Beginning Anomaly Detection Using

d – 1 is, where 

d is the dilation factor. For a dilation factor of three, this spacing will be two apart. Now, 

for the second entry, the convolution process proceeds as normal (see Figure 

7-9

).

Feature Map

Figure 7-8.  A standard convolution with a dilation factor of two defining the first 

entry in the feature map

Feature Map

Figure 7-9.  The convolution with a dilation factor of two defining the second 

entry in the feature map

Chapter 7   temporal Convolutional networks

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264

Once the process terminates, we will have our feature map. Notice the reduction 

in dimensionality of the feature map, which is a direct result of increasing the dilation 

factor. In the standard two-dimensional convolutional layer, we had a 4x4 feature map 

since the dilation factor was one, but now we have a 3x3 feature map after increasing this 

factor to two.

A one-dimensional dilated convolution is similar. Let’s revisit the one-dimensional 

convolution example and modify it a bit to illustrate this concept.

Assume now that the new input vector and filter weights are as shown in Figure 

7-10

 

and Figure 

7-11

.

and

Let’s also assume now that the dilation factor is two, not one. The new output vector 

is the following, using dilated one-dimensional convolutions with a dilation factor of two 

(see Figure 

7-12

, Figure 

7-13

, Figure 

7-14

, and Figure 

7-15

).

2   8   12   4   6   4   2   12   

x =