基于WPF开发动态可交互混淆矩阵

最近在项目中，为了算法结果的可视化，需要用到混淆矩阵(Confusion Matrix)，而网上资源大多是基于Python绘制的混淆矩阵，并且是输出图片格式，并不能响应用户点击，今天以一个简单的小例子，简述如何通过WPF绘制混淆矩阵，并可响应用户点击事件，仅供学习分享使用，如有不足之处，还请指正。

什么是混淆矩阵？

在机器学习中, 混淆矩阵是一个误差矩阵, 常用来可视化地评估监督学习算法的性能. 混淆矩阵大小为 (n_classes, n_classes) 的方阵, 其中 n_classes 表示类的数量. 这个矩阵的每一行表示真实类中的实例, 而每一列表示预测类中的实例 (Tensorflow 和 scikit-learn 采用的实现方式). 也可以是, 每一行表示预测类中的实例, 而每一列表示真实类中的实例 (Confusion matrix From Wikipedia 中的定义). 通过混淆矩阵, 可以很容易看出系统是否会弄混两个类, 这也是混淆矩阵名字的由来.

混淆矩阵是一种特殊类型的列联表(contingency table)或交叉制表(cross tabulation or crosstab). 其有两维 (真实值 "actual" 和预测值 "predicted" ), 这两维都具有相同的类("classes")的集合. 在列联表中, 每个维度和类的组合是一个变量. 列联表以表的形式, 可视化地表示多个变量的频率分布.

对于应用程序开发人员而言，混淆矩阵就是一个二维数组，分别表示预测值和真实值，里面的值表示对应值的占比。

开发步骤

创建WPF应用程序项目

在了解了混淆矩阵的用途和原理后，就可以着手去开发，首先创建一个WPF应用程序项目，然后创建模型MatrixM，主要包括标题，x轴，y轴的标签和刻度说明，数据，颜色设置。如下所示：

cs 复制代码

public class MatrixM:ObservableObject
{
	private string title;
	public string Title { get { return title; } set { SetProperty(ref title, value); } }
 
	private string xLabel;
	public string XLabel { get { return xLabel; } set { SetProperty(ref xLabel, value); } }
 
	private string yLabel;
	public string YLabel { get { return yLabel; } set { SetProperty(ref yLabel,value); } }
 
	private string[] yaxis;
	public string[] Yaxis { get { return yaxis; } set { SetProperty(ref yaxis, value); } }
 
	private string[] xaxis;
	public string[] Xaxis { get { return xaxis; } set { SetProperty(ref xaxis, value); } }
 
	public double[,] Data { get; set; }
 
	private Color minBrush;
	public Color MinBrush { get { return minBrush; } set { SetProperty(ref minBrush, value); } }
 
	private Color maxBrush;
	public Color MaxBrush { get { return maxBrush; } set { SetProperty(ref maxBrush, value); } }
}

注意：在本示例中，矩阵的数据采用二维数组进行存储。

构造数据

构造示例数据，在实际开发中，数据来源于算法的真实分析，本例主要用于演示前端开发，所以构造一些测试数据，如下所示：

cs 复制代码

private MatrixM dataM;
public MatrixM DataM { get { return dataM; } set { SetProperty(ref dataM,value); } }
 
private UniformGrid matrix;
 
public MainWindowViewModel()
{
	this.DataM = new MatrixM();
	this.DataM.Title = "Confusion  Matrix on Fer2024";
	this.DataM.XLabel = "Predict Label";
	this.DataM.YLabel = "Truth Label";
	this.DataM.Xaxis = new string[] { "Angry","Disgust","Fear","Happy","Sad","Surprise","Neutral"};
	this.DataM.Yaxis = new string[] { "Angry", "Disgust", "Fear", "Happy", "Sad", "Surprise", "Neutral" };
	this.DataM.MinBrush = Colors.White;
	this.DataM.MaxBrush= Colors.DarkSlateBlue;
	this.DataM.Data = new double[,] {
		{0.66,0.01,0.09,0.04,0.11,0.01,0.09 },
		{0.23,0.64,0.0,0.04,0.09,0.0,0.0},
		{0.08,0.0,0.58,0.02,0.15,0.08,0.1},
		{0.01,0.0,0.01,0.89,0.01,0.02,0.06 },
		{0.09,0.0,0.11,0.03,0.6,0.01,0.15},
		{0.02,0.0,0.05,0.04,0.02,0.85,0.02 },
		{0.05,0.0,0.04,0.07,0.11,0.01,0.72 }
	};
}

