我设计了一个CNN并使用以下参数进行编译，

training_file_loc = "8-SignLanguageMNIST/sign_mnist_train.csv"testing_file_loc = "8-SignLanguageMNIST/sign_mnist_test.csv"def getData(filename):    images = []    labels = []    with open(filename) as csv_file:        file = csv.reader(csv_file, delimiter = ",")        next(file, None)                for row in file:            label = row[0]            data = row[1:]            img = np.array(data).reshape(28,28)                        images.append(img)            labels.append(label)                images = np.array(images).astype("float64")        labels = np.array(labels).astype("float64")            return images, labelstraining_images, training_labels = getData(training_file_loc)testing_images, testing_labels = getData(testing_file_loc)print(training_images.shape, training_labels.shape)print(testing_images.shape, testing_labels.shape)training_images = np.expand_dims(training_images, axis = 3)testing_images = np.expand_dims(testing_images, axis = 3)training_datagen = ImageDataGenerator(    rescale = 1/255,    rotation_range = 45,    width_shift_range = 0.2,    height_shift_range = 0.2,    shear_range = 0.2,    zoom_range = 0.2,    horizontal_flip = True,    fill_mode = "nearest")training_generator = training_datagen.flow(    training_images,    training_labels,    batch_size = 64,)validation_datagen = ImageDataGenerator(    rescale = 1/255,    rotation_range = 45,    width_shift_range = 0.2,    height_shift_range = 0.2,    shear_range = 0.2,    zoom_range = 0.2,    horizontal_flip = True,    fill_mode = "nearest")validation_generator = training_datagen.flow(    testing_images,    testing_labels,    batch_size = 64,)model = tf.keras.Sequential([    keras.layers.Conv2D(16, (3, 3), input_shape = (28, 28, 1), activation = "relu"),    keras.layers.MaxPooling2D(2, 2),    keras.layers.Conv2D(32, (3, 3), activation = "relu"),    keras.layers.MaxPooling2D(2, 2),    keras.layers.Flatten(),    keras.layers.Dense(256, activation = "relu"),    keras.layers.Dropout(0.25),    keras.layers.Dense(512, activation = "relu"),    keras.layers.Dropout(0.25),    keras.layers.Dense(26, activation = "softmax")])model.compile(    loss = "categorical_crossentropy",    optimizer = RMSprop(lr = 0.001),    metrics = ["accuracy"])

但是，当我运行model.fit()时，出现了以下错误，

ValueError: Shapes (None, 1) and (None, 24) are incompatible

在将损失函数更改为sparse_categorical_crossentropy后，程序正常运行。

我不明白这是为什么。

谁能解释一下这是怎么回事，以及这两种损失函数的区别？

回答：

问题在于，categorical_crossentropy期望标签是一热编码的，这意味着，对于每个样本，它期望一个长度为num_classes的张量，其中label位置的元素被设置为1，其余为0。

另一方面，sparse_categorical_crossentropy直接使用整数标签（因为这里的用例是类别数目很大，所以一热编码标签会浪费大量内存）。我认为，但不能确定，categorical_crossentropy的运行速度比其稀疏版本更快。

对于你的情况，有26个类别，我建议使用非稀疏版本，并将你的标签转换为一热编码，如下所示：

def getData(filename):    images = []    labels = []    with open(filename) as csv_file:        file = csv.reader(csv_file, delimiter = ",")        next(file, None)                for row in file:            label = row[0]            data = row[1:]            img = np.array(data).reshape(28,28)                        images.append(img)            labels.append(label)                images = np.array(images).astype("float64")        labels = np.array(labels).astype("float64")            return images, tf.keras.utils.to_categorical(labels, num_classes=26) # 你可以省略num_classes，让它从数据中计算

补充说明：除非你有理由使用float64来处理图像，否则我建议改用float32（这样可以将数据集所需的内存减半，而且模型很可能在第一步操作中就将它们转换为float32）