我有一个小矩阵+-100点/值，测试结果和它们彼此之间的距离(0- 10,10是最接近的):http://vis.arcs.cz.
我想在2D中可视化它，以便快速找到一组接近的值。所以我需要处理这个矩阵，得到二维中点的坐标。
方法可能是多维缩放，但我没能找到一个算法，库或扩展，也没有使用数学公式到PHP代码。
我最近两天在谷歌上搜索，最接近的结果是http://www.php.net/manual/en/lapack.leastsquaresbysvd.php - ?(作为新手不能分享更多链接)
我将感谢任何适用于php项目的解决方案(在c++中编译MathLab代码…)
index.php:
<?php
require("data.php");
require("Mds.php");
$mds = new Mds();
$mds->prepareData($data);
//cislo udava pocet iteraci algoritmu,
//idealne by melo mit hodnotu pocetUzlu na druhou, prakticky muze byt o dost mensi, 5 az 10 krat pocet uzlu.
$mds->scale(100);
//mira splneni podminek - vraci cislo < mensi nez 1. Cim blizsi k 1, tim lepe vyhovuji vzdalenosti
//z vypocteneho rozlozeni zadanym vzdalenostem.
//v nemetrickych datech ovsem dochazi rychle k poklesu az do zapornych hodnot, protoze ve 2D neexistuje
//pro nektere body zadne spravne misto.
echo $mds->getRSquared();
?>
<!DOCTYPE HTML>
<html>
<head>
<script type="text/javascript" src="http://canvasjs.com/assets/script/canvasjs.min.js"></script>
<script type="text/javascript">
window.onload = function () {
var chart = new CanvasJS.Chart("chartContainer",
{
title:{
text: "MDS",
fontFamily: "arial black",
fontColor: "black"
},
axisX: {
title:"",
titleFontFamily: "arial"
},
axisY:{
title: "",
titleFontFamily: "arial",
titleFontSize: 12
},
data: [
{
type: "scatter",
toolTipContent: "<span style='"'color: {color};'"'><strong>{name}</strong></span> x: {y}, y: {y}",
dataPoints:
<?php
echo $mds->printCoords('{x: %X, y: %Y, name: "%LABEL"}');
?>
}]
});
chart.render();
}
</script>
</head>
<body>
<div id="chartContainer" style="height: 600px; width: 600px;">
</div>
<a href="mds.zip">mds.zip</a>
</body>
</html>
data.php:
$data = array(
array ("Jablko", "Voda", 2),
array("Jablko", "Ohen", 7),
array("Jablko", "Cervena", 3),
array("Jablko", "Zelena", 2),
array("Voda", "Ohen", 8),
array("Voda", "Cervena", 8),
array("Voda", "Zelena", 2),
array("Ohen", "Cervena", 1),
array("Ohen", "Zelena", 5),
array("Cervena", "Zelena", 3)
);
Mds.php:
<?php
class Mds {
//node - pole tvaru [[x, y, label], ...]