页面布局

在WPF中，为了弹性呈现数据及自动缩放，主要用Grid，UniformGrid进行页面布局，交互主要用Button来实现，都是基础知识。如下所示：

XML 复制代码

<Grid>
    <Grid.ColumnDefinitions>
        <ColumnDefinition Width="Auto"></ColumnDefinition>
        <ColumnDefinition Width="*"></ColumnDefinition>
        <ColumnDefinition Width="Auto"></ColumnDefinition>
    </Grid.ColumnDefinitions>
    <Grid.RowDefinitions>
        <RowDefinition Height="Auto"></RowDefinition>
        <RowDefinition></RowDefinition>
        <RowDefinition Height="Auto"></RowDefinition>
    </Grid.RowDefinitions>
    <TextBlock Text="{Binding DataM.Title}" FontSize="20" FontWeight="Bold" Grid.Row="0" Grid.Column="0" Grid.ColumnSpan="3" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="5"></TextBlock>
    <TextBlock Text="{Binding DataM.YLabel}" Grid.Row="1" Grid.Column="0" FontWeight="Bold" FontSize="14" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="5">
        <TextBlock.LayoutTransform>
            <RotateTransform Angle="270"></RotateTransform>
        </TextBlock.LayoutTransform>
    </TextBlock>
    <Grid Grid.Row="1" Grid.Column="1">
        <Grid.RowDefinitions>
            <RowDefinition Height="*"></RowDefinition>
            <RowDefinition Height="Auto"></RowDefinition>
        </Grid.RowDefinitions>
        <Grid.ColumnDefinitions>
            <ColumnDefinition Width="Auto"></ColumnDefinition>
            <ColumnDefinition Width="*"></ColumnDefinition>
            <ColumnDefinition Width="Auto"></ColumnDefinition>
        </Grid.ColumnDefinitions>
        <ItemsControl Grid.Row="0" Grid.Column="0" Grid.RowSpan="1" ItemsSource="{Binding DataM.Yaxis}">
            <ItemsControl.ItemsPanel>
                <ItemsPanelTemplate>
                    <UniformGrid Columns="1"></UniformGrid>
                </ItemsPanelTemplate>
            </ItemsControl.ItemsPanel>
            <ItemsControl.ItemTemplate>
                <DataTemplate>
                    <StackPanel Orientation="Horizontal" VerticalAlignment="Center" HorizontalAlignment="Right">
                        <TextBlock Text="{Binding}"></TextBlock>
                        <Border Width="10" Height="1" BorderBrush="Black" BorderThickness="1" HorizontalAlignment="Right" Margin="10 0 0 0"></Border>
                    </StackPanel>
                </DataTemplate>
            </ItemsControl.ItemTemplate>
        </ItemsControl>
        <Border BorderBrush="Black" BorderThickness="1" Grid.Row="0" Grid.Column="1" >
            <UniformGrid x:Name="matrix" >
                <UniformGrid.Resources>
                    <Style TargetType="Button">
                        <Style.Triggers>
                            <Trigger Property="IsMouseOver" Value="True">
                                <Setter Property="Opacity" Value="0.5"></Setter>
                                <Setter Property="FontWeight" Value="Bold"></Setter>
                                <Setter Property="FontSize" Value="16"></Setter>
                                <Setter Property="Cursor" Value="Hand"></Setter>
                            </Trigger>
                        </Style.Triggers>
                    </Style>
                </UniformGrid.Resources>
            </UniformGrid>
        </Border>
        <ItemsControl Grid.Row="1" Grid.Column="1" ItemsSource="{Binding DataM.Xaxis}">
            <ItemsControl.ItemsPanel>
                <ItemsPanelTemplate>
                    <UniformGrid Rows="1"></UniformGrid>
                </ItemsPanelTemplate>
            </ItemsControl.ItemsPanel>
            <ItemsControl.ItemTemplate>
                <DataTemplate>
                    <StackPanel Orientation="Vertical" VerticalAlignment="Top" HorizontalAlignment="Center">
 
