #262)
(function(d) {
let res = {};
d.querySelectorAll('.remark-help-content table tr').forEach(tr => {
const t = tr.querySelector('td:nth-child(2)').innerText;
tr.querySelectorAll('td:first-child .key').forEach(key => {
const k = key.innerText;
if (/^[a-z]$/.test(k)) res[k] = t; // must be a single letter (key)
});
});
d.body.setAttribute('data-at-shortcutkeys', JSON.stringify(res));
})(document);
(function() {
"use strict"
// Replace <script> tags in slides area to make them executable
var scripts = document.querySelectorAll(
'.remark-slides-area .remark-slide-container script'
);
if (!scripts.length) return;
for (var i = 0; i < scripts.length; i++) {
var s = document.createElement('script');
var code = document.createTextNode(scripts[i].textContent);
s.appendChild(code);
var scriptAttrs = scripts[i].attributes;
for (var j = 0; j < scriptAttrs.length; j++) {
s.setAttribute(scriptAttrs[j].name, scriptAttrs[j].value);
}
scripts[i].parentElement.replaceChild(s, scripts[i]);
}
})();
(function() {
var links = document.getElementsByTagName('a');
for (var i = 0; i < links.length; i++) {
if (/^(https?:)?\/\//.test(links[i].getAttribute('href'))) {
links[i].target = '_blank';
}
}
})();
// adds .remark-code-has-line-highlighted class to <pre> parent elements
// of code chunks containing highlighted lines with class .remark-code-line-highlighted
(function(d) {
const hlines = d.querySelectorAll('.remark-code-line-highlighted');
const preParents = [];
const findPreParent = function(line, p = 0) {
if (p > 1) return null; // traverse up no further than grandparent
const el = line.parentElement;
return el.tagName === "PRE" ? el : findPreParent(el, ++p);
};
for (let line of hlines) {
let pre = findPreParent(line);
if (pre && !preParents.includes(pre)) preParents.push(pre);
}
preParents.forEach(p => p.classList.add("remark-code-has-line-highlighted"));
})(document);</script>
<script>
slideshow._releaseMath = function(el) {
var i, text, code, codes = el.getElementsByTagName('code');
for (i = 0; i < codes.length;) {
code = codes[i];
if (code.parentNode.tagName !== 'PRE' && code.childElementCount === 0) {
text = code.textContent;
if (/^\\\((.|\s)+\\\)$/.test(text) || /^\\\[(.|\s)+\\\]$/.test(text) ||
/^\$\$(.|\s)+\$\$$/.test(text) ||
/^\\begin\{([^}]+)\}(.|\s)+\\end\{[^}]+\}$/.test(text)) {
code.outerHTML = code.innerHTML; // remove <code></code>
continue;
}
}
i++;
}
};
slideshow._releaseMath(document);
</script>
<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
(function () {
var script = document.createElement('script');
script.type = 'text/javascript';
script.src = 'https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-MML-AM_CHTML';
if (location.protocol !== 'file:' && /^https?:/.test(script.src))
script.src = script.src.replace(/^https?:/, '');
document.getElementsByTagName('head')[0].appendChild(script);
})();
</script>
</body>
</html>