损失函数正在减少，但度量函数保持不变？

Posted 2023-03-27

【中文标题】损失函数正在减少，但度量函数保持不变？

【英文标题】：Loss Function is decreasing but metric function remains constant?

【发布时间】：2019-06-12 09:40:11

【问题描述】：

我正在研究医学图像分割。我有两节课。 0 级作为背景，1 级作为病变。由于数据集高度不平衡，我使用损失函数作为（1 - 加权骰子系数）和度量函数作为骰子系数。我已将数据集从 0-255 标准化为 0-1。我正在使用带有 tensorflow 后端的 keras 来训练模型。在训练 UNet++ 模型时，我的损失函数随着每个时期而减少，但我的指标保持不变。我无法理解为什么指标是恒定的，因为损失正在按预期减少？另外，我不明白，为什么骰子系数返回的值介于 0 和 1 之间，损失大于 1？

这是我的损失函数：

def dice_loss(y_true, y_pred):
    smooth = 1.
    w1 = 0.3
    w2 = 0.7

    y_true_f = K.flatten(y_true[...,0])
    y_pred_f = K.flatten(y_pred[...,0])
    intersect = K.abs(K.sum(y_true_f * y_pred_f, axis = -1))
    denom = K.abs(K.sum(y_true_f, axis = -1)) + K.abs(K.sum(y_pred_f, axis = -1))
    coef1 = (2 * intersect + smooth) / (denom + smooth)

    y_true_f1 = K.flatten(y_true[...,1])
    y_pred_f1 = K.flatten(y_pred[...,1])
    intersect1 = K.abs(K.sum(y_true_f1 * y_pred_f1, axis = -1))
    denom1 = K.abs(K.sum(y_true_f1, axis = -1)) + K.abs(K.sum(y_pred_f1, axis = -1))
    coef2 = (2 * intersect1 + smooth) / (denom1 + smooth)

    weighted_dice_coef = w1 * coef1 + w2 * coef2
    return (1 - weighted_dice_coef)

而且，这是度量函数：

def dsc(y_true, y_pred):
    """
    DSC = (|X and Y|)/ (|X| + |Y|)
    """
    smooth = 1.
    y_true_f = K.flatten(y_true[...,1])
    y_pred_f = K.flatten(y_pred[...,1])
    intersect = K.abs(K.sum(y_true_f * y_pred_f, axis = -1))
    denom = K.abs(K.sum(y_true_f, axis = -1)) + K.abs(K.sum(y_pred_f, axis = -1))
    coef = (2 * intersect + smooth) / (denom + smooth)

    return coef

训练损失 vs epoch：

这里是示例代码：

def standard_unit(input_tensor, stage, nb_filter, kernel_size = 3):

x = Conv2D(nb_filter, kernel_size, padding = 'same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name = 'conv' + stage + '_1')(input_tensor)
x = Dropout(dropout_rate, name = 'dp' + stage + '_1')(x)
x = Conv2D(nb_filter, kernel_size, padding = 'same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name = 'conv' + stage + '_2')(x)
x = Dropout(dropout_rate, name = 'dp' + stage + '_2')(x)

return x
dropout_rate = 0.5
act = "relu"

def Nest_UNet(input_size = (None, None, 1), num_class = 2, deep_supervision = False):

#class 0: Background
#class 1: Lesions
nb_filter = [32,64,128,256,512]

#Handle Dimension Ordering for different backends
global bn_axis
if K.image_dim_ordering() == 'tf':
    bn_axis = 3
else:
    bn_axis = 1
img_input = Input(input_size, name = 'main_input')

conv1_1 = standard_unit(img_input, stage = '11', nb_filter = nb_filter[0])
pool1 = MaxPooling2D(2, strides=2, name='pool1')(conv1_1)
#pool1 = dilatedConv(conv1_1, stage = '11', nb_filter = nb_filter[0])

conv2_1 = standard_unit(pool1, stage='21', nb_filter=nb_filter[1])
pool2 = MaxPooling2D(2, strides=2, name='pool2')(conv2_1)
#pool2 = dilatedConv(conv2_1, stage = '21', nb_filter = nb_filter[1])

up1_2 = Conv2DTranspose(nb_filter[0], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up12')(conv2_1)
conv1_2 = concatenate([up1_2, conv1_1], name='merge12', axis=bn_axis)
conv1_2 = standard_unit(conv1_2, stage='12', nb_filter=nb_filter[0])