public $nodes = array();
//tvaru [source][target]=distance
public $givenDistances = array();
public $currentDistances = array();
public function prepareData($data) {
$nodesMap = array();
$xxxx = 10000;
$xxx= 1000;
// $xxxx = 5000;
// $xxx = 600;
foreach($data as $link) {
$source = $link[0];
$target = $link[1];
if(!isset($nodesMap[$source])) {
$nodesMap[$source] = true;
$this->nodes[]=array((float) rand(1,$xxxx) / $xxx, (float) rand(1,$xxxx) / $xxx, $source);
}
if(!isset($nodesMap[$target])) {
$nodesMap[$target] = true;
$this->nodes[]= array((float) rand(1,$xxxx) / $xxx, (float) rand(1,$xxxx) / $xxx, $target);
}
}
//vytvori matici pro ulozeni vzdalenosti
foreach($this->nodes as $node) {
$this->givenDistances[$node[2]] = array();
$this->currentDistances[$node[2]] = array();
}
foreach($data as $link) {
$source = $link[0];
$target = $link[1];
$distance = $link[2];
$this->givenDistances[$source][$target] = $distance;
$this->givenDistances[$target][$source] = $distance;
}
}
protected function countCurrentDistances() {
$mean = 0;
$i = 0;
foreach($this->nodes as $nodeA) {
foreach($this->nodes as $nodeB) {
$dist = sqrt(($nodeB[0]-$nodeA[0])*($nodeB[0]-$nodeA[0]) + ($nodeB[1]-$nodeA[1])*($nodeB[1]-$nodeA[1]));
$this->currentDistances[$nodeA[2]][$nodeB[2]] = $dist;
if($nodeA[2]!==$nodeB[2]) {
$mean += $this->givenDistances[$nodeA[2]][$nodeB[2]];
}
}
}
// echo "<pre>";
// var_dump($this->currentDistances);
// echo "</pre>";
$check = array();
$nodesCount = count($this->nodes);
$this->mean = $mean/($nodesCount*$nodesCount);
}
public function getRSquared() {
$this->countCurrentDistances();
$sum = 0;
$SStot = 0;
$SSres = 0;
foreach($this->nodes as $nodeA) {
foreach($this->nodes as $nodeB) {
$aLab = $nodeA[2];
$bLab = $nodeB[2];
if($aLab===$bLab) {
continue;
}
$given = $this->givenDistances[$aLab][$bLab];
$computed = $this->currentDistances[$aLab][$bLab];
$SSres+=(($given-$computed)*($given-$computed));
$SStot+= ($given-$this->mean)*($given-$this->mean);
}
}
return 1 - ($SSres/$SStot);
}
protected function iterate($inverseCoefStrenth=1) {
for($i=0; $i<count($this->nodes); $i++) {
$nodeA = $this->nodes[$i];
$move = array(0,0);
$moves = 0;
for($j=0; $j<count($this->nodes); $j++) {
if($j===$i) {
continue;
}
$nodeB = $this->nodes[$j];
$dist = $this->givenDistances[$nodeA[2]][$nodeB[2]];
$AB = array($nodeB[0]-$nodeA[0], $nodeB[1]-$nodeA[1]);
$lAB = sqrt(($AB[0]*$AB[0])+($AB[1]*$AB[1]));
$coef = ($lAB - $dist)/$lAB;
$AA1 = array($AB[0]*$coef, $AB[1]*$coef);
$moves++;
$move[0]+=$AA1[0];
$move[1]+=$AA1[1];
}
if($moves>0) {
$resultingMoveX = $move[0]/($moves*$inverseCoefStrenth);
$resultingMoveY = $move[1]/($moves*$inverseCoefStrenth);
$this->nodes[$i][0]+=$resultingMoveX;
$this->nodes[$i][1]+=$resultingMoveY;
}
}
}
public function scale($iterations, $coefIncrease=0) {
$basicCoef=1;
for($i=0; $i<$iterations; $i++) {
$this->iterate($basicCoef);
//echo $this->getRSquared();
//echo " | ";
$basicCoef+=$coefIncrease;
}
}
public function coordsAsString() {
$coords = array();
foreach($this->nodes as $node) {
$coords[]="[{$node[0]}, {$node[1]}]";
}
$res = join(", ",$coords);
return "[$res]";
}
public function printCoords($pattern='[%X,%Y,"%LABEL"]') {
$coords = array();
foreach($this->nodes as $node) {
$x = $node[0];
$y = $node[1];
$label = $node[2];
$res = str_replace('%X', $x, $pattern);
$res = str_replace('%Y', $y, $res);
$res = str_replace('%LABEL', $label, $res);
$coords[]=$res;
}
$res = join(", ",$coords);
return "[$res]";
}
public function pointsCoords() {
$coords = array();
foreach($this->nodes as $node) {
$res['x'] = round($node[0]*100);
$res['y'] = round($node[1]*100);
$res['label'] = $node[2];
$coords[] = $res;
}
return $coords;
}
}