Beginning Anomaly Detection Using

mean normalization, standardization (z-score 

normalization), and unit length scaling.

The formulas for each method are as follows:

Mean normalization (Figure 

3-25

)

This formula is similar to min-max normalization, except you use x

average

 in the 

numerator over x

min

.

Standardization (Figure 

3-26

)

You basically find z-score values for each x and use those instead of the original x values.

Unit length scaling (Figure 

3-27

)

Figure 3-24.  Formula for min-max normalization

Figure 3-25.  Formula for mean normalization

Figure 3-26.  Formula for standardization

Figure 3-27.  Formula for unit length scaling

Chapter 3   IntroduCtIon to deep LearnIng

---

92

You find the unit vector for x and use that instead. Unit vectors have a magnitude of 1.

The next block of code is shown in Figure 

3-28

.

What keras.utils.to_categorical() does is take the vector of classes and create a 

binary class matrix of the number of classes. Assume that you have a vector representing 

y_train with 6 classes at most, going from 0-5 (Figure 

3-29

).

After running keras.utils.to_categorical(y_train, n_classes) where  

n_classes = 5, Figure 

3-30

 shows what you would now get for y_train.

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Figure 3-28.  Converting x_train and x_test to float32 and applying min-max 

normalization by dividing by 255. For y_train and y_test, you convert them to a 

one-hot encoded format

Figure 3-29.  A vector representing y_train that has 6 classes with values ranging 

from 0-5

Chapter 3   IntroduCtIon to deep LearnIng

---

93

The classes are still the same, but this time you have to get the class by their index 

and not by direct value. At index 1 (row 1 if you think of this as a matrix with 1 column) 

of the original vector, you see that the class label is 5. In your transformed y_train data 

(which is now a matrix), at row 1 (previously index 1 before the transformation), you see 

that everything is a 0 in the vector at that index except for the value at column 5. And so, 

y_train is still 5 at index 1, but it’s formatted differently.

Now let’s check the shapes of your transformed data in Figure 

3-31

 and Figure 

3-32

.

Figure 3-30.  A one-hot encoded representation of the y_train vector in Figure 

3-39

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