conv3_1 = standard_unit(pool2, stage='31', nb_filter=nb_filter[2])
pool3 = MaxPooling2D(2, strides=2, name='pool3')(conv3_1)
#pool3 = dilatedConv(conv3_1, stage = '31', nb_filter = nb_filter[2])

up2_2 = Conv2DTranspose(nb_filter[1], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up22')(conv3_1)
conv2_2 = concatenate([up2_2, conv2_1], name='merge22', axis=bn_axis)
conv2_2 = standard_unit(conv2_2, stage='22', nb_filter=nb_filter[1])

up1_3 = Conv2DTranspose(nb_filter[0], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up13')(conv2_2)
conv1_3 = concatenate([up1_3, conv1_1, conv1_2], name='merge13', axis=bn_axis)
conv1_3 = standard_unit(conv1_3, stage='13', nb_filter=nb_filter[0])

conv4_1 = standard_unit(pool3, stage='41', nb_filter=nb_filter[3])
pool4 = MaxPooling2D(2, strides=2, name='pool4')(conv4_1)
#pool4 = dilatedConv(conv4_1, stage = '41', nb_filter = nb_filter[3])

up3_2 = Conv2DTranspose(nb_filter[2], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up32')(conv4_1)
conv3_2 = concatenate([up3_2, conv3_1], name='merge32', axis=bn_axis)
conv3_2 = standard_unit(conv3_2, stage='32', nb_filter=nb_filter[2])

up2_3 = Conv2DTranspose(nb_filter[1], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up23')(conv3_2)
conv2_3 = concatenate([up2_3, conv2_1, conv2_2], name='merge23', axis=bn_axis)
conv2_3 = standard_unit(conv2_3, stage='23', nb_filter=nb_filter[1])

up1_4 = Conv2DTranspose(nb_filter[0], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up14')(conv2_3)
conv1_4 = concatenate([up1_4, conv1_1, conv1_2, conv1_3], name='merge14', axis=bn_axis)
conv1_4 = standard_unit(conv1_4, stage='14', nb_filter=nb_filter[0])

conv5_1 = standard_unit(pool4, stage='51', nb_filter=nb_filter[4])

up4_2 = Conv2DTranspose(nb_filter[3], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up42')(conv5_1)
conv4_2 = concatenate([up4_2, conv4_1], name='merge42', axis=bn_axis)
conv4_2 = standard_unit(conv4_2, stage='42', nb_filter=nb_filter[3])

up3_3 = Conv2DTranspose(nb_filter[2], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up33')(conv4_2)
conv3_3 = concatenate([up3_3, conv3_1, conv3_2], name='merge33', axis=bn_axis)
conv3_3 = standard_unit(conv3_3, stage='33', nb_filter=nb_filter[2])

up2_4 = Conv2DTranspose(nb_filter[1], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up24')(conv3_3)
conv2_4 = concatenate([up2_4, conv2_1, conv2_2, conv2_3], name='merge24', axis=bn_axis)
conv2_4 = standard_unit(conv2_4, stage='24', nb_filter=nb_filter[1])

up1_5 = Conv2DTranspose(nb_filter[0], 2, strides=2, padding='same', activation = act, kernel_initializer = 'he_normal', kernel_regularizer=l2(1e-4), name='up15')(conv2_4)
conv1_5 = concatenate([up1_5, conv1_1, conv1_2, conv1_3, conv1_4], name='merge15', axis=bn_axis)
conv1_5 = standard_unit(conv1_5, stage='15', nb_filter=nb_filter[0])

nestnet_output_1 = Conv2D(num_class, 1, activation='softmax', name='output_1', kernel_initializer = 'he_normal', padding='same', kernel_regularizer=l2(1e-4))(conv1_2)
nestnet_output_2 = Conv2D(num_class, 1, activation='softmax', name='output_2', kernel_initializer = 'he_normal', padding='same', kernel_regularizer=l2(1e-4))(conv1_3)
nestnet_output_3 = Conv2D(num_class, 1, activation='softmax', name='output_3', kernel_initializer = 'he_normal', padding='same', kernel_regularizer=l2(1e-4))(conv1_4)
nestnet_output_4 = Conv2D(num_class, 1, activation='softmax', name='output_4', kernel_initializer = 'he_normal', padding='same', kernel_regularizer=l2(1e-4))(conv1_5)
nestnet_output_5 = concatenate([nestnet_output_4, nestnet_output_3, nestnet_output_2, nestnet_output_1], name = "mergeAll", axis = bn_axis)
nestnet_output_5 = Conv2D(num_class, 1, activation='softmax', name='output_5', kernel_initializer = 'he_normal', padding='same', kernel_regularizer=l2(1e-4))(nestnet_output_5)

