-
Notifications
You must be signed in to change notification settings - Fork 0
/
Copy pathmultivariate_analysis.html
514 lines (486 loc) · 21.1 KB
/
multivariate_analysis.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
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
<meta charset="utf-8">
<meta name="generator" content="quarto-1.3.340">
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
<meta name="author" content="Carmen Gómez Valenzuela">
<meta name="dcterms.date" content="2023-05-13">
<title>CGoDataScience - Multivariate Analyisis</title>
<style>
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
div.columns{display: flex; gap: min(4vw, 1.5em);}
div.column{flex: auto; overflow-x: auto;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
ul.task-list li input[type="checkbox"] {
width: 0.8em;
margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */
vertical-align: middle;
}
</style>
<script src="site_libs/quarto-nav/quarto-nav.js"></script>
<script src="site_libs/quarto-nav/headroom.min.js"></script>
<script src="site_libs/clipboard/clipboard.min.js"></script>
<script src="site_libs/quarto-search/autocomplete.umd.js"></script>
<script src="site_libs/quarto-search/fuse.min.js"></script>
<script src="site_libs/quarto-search/quarto-search.js"></script>
<meta name="quarto:offset" content="./">
<link href="./multivariate_analysis/1-Introduction.html" rel="next">
<script src="site_libs/quarto-html/quarto.js"></script>
<script src="site_libs/quarto-html/popper.min.js"></script>
<script src="site_libs/quarto-html/tippy.umd.min.js"></script>
<script src="site_libs/quarto-html/anchor.min.js"></script>
<link href="site_libs/quarto-html/tippy.css" rel="stylesheet">
<link href="site_libs/quarto-html/quarto-syntax-highlighting.css" rel="stylesheet" id="quarto-text-highlighting-styles">
<script src="site_libs/bootstrap/bootstrap.min.js"></script>
<link href="site_libs/bootstrap/bootstrap-icons.css" rel="stylesheet">
<link href="site_libs/bootstrap/bootstrap.min.css" rel="stylesheet" id="quarto-bootstrap" data-mode="light">
<script id="quarto-search-options" type="application/json">{
"location": "navbar",
"copy-button": false,
"collapse-after": 3,
"panel-placement": "end",
"type": "overlay",
"limit": 20,
"language": {
"search-no-results-text": "No results",
"search-matching-documents-text": "matching documents",
"search-copy-link-title": "Copy link to search",
"search-hide-matches-text": "Hide additional matches",
"search-more-match-text": "more match in this document",
"search-more-matches-text": "more matches in this document",
"search-clear-button-title": "Clear",
"search-detached-cancel-button-title": "Cancel",
"search-submit-button-title": "Submit"
}
}</script>
<link rel="stylesheet" href="styles.css">
</head>
<body class="nav-sidebar floating nav-fixed">
<div id="quarto-search-results"></div>
<header id="quarto-header" class="headroom fixed-top">
<nav class="navbar navbar-expand-lg navbar-dark ">
<div class="navbar-container container-fluid">
<div class="navbar-brand-container">
<a class="navbar-brand" href="./index.html">
<span class="navbar-title">CGoDataScience</span>
</a>
</div>
<div id="quarto-search" class="" title="Search"></div>
<button class="navbar-toggler" type="button" data-bs-toggle="collapse" data-bs-target="#navbarCollapse" aria-controls="navbarCollapse" aria-expanded="false" aria-label="Toggle navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
<span class="navbar-toggler-icon"></span>
</button>
<div class="collapse navbar-collapse" id="navbarCollapse">
<ul class="navbar-nav navbar-nav-scroll me-auto">
<li class="nav-item">
<a class="nav-link" href="./index.html" rel="" target="">
<span class="menu-text">Home</span></a>
</li>
<li class="nav-item">