                        <Border Width="10" Height="1" BorderBrush="Black" BorderThickness="1" HorizontalAlignment="Center" Margin="0 0 0 0">
                            <Border.RenderTransformOrigin>
                                <Point X="0.5" Y="0.5"></Point>
                            </Border.RenderTransformOrigin>
                            <Border.LayoutTransform>
                                <TransformGroup>
                                    <RotateTransform Angle="90"></RotateTransform>
                                </TransformGroup>
                            </Border.LayoutTransform>
                        </Border>
                        <TextBlock Text="{Binding}">
                            <TextBlock.RenderTransformOrigin>
                                <Point X="0.5" Y="0.5"></Point>
                            </TextBlock.RenderTransformOrigin>
                            <TextBlock.LayoutTransform>
                                <TransformGroup>
                                    <RotateTransform Angle="-45"></RotateTransform>
                                    <TranslateTransform Y="20"></TranslateTransform>
                                </TransformGroup>
 
                            </TextBlock.LayoutTransform>
                        </TextBlock>
                    </StackPanel>
                </DataTemplate>
            </ItemsControl.ItemTemplate>
        </ItemsControl>
        <Rectangle  Grid.Row="0" Grid.Column="2" Width="20" Margin="10 0">
            <Rectangle.Fill>
                <LinearGradientBrush StartPoint="0 0" EndPoint="1 1">
                    <GradientStop Offset="0" Color="{Binding DataM.MaxBrush}"></GradientStop>
                    <GradientStop Offset="1" Color="{Binding DataM.MinBrush}"></GradientStop>
                </LinearGradientBrush>
            </Rectangle.Fill>
        </Rectangle>
    </Grid>
 
    <TextBlock Text="{Binding DataM.XLabel}" Grid.Row="2" Grid.Column="0" Grid.ColumnSpan="2" FontWeight="Bold" FontSize="14" HorizontalAlignment="Center" VerticalAlignment="Center" Margin="5"></TextBlock>
 
</Grid>

注意：标题，刻度，轴说明，都是固定布局，可以进行数据绑定，而矩阵内容需要动态创建，所以分开处理。

构造矩阵

在本示例中，混淆矩阵以UniformGrid为容器，动态根据数据创建，并填充到容器中，如下所示：

cs 复制代码

private IRelayCommand<object> loadedCommand;
 
public IRelayCommand<object> LoadedCommand =>loadedCommand??=new RelayCommand<object>(Loaded);
 
private void Loaded(object obj)
{
	if (obj != null)
	{
		var win = obj as MainWindow;
		if (win != null)
		{
			this.matrix = win.matrix;
			InitMatrix();
		}
	}
}
 
private void InitMatrix()
{
	if(this.matrix == null)
	{
		return;
	}
	this.matrix.Children.Clear();
	this.matrix.Rows = this.DataM.Data.GetLength(0);
	this.matrix.Columns = this.DataM.Data.GetLength(1);
	var color = this.DataM.MaxBrush;
	for(int row = 0; row < this.DataM.Data.GetLength(0); row++)
	{
		for(int col = 0; col < this.DataM.Data.GetLength(1); col++)
		{
			Border border = new Border();
			border.Background = new SolidColorBrush(Color.FromArgb((byte)(this.DataM.Data[row, col] * color.A), color.R, color.G, color.B));
			var button = new Button();
			button.Content = this.DataM.Data[row, col].ToString("0.00");
			button.FontSize = 12;
			button.HorizontalContentAlignment= System.Windows.HorizontalAlignment.Center;
			button.VerticalContentAlignment= System.Windows.VerticalAlignment.Center;
			button.Background = Brushes.Transparent;
			button.BorderThickness = new System.Windows.Thickness(0);
			border.Child= button;
			this.matrix.Children.Add(border);
		}
	}
}

注意，在Grid，UniformGrid此类容器中，控件不需要设置宽和高，会自动根据容器大小进行自适应。且不能设置对齐属性，否则控件大小则不会自适应调整大小。

示例效果

运行VS，实例效果如下所示：

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