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+-100 ポイント/値、テストの結果、およびそれらの距離 (0-10、10 が最も近い) の小さなマトリックスがあります: http://vis.arcs.cz。

近い値のグループをすばやく見つけるために、2D で視覚化したいと思います。したがって、この行列を処理して、2D の点の座標を取得する必要があります。

その方法はおそらく多次元スケーリングですが、アルゴリズム、ライブラリ、または拡張機能を見つけることも、数式を PHP コードに使用することもできませんでした。

私は過去 2 日間グーグルで検索しましたが、最も近い結果は http://www.php.net/manual/en/lapack.leastsquaresbysvd.phpです。（初心者としてこれ以上のリンクを共有することはできません）

PHPプロジェクト（C++でコンパイルされたMathLabコード...）に適用可能なソリューションに感謝します。

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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;
}

}
于 2014-06-27T13:00:14.227 に答える