<a class="nav-link" href="./portfolio.html" rel="" target="">
<span class="menu-text">Portfolio</span></a>
</li>
<li class="nav-item dropdown ">
<a class="nav-link dropdown-toggle" href="#" id="nav-menu-statistics" role="button" data-bs-toggle="dropdown" aria-expanded="false" rel="" target="">
<span class="menu-text">Statistics</span>
</a>
<ul class="dropdown-menu" aria-labelledby="nav-menu-statistics">
<li>
<a class="dropdown-item" href="./statistical_inference.html" rel="" target="">
<span class="dropdown-text">Statistical Inference</span></a>
</li>
<li>
<a class="dropdown-item" href="./regression.html" rel="" target="">
<span class="dropdown-text">Regression: Models and Methods</span></a>
</li>
<li>
<a class="dropdown-item" href="./multivariate_analysis.html" rel="" target="">
<span class="dropdown-text">Multivariate Analysis</span></a>
</li>
<li>
<a class="dropdown-item" href="./longitudinal_analysis.html" rel="" target="">
<span class="dropdown-text">Longitudinal data analysis</span></a>
</li>
</ul>
</li>
<li class="nav-item dropdown ">
<a class="nav-link dropdown-toggle" href="#" id="nav-menu-artificial-intelligence" role="button" data-bs-toggle="dropdown" aria-expanded="false" rel="" target="">
<span class="menu-text">Artificial Intelligence</span>
</a>
<ul class="dropdown-menu" aria-labelledby="nav-menu-artificial-intelligence">
<li>
<a class="dropdown-item" href="./machine_learning.html" rel="" target="">
<span class="dropdown-text">Machine Learning</span></a>
</li>
<li>
<a class="dropdown-item" href="./deep_learning.html" rel="" target="">
<span class="dropdown-text">Deep Learning</span></a>
</li>
<li>
<a class="dropdown-item" href="./automated_planning.html" rel="" target="">
<span class="dropdown-text">Automated planning</span></a>
</li>
</ul>
</li>
<li class="nav-item dropdown ">
<a class="nav-link dropdown-toggle" href="#" id="nav-menu-bioinformatics" role="button" data-bs-toggle="dropdown" aria-expanded="false" rel="" target="">
<span class="menu-text">Bioinformatics</span>
</a>
<ul class="dropdown-menu" aria-labelledby="nav-menu-bioinformatics">
<li>
<a class="dropdown-item" href="./molecular_biology.html" rel="" target="">
<span class="dropdown-text">Molecular biology</span></a>
</li>
<li>
<a class="dropdown-item" href="./analysis_of_omics_data.html" rel="" target="">
<span class="dropdown-text">Analysis of omics data</span></a>
</li>
<li>
<a class="dropdown-item" href="./computational_genomics.html" rel="" target="">
<span class="dropdown-text">Computational genomics</span></a>
</li>
</ul>
</li>
<li class="nav-item">
<a class="nav-link" href="./blog.html" rel="" target="">
<span class="menu-text">Blog</span></a>
</li>
</ul>
<div class="quarto-navbar-tools ms-auto">
<a href="https://www.linkedin.com/in/cgomezvalenzuela/" title="" class="quarto-navigation-tool px-1" aria-label=""><i class="bi bi-linkedin"></i></a>
<div class="dropdown">
<a href="" title="" id="quarto-navigation-tool-dropdown-0" class="quarto-navigation-tool dropdown-toggle px-1" data-bs-toggle="dropdown" aria-expanded="false" aria-label=""><i class="bi bi-github"></i></a>
<ul class="dropdown-menu dropdown-menu-end" aria-labelledby="quarto-navigation-tool-dropdown-0">
<li>
<a class="dropdown-item quarto-navbar-tools ms-auto-item" href="https://code.com">
Source Code
</a>
</li>
<li>
<a class="dropdown-item quarto-navbar-tools ms-auto-item" href="https://bugs.com">
Report a Bug
</a>
</li>
</ul>
</div>
</div>
</div> <!-- /navcollapse -->
</div> <!-- /container-fluid -->
</nav>
<nav class="quarto-secondary-nav">
<div class="container-fluid d-flex">
<button type="button" class="quarto-btn-toggle btn" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
<i class="bi bi-layout-text-sidebar-reverse"></i>
</button>
