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Some Metric Implementation in Keras (Such as Pearsons Correlation Coefficient, Mean Relative Error)

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# Keras_Metrics
Some Metric Implementation in Keras (Such as Pearsons Correlation Coefficient, MRE)

Now Including:
- Pearsons Correlation Coefficient
- Mean Relative Error
- Jaccard Loss (**Derivable**, can be used as LOSS for training in Keras)
- Jaccard Index
- Dice Similarity Coefficient (aka. DSC)

----
# How to use

Just an example ~ 
```
inp = Input(shape=(timesteps, 1))
gru = Bidirectional(GRU(500, return_sequences=True))(inp)

max1 = GlobalMaxPool1D()(gru_1)
att1 = Attention()(gru_1)
cont1 = keras.layers.concatenate([max1, att1])

out = Dense(1, activation='relu')(cont1)

opt = keras.optimizers.Adam(lr=0.002, beta_1=0.9, beta_2=0.9, epsilon=1e-08, amsgrad=True)

model = Model(inputs=inp, outputs=out)
model.compile(loss='mse',
              optimizer=opt,
              metrics=['mse', pearson_r, mre])
```

----

# Related Formula
- Pearsons Correlation Coefficient
> ![这里写图片描述](https://www.zhihu.com/equation?tex=%5Crho%28X%2CY%29%3D%5Cfrac%7BE%5B%28X-%5Cmu_%7BX%7D%29%28Y-%5Cmu_%7BY%7D%29%5D%7D%7B%5Csigma_X%5Csigma_Y%7D+%3D%5Cfrac%7BE%5B%28X-%5Cmu_%7BX%7D%29%28Y-%5Cmu_%7BY%7D%29%5D%7D%7B%5Csqrt%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%7B%28X_i-%5Cmu_X%29%5E2%7D%7D%5Csqrt%7B%5Csum_%7Bi%3D1%7D%5E%7Bn%7D%7B%28Y_i-%5Cmu_Y%29%5E2%7D%7D%7D)

- Jaccard Loss
>![这里写图片描述](https://upload.wikimedia.org/math/1/8/6/186c7f4e83da32e889d606140fae25a0.png)

- Dice Similarity Coefficient
>![这里写图片描述](https://upload.wikimedia.org/math/2/3/5/2354a9c697d2bf4ae114b8f1f72d5090.png)

- Mean Relative Error

See [here](http://akademikpersonel.kocaeli.edu.tr/hmertunc/sci/hmertunc09.10.2015_14.07.20sci.pdf)
> Sayin C, Ertunc H M, Hosoz M, et al. Performance and exhaust emissions of a gasoline engine using artificial neural network[J]. Applied Thermal Engineering, 2007, 27(1):46-54.

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