了解KNN的标准化过程

Question

所以我在理解这个 KNN 分类器的标准化过程时遇到了一些麻烦。基本上我需要知道标准化过程中发生了什么。如果有人可以提供帮助，将不胜感激。我知道有一个由 "train examples" 组成的均值和标准差的变量，但在那之后实际发生的事情是我遇到的困难。

classdef myknn
methods(Static)

                %the function m calls the train examples, train labels
                %and the no. of nearest neighbours.
    function m = fit(train_examples, train_labels, k)

            % start of standardisation process
        m.mean = mean(train_examples{:,:});  %mean variable
        m.std = std(train_examples{:,:}); %standard deviation variable
        for i=1:size(train_examples,1)
            train_examples{i,:} = train_examples{i,:} - m.mean;
            train_examples{i,:} = train_examples{i,:} ./ m.std;
        end
            % end of standardisation process

        m.train_examples = train_examples;
        m.train_labels = train_labels;
        m.k = k;

    end

    function predictions = predict(m, test_examples)

        predictions = categorical;

        for i=1:size(test_examples,1)

            fprintf('classifying example example %i/%i\n', i, size(test_examples,1));

            this_test_example = test_examples{i,:};

            % start of standardisation process
            this_test_example = this_test_example - m.mean;
            this_test_example = this_test_example ./ m.std;
            % end of standardisation process

            this_prediction = myknn.predict_one(m, this_test_example);
            predictions(end+1) = this_prediction;

        end

    end

    function prediction = predict_one(m, this_test_example)

        distances = myknn.calculate_distances(m, this_test_example);
        neighbour_indices = myknn.find_nn_indices(m, distances);
        prediction = myknn.make_prediction(m, neighbour_indices);

    end

    function distances = calculate_distances(m, this_test_example)

        distances = [];

        for i=1:size(m.train_examples,1)

            this_training_example = m.train_examples{i,:};
            this_distance = myknn.calculate_distance(this_training_example, this_test_example);
            distances(end+1) = this_distance;
        end

    end

    function distance = calculate_distance(p, q)

        differences = q - p;
        squares = differences .^ 2;
        total = sum(squares);
        distance = sqrt(total);

    end

    function neighbour_indices = find_nn_indices(m, distances)

        [sorted, indices] = sort(distances);
        neighbour_indices = indices(1:m.k);

    end

    function prediction = make_prediction(m, neighbour_indices)

        neighbour_labels = m.train_labels(neighbour_indices);
        prediction = mode(neighbour_labels);

    end

end

结束

Answer 1

标准化是对训练示例中的每个特征进行归一化的过程，这样每个特征的均值为零，标准差为 1。这样做的过程是找到每个特征的平均值和每个特征的标准差。之后，我们取每个特征并减去其对应的均值并除以其对应的标准差。

通过这段代码可以清楚地看出：

    m.mean = mean(train_examples{:,:});  %mean variable
    m.std = std(train_examples{:,:}); %standard deviation variable
    for i=1:size(train_examples,1)
        train_examples{i,:} = train_examples{i,:} - m.mean;
        train_examples{i,:} = train_examples{i,:} ./ m.std;
    end

m.mean 记住每个特征的均值，而 m.std 记住每个特征的标准差。请注意，当您想要在测试时执行分类时，您必须记住这两个。这可以通过 predict 方法看到，它采用测试特征，并从 training 示例中减去每个特征的均值和标准差。

function predictions = predict(m, test_examples)

    predictions = categorical;

    for i=1:size(test_examples,1)

        fprintf('classifying example example %i/%i\n', i, size(test_examples,1));

        this_test_example = test_examples{i,:};

        % start of standardisation process
        this_test_example = this_test_example - m.mean;
        this_test_example = this_test_example ./ m.std;
        % end of standardisation process

        this_prediction = myknn.predict_one(m, this_test_example);
        predictions(end+1) = this_prediction;

    end

请注意，我们在测试示例中使用 m.mean 和 m.std，这些数量来自训练示例。

我关于标准化的 post 应该提供更多背景信息。此外，它实现了与您提供的代码相同的效果，但更加矢量化：

了解KNN的标准化过程

Understanding the standardisation process of KNN

matlab

machine-learning

knn