<nav class="quarto-page-breadcrumbs" aria-label="breadcrumb"><ol class="breadcrumb"><li class="breadcrumb-item"><a href="./multivariate_analysis.html">Multivariate Analyisis</a></li></ol></nav>
<a class="flex-grow-1" role="button" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass" aria-controls="quarto-sidebar" aria-expanded="false" aria-label="Toggle sidebar navigation" onclick="if (window.quartoToggleHeadroom) { window.quartoToggleHeadroom(); }">
</a>
</div>
</nav>
</header>
<!-- content -->
<div id="quarto-content" class="quarto-container page-columns page-rows-contents page-layout-article page-navbar">
<!-- sidebar -->
<nav id="quarto-sidebar" class="sidebar collapse collapse-horizontal sidebar-navigation floating overflow-auto">
<div class="sidebar-menu-container">
<ul class="list-unstyled mt-1">
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./multivariate_analysis.html" class="sidebar-item-text sidebar-link active">
<span class="menu-text">Multivariate Analyisis</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./multivariate_analysis/1-Introduction.html" class="sidebar-item-text sidebar-link">
<span class="menu-text">1. Introduction.</span></a>
</div>
</li>
<li class="sidebar-item">
<div class="sidebar-item-container">
<a href="./multivariate_analysis/2- Principal_Components_Analysis.html" class="sidebar-item-text sidebar-link">
<span class="menu-text">2. Principal Component Analysis</span></a>
</div>
</li>
</ul>
</div>
</nav>
<div id="quarto-sidebar-glass" data-bs-toggle="collapse" data-bs-target="#quarto-sidebar,#quarto-sidebar-glass"></div>
<!-- margin-sidebar -->
<div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
</div>
<!-- main -->
<main class="content" id="quarto-document-content">
<header id="title-block-header" class="quarto-title-block default">
<div class="quarto-title">
<h1 class="title">Multivariate Analyisis</h1>
<div class="quarto-categories">
<div class="quarto-category">Multivariate Analysis</div>
</div>
</div>
<div class="quarto-title-meta">
<div>
<div class="quarto-title-meta-heading">Author</div>
<div class="quarto-title-meta-contents">
<p>Carmen Gómez Valenzuela </p>
</div>
</div>
<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">May 13, 2023</p>
</div>
</div>
</div>
</header>
<p>Welcome to my notes on multivariate statistical analysis! As a data scientist, I have found that understanding and applying multivariate statistical techniques is essential for extracting insights from complex datasets. These notes are my personal collection of key concepts, techniques, and practical applications that I have learned and used over the years.</p>
<p>My goal in creating these notes is to provide a useful resource for myself to review and reference in the future, as well as to share my knowledge with others who are interested in learning about multivariate statistical analysis. Whether you are just starting out in the field or have years of experience, I hope you will find these notes to be a valuable reference and a source of inspiration for your own work.</p>
<p>Throughout these notes, I will cover a range of topics related to multivariate statistical analysis, including exploratory data analysis, principal component analysis, factor analysis, clustering, discriminant analysis, and more. I will provide clear explanations of key concepts, step-by-step instructions for implementing techniques in Python, and real-world examples to demonstrate how these techniques can be used to extract insights from complex datasets.</p>
<p>I invite you to join me on this journey through the world of multivariate statistical analysis. Let’s explore together how these powerful techniques can be used to unlock the hidden patterns and relationships in data, and turn raw data into actionable insights.</p>
