# CNN-Based Model for Landslide Susceptibility Assessment from Multispectral Data
## 3 Proposed Landslide Susceptibility Identification Model  
The adoption of convolutional neural networks (CNN) in the context of the ImageNet Challenge is one of the keystones that has driven the progress of the computer vision field in recent years. Recently, in addition to CNN, other types of architectures have also been important tools for object recognition. For example, Transformers have been shown to work well not only for natural language processing applications but also for computer vision, proving to be an alternative for convolutional networks [34]. Similarly, recent research has led to proposals based on classical architectures that are competitive with those widely adopted. For example, the Brain Team at Google Research proposed the MLP-Mixer architecture, which does not use convolutions or self-attention, so it is based only on basic matrix multiplication routines [35]. This same team also proposed another MLP-based alternative to Transformers [34], which consists of channel projections, spatial projections, and gating, obtaining solid classification results in ImageNet [34]. These MLP-type architectures are competitive but conceptually and technically simpler alternatives to techniques such as Transformers or deep convolutional network architectures [34,35]. Indeed, the basis of these architectures is the multilayer perceptron (MLP), which basically consists of multiple layers of neurons, each fully connected to those in the layer below. When stacking many fully connected layers, usually the first L-1 layers are the representation, and the last layer is the linear predictor. This stacking also involves the use of a nonlinear activation function, which decides whether a neuron should be activated or not by calculating the weighted sum and adding the bias [36]. In view of the above, the architecture shown in Figure 1 is proposed for the identification of landslide susceptible zones. The proposed architecture uses two blocks consisting of a convolutional layer, a Batch normalization (_BN_) layer, _GELU_ (Gaussian error linear unit) activation function, and an additional convolution layer without an activation function. The first block uses a convolutional layer with \(n\) filters, filter size \(5\times 5\), padding _same_ and stride 1. The other convolutional layer uses the same number of filters and the same filter size, but a padding _valid_. The second block differs by using a \(1\times 1\) filter and padding _valid_ in both convolutions. The idea in using the first block is to involve the spatial information surrounding the pixel by convolutions in a \(5\times 5\) neighborhood and, in the second block, to perform \(1\times 1\) convolutions for channel mixing. As discussed so far, _BN_ is used in each block after the first convolution. _BN_ is a technique that systematically accelerates convergence in deep network training. It basically consists of normalizing an input by subtracting the mean and dividing by its standard deviation and then applying a scaling coefficient and a scaling offset, values that are learned during training [37]. Regarding the activation function, _GELU_ is used as in the MLP-based proposals [34,35] after _BN_. For an input \(x\) and a standard Gaussian cumulative distribution function \(\phi(x)\), the _GELU_ activation function is defined as \(x\phi(x)\). The non-linearity of _GELU_ weights the inputs by their value, unlike in _ReLU_ where they are activated by their sign [38,39]. In the case of the input of the network, it is a tensor of size \(5\times 5\) extracted around each pixel of the input image, stacked in the channel dimension. The result is a 4D tensor indexed by batch, row, column, and depth. This means that for an image of \(p\) pixels, the total number of input samples is the number of pixels, and the 4D tensor dimension will be \(p\times 5\times 5\times c\) (where \(c\) is the number of channels of the input image).