if deep_supervision:
    model = Model(input=img_input, output = nestnet_output_5)
else:
    model = Model(input=img_input, output = nestnet_output_4)

return model

with tf.device("/cpu:0"):
    #initialize the model
    model = Nest_UNet(deep_supervision = False)
#make the model parallel
model = multi_gpu_model(model, gpus = Gpu)
#initialize the optimizer and model
optimizer = Adam(lr = init_lr, beta_1 = beta1, beta_2 = beta2)
model.compile(loss = dice_loss, optimizer = optimizer, metrics = [dsc])
callbacks = [LearningRateScheduler(poly_decay)]
#train the network
aug = ImageDataGenerator(rotation_range = 10, width_shift_range = 0.1, height_shift_range = 0.1, horizontal_flip = True, fill_mode = "nearest")
aug.fit(trainX)
train = model.fit_generator(aug.flow(x = trainX, y = trainY, batch_size = batch_size * Gpu), steps_per_epoch = len(trainX) // (batch_size * Gpu),
epochs = n_epoch, verbose = 2, callbacks = callbacks, validation_data = (validX, validY), shuffle = True)

【问题讨论】：

您能否提供一个可重现的示例，仅用于复制粘贴和运行？您是否尝试过打印部分结果，例如 intersect 和 denom？顺便提一句。您可以在dice_loss() 中使用dsc() 函数来代替coef2，这样可以减少可能出错的地方。

我怀疑您的通道 1 存在问题。模型在通道 1 中被冻结，或者与您的激活相比，您的数据超出了范围。 --- 另外，验证您的图表是否有正确的标签。我很难相信验证值比训练值更稳定。

@DanielMöller，我验证了图表。它有正确的标签。您能解释一下“模型在通道 1 中冻结”是什么意思吗？我该如何纠正？

@wind，我会尝试打印部分结果并回复您。另外，我在dice_loss() 中使用了dsc() 函数，但没有任何改变

@MdShalique：问题解决了吗？如果没有，您可以尝试将度量函数修改为Weighted Dice Coefficient，而不是Dice Coefficient。谢谢！

【参考方案1】：

看起来您已经使用了model code 并基本保持原样。你从 sigmoid 到 softmax 的切换有点可疑。您是否将来自网络的 one-hot 编码 y_pred 与非 one-hot 编码的 y_true 进行比较？也许您可以打印输出层的形状并将其与 y_true 的形状进行比较。

我在我的语义分割解决方案中使用了Tversky Index，因为它是 Intersection-over-Union 和 Sørensen-Dice 系数计算的推广，让我们比加权 Dice 系数方法更优雅地强调误报或误报而且您不必使用axis=-1，我认为这是您问题的根源。对于损失，我只是颠倒了 Tversky 指数指标。

def tversky_index(y_true, y_pred):
    # generalization of dice coefficient algorithm
    #   alpha corresponds to emphasis on False Positives
    #   beta corresponds to emphasis on False Negatives (our focus)
    #   if alpha = beta = 0.5, then same as dice
    #   if alpha = beta = 1.0, then same as IoU/Jaccard
    alpha = 0.5
    beta = 0.5
    y_true_f = K.flatten(y_true)
    y_pred_f = K.flatten(y_pred)
    intersection = K.sum(y_true_f * y_pred_f)
    return (intersection) / (intersection + alpha * (K.sum(y_pred_f*(1. - y_true_f))) + beta *  (K.sum((1-y_pred_f)*y_true_f)))

def tversky_index_loss(y_true, y_pred):
    return -tversky_index(y_true, y_pred)

learning_rate = 5e-5  # also try 5e-4, 5e-3, depending on your network
optimizer = Adam(lr=learning_rate)
unet_model.compile(optimizer=optimizer, loss=tversky_index_loss, metrics=['accuracy','sparse_categorical_accuracy',tversky_index])

【参考方案2】：

1.只有当loss值低到一定程度时，metric值才会出现显着下降。两者在图像分割问题中不存在正相关关系。

2.Dice loss大于1，因为总loss是batch中各个loss相加。