<p>Lastly, I would like to add that if you find any errors, please do not hesitate to contact me through LinkedIn. I would be very grateful for your feedback.</p>
</main> <!-- /main -->
<script id="quarto-html-after-body" type="application/javascript">
window.document.addEventListener("DOMContentLoaded", function (event) {
const toggleBodyColorMode = (bsSheetEl) => {
const mode = bsSheetEl.getAttribute("data-mode");
const bodyEl = window.document.querySelector("body");
if (mode === "dark") {
bodyEl.classList.add("quarto-dark");
bodyEl.classList.remove("quarto-light");
} else {
bodyEl.classList.add("quarto-light");
bodyEl.classList.remove("quarto-dark");
}
}
const toggleBodyColorPrimary = () => {
const bsSheetEl = window.document.querySelector("link#quarto-bootstrap");
if (bsSheetEl) {
toggleBodyColorMode(bsSheetEl);
}
}
toggleBodyColorPrimary();
const icon = "";
const anchorJS = new window.AnchorJS();
anchorJS.options = {
placement: 'right',
icon: icon
};
anchorJS.add('.anchored');
const isCodeAnnotation = (el) => {
for (const clz of el.classList) {
if (clz.startsWith('code-annotation-')) {
return true;
}
}
return false;
}
const clipboard = new window.ClipboardJS('.code-copy-button', {
text: function(trigger) {
const codeEl = trigger.previousElementSibling.cloneNode(true);
for (const childEl of codeEl.children) {
if (isCodeAnnotation(childEl)) {
childEl.remove();
}
}
return codeEl.innerText;
}
});
clipboard.on('success', function(e) {
// button target
const button = e.trigger;
// don't keep focus
button.blur();
// flash "checked"
button.classList.add('code-copy-button-checked');
var currentTitle = button.getAttribute("title");
button.setAttribute("title", "Copied!");
let tooltip;
if (window.bootstrap) {
button.setAttribute("data-bs-toggle", "tooltip");
button.setAttribute("data-bs-placement", "left");
button.setAttribute("data-bs-title", "Copied!");
tooltip = new bootstrap.Tooltip(button,
{ trigger: "manual",
customClass: "code-copy-button-tooltip",
offset: [0, -8]});
tooltip.show();
}
setTimeout(function() {
if (tooltip) {
tooltip.hide();
button.removeAttribute("data-bs-title");
button.removeAttribute("data-bs-toggle");
button.removeAttribute("data-bs-placement");
}
button.setAttribute("title", currentTitle);
button.classList.remove('code-copy-button-checked');
}, 1000);
// clear code selection
e.clearSelection();
});
function tippyHover(el, contentFn) {
const config = {
allowHTML: true,
content: contentFn,
maxWidth: 500,
delay: 100,
arrow: false,
appendTo: function(el) {
return el.parentElement;
},
interactive: true,
interactiveBorder: 10,
theme: 'quarto',
placement: 'bottom-start'
};
window.tippy(el, config);
}
const noterefs = window.document.querySelectorAll('a[role="doc-noteref"]');
for (var i=0; i<noterefs.length; i++) {
const ref = noterefs[i];
tippyHover(ref, function() {
// use id or data attribute instead here
let href = ref.getAttribute('data-footnote-href') || ref.getAttribute('href');
try { href = new URL(href).hash; } catch {}
const id = href.replace(/^#\/?/, "");
const note = window.document.getElementById(id);
return note.innerHTML;
});
}
let selectedAnnoteEl;
const selectorForAnnotation = ( cell, annotation) => {
let cellAttr = 'data-code-cell="' + cell + '"';
let lineAttr = 'data-code-annotation="' + annotation + '"';
const selector = 'span[' + cellAttr + '][' + lineAttr + ']';
return selector;
}
const selectCodeLines = (annoteEl) => {
const doc = window.document;
const targetCell = annoteEl.getAttribute("data-target-cell");
const targetAnnotation = annoteEl.getAttribute("data-target-annotation");
const annoteSpan = window.document.querySelector(selectorForAnnotation(targetCell, targetAnnotation));
