Trying to extract child node values from xml in Powershell

I have the following xml:

<?xml version="1.0"?>
<AdminDirectorUsers>
    <Users>
        <User>
            <UserName>PC1</UserName>
            <Installation>
                <Products>
                    <Product>
                        <ProductID>Product1</ProductID>
                        <Selected>Yes</Selected>
                    </Product>
                    <Product>
                        <ProductID>Product2</ProductID>
                        <Selected>No</Selected>
                    </Product>
                    <Product>
                        <ProductID>Product3</ProductID>
                        <Selected>No</Selected>
                    </Product>
                    <Product>
                        <ProductID>Product4</ProductID>
                        <Selected>Yes</Selected>                        
                    </Product>
                </Products>
            </Installation>
        </User>
        <User>
            <UserName>PC2</UserName>
            <Installation>
                <Products>
                    <Product>
                        <ProductID>Product1</ProductID>
                        <Selected>Yes</Selected>
                    </Product>
                    <Product>
                        <ProductID>Product2</ProductID>
                        <Selected>Yes</Selected>
                    </Product>
                    <Product>
                        <ProductID>Product3</ProductID>
                        <Selected>No</Selected>
                    </Product>
                    <Product>
                        <ProductID>Product4</ProductID>
                        <Selected>Yes</Selected>                        
                    </Product>
                </Products>
            </Installation>
        </User>
    </Users>
</AdminDirectorUsers>

I would like to loop through and extract a list of each UserName with all ProductIDs that has a sibling node Selected with a value of Yes, while ignoring the values of No.

$path = 'C:\Temp\test.xml'
$xml = New-Object -TypeName XML
$xml.Load($Path)
$UserNode = $xml.SelectNodes('//User')
$ProductNode = $xml.SelectNodes('//Product')

foreach ($PC in $usernode)
{
  $PC.username
  foreach($Node in $ProductNode){
    # Test if selected == 'yes'
    if($Node.Selected -eq 'yes') {
      $Node.ProductID
    }
  }
}

My output is:

PC1
Product1
Product4
Product1
Product2
Product4
PC2
Product1
Product4
Product1
Product2
Product4

...but I'm looking for:

PC1
Product1
Product4
PC2
Product1
Product2
Product4

I've tried many ways to do this but nothing seems to work. What am I missing?

Change the second XPath expression used for the Product/ProductID to only get the descendants of a specific <User> element, by anchoring against . (the "current node"):

# Enumerate each `<User>` element
$xml |Select-Xml '//User' |%{
  # Grab the exact username value
  $username = $_.Node.UserName

  # Then enumerate all descendant `<ProductID>` nodes who has a sibling `<Selected>Yes</Selected>` and attach username
  $_.Node |Select-Xml './/ProductID[../Selected[. = "Yes"]]' |Select -Expand Node |Select @{Name='Username';Expression={$username}},InnerText
}

(I'm using Select-Xml here but this works the same with the SelectNodes() method)