手写数字识别神经网络的构建与训练
在这个例子中，我们将考虑基于神经网络模型进行图像分类的数据处理和训练。 MNIST数据集被选为一组观察对象，其中包含70,000张手写数字的标记图像。 该示例使用**。csv**格式文件，其中图像被扩展为包含每个像素的亮度值的表格数据。
连接用于数据处理的库:
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Pkg.add(["Colors", "CSV", "Flux", "Optimisers"])
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using CSV, DataFrames
将数据加载到变量中:
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df = DataFrame(CSV.File("$(@__DIR__)/mnist_784.csv"));
Dataframe前五行的输出:
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first(df,5)
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带数据的前五行和最后一列的输出，该数据指示观察对象属于哪个类。:
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df[1:5,780:785]
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以8比2的比例将数据集拆分为训练和测试样本:
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X_train, y_train = Matrix(df[1:56000,1:784]), df[1:56000,785]
X_test, y__test = Matrix(df[56001:end,1:784]), df[56001:end,785]
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将样本转换为神经网络处理可接受的格式:
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X_train, X_test = convert(Matrix{Float32}, X_train), convert(Matrix{Float32}, X_test)
y_train, y__test = convert(Vector{Float32}, y_train), convert(Vector{Float32}, y__test)
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连接用于数据可视化的库:
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using Plots
显示对象及其类:
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test_img = Vector(df[60000,1:784])
test_img = (reshape(test_img, 28, 28)) / 256
using Colors
println("Класс объекта: ", df[60000,785])
plot(Gray.(test_img))
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由神经网络处理的数据的最终转换:
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X_train, X_test = X_train', X_test'
y_train, y__test = y_train', y__test'
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连接机器学习库:
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using Flux, Optimisers;
定义神经网络的结构:
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model = Chain(
Dense(784, 15,elu),
Dense(15, 10,sigmoid),
softmax
)
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测试识别结果（训练模型前）:
定义学习参数:
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learning_rate = 0.01f0
opt = Optimisers.Adam(learning_rate)
state = Optimisers.setup(opt, model)
function loss(model, x, y)
y_oh = Flux.onehotbatch(y, 0:9) # размер (10, 1, N)
y_pred = model(x) # размер (10, N)
# Добавляем размерность для совпадения с y_oh
y_pred_reshaped = Flux.unsqueeze(y_pred, dims=2) # теперь (10, 1, N)
return Flux.mse(y_pred_reshaped, y_oh)
end
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定义一个函数来计算模型的精度:
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function accuracy(model, X, y)
correct = 0
for i in 1:length(y)
# Подготовка входа: добавить измерение батча
x_input = reshape(X[:, i], :, 1) # (features, 1)
# Предсказание модели
probs = model(x_input) # размер (10, 1)
# Преобразование в цифру
predicted_digit = argmax(probs)[1] - 1
# Сравнение с истинной меткой
if predicted_digit == y[i]
correct += 1
end
end
return correct / length(y)
end
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模型的迭代学习过程:
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loss_history = []
epochs = 100
for epoch in 1:epochs
# Вычисление градиентов
grads = gradient(model) do m
loss(m, X_train, y_train)
end
# Обновление модели и состояния
state, model = Optimisers.update(state, model, grads[1])
# Расчет и сохранение потерь
current_loss = loss(model, X_train, y_train)
push!(loss_history, current_loss)
# Расчет точности
acc = accuracy(model, X_test, y__test) * 100
# Логирование
if epoch == 1 || epoch % 1 == 0
println("Epoch $epoch: Training Loss = $current_loss, Accuracy = $acc%")
end
end
可视化每个训练步骤中损失函数的变化:
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plot((1:epochs), loss_history, title="Изменение функции потерь", xlabel="Шаг обучения", ylabel="Функция потерь")
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显示结果:
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number = 3000
test_img = Vector(df[56000+number,1:784])
test_img = (reshape(test_img, 28, 28)) / 256
using Colors
result = model(X_test[:,number])
println("Известный класс объекта: ", df[56000+number,785], "\n ", "Распознанная нейросетью цифра: ", (findfirst(x -> x == maximum(result), result)-1))
plot(Gray.(test_img'))
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结论
在本例中，对像素亮度数据进行预处理，并确定神经网络架构、优化器参数和损失函数。
该模型经过训练，显示出相当准确但并不完美的班级细分。 为了提高识别质量，可以通过改变层的体系结构和增加训练样本来修改神经网络。