const lines = annoteSpan.getAttribute("data-code-lines").split(",");
const lineIds = lines.map((line) => {
return targetCell + "-" + line;
})
let top = null;
let height = null;
let parent = null;
if (lineIds.length > 0) {
//compute the position of the single el (top and bottom and make a div)
const el = window.document.getElementById(lineIds[0]);
top = el.offsetTop;
height = el.offsetHeight;
parent = el.parentElement.parentElement;
if (lineIds.length > 1) {
const lastEl = window.document.getElementById(lineIds[lineIds.length - 1]);
const bottom = lastEl.offsetTop + lastEl.offsetHeight;
height = bottom - top;
}
if (top !== null && height !== null && parent !== null) {
// cook up a div (if necessary) and position it
let div = window.document.getElementById("code-annotation-line-highlight");
if (div === null) {
div = window.document.createElement("div");
div.setAttribute("id", "code-annotation-line-highlight");
div.style.position = 'absolute';
parent.appendChild(div);
}
div.style.top = top - 2 + "px";
div.style.height = height + 4 + "px";
let gutterDiv = window.document.getElementById("code-annotation-line-highlight-gutter");
if (gutterDiv === null) {
gutterDiv = window.document.createElement("div");
gutterDiv.setAttribute("id", "code-annotation-line-highlight-gutter");
gutterDiv.style.position = 'absolute';
const codeCell = window.document.getElementById(targetCell);
const gutter = codeCell.querySelector('.code-annotation-gutter');
gutter.appendChild(gutterDiv);
}
gutterDiv.style.top = top - 2 + "px";
gutterDiv.style.height = height + 4 + "px";
}
selectedAnnoteEl = annoteEl;
}
};
const unselectCodeLines = () => {
const elementsIds = ["code-annotation-line-highlight", "code-annotation-line-highlight-gutter"];
elementsIds.forEach((elId) => {
const div = window.document.getElementById(elId);
if (div) {
div.remove();
}
});
selectedAnnoteEl = undefined;
};
// Attach click handler to the DT
const annoteDls = window.document.querySelectorAll('dt[data-target-cell]');
for (const annoteDlNode of annoteDls) {
annoteDlNode.addEventListener('click', (event) => {
const clickedEl = event.target;
if (clickedEl !== selectedAnnoteEl) {
unselectCodeLines();
const activeEl = window.document.querySelector('dt[data-target-cell].code-annotation-active');
if (activeEl) {
activeEl.classList.remove('code-annotation-active');
}
selectCodeLines(clickedEl);
clickedEl.classList.add('code-annotation-active');
} else {
// Unselect the line
unselectCodeLines();
clickedEl.classList.remove('code-annotation-active');
}
});
}
const findCites = (el) => {
const parentEl = el.parentElement;
if (parentEl) {
const cites = parentEl.dataset.cites;
if (cites) {
return {
el,
cites: cites.split(' ')
};
} else {
return findCites(el.parentElement)
}
} else {
return undefined;
}
};
var bibliorefs = window.document.querySelectorAll('a[role="doc-biblioref"]');
for (var i=0; i<bibliorefs.length; i++) {
const ref = bibliorefs[i];
const citeInfo = findCites(ref);
if (citeInfo) {
tippyHover(citeInfo.el, function() {
var popup = window.document.createElement('div');
citeInfo.cites.forEach(function(cite) {
var citeDiv = window.document.createElement('div');
citeDiv.classList.add('hanging-indent');
citeDiv.classList.add('csl-entry');
var biblioDiv = window.document.getElementById('ref-' + cite);
if (biblioDiv) {
citeDiv.innerHTML = biblioDiv.innerHTML;
}
popup.appendChild(citeDiv);
});
return popup.innerHTML;
});
}
}
});
</script>
<nav class="page-navigation">
<div class="nav-page nav-page-previous">
</div>
<div class="nav-page nav-page-next">
<a href="./multivariate_analysis/1-Introduction.html" class="pagination-link">
<span class="nav-page-text">1. Introduction.</span> <i class="bi bi-arrow-right-short"></i>
</a>
</div>
</nav>
</div> <!-- /content -->
</body></html>