A helpful website for understanding how CNN works:
https://towardsdatascience.com/a-comprehensive-guide-to-convolutional-neural-networks-the-eli5-way-3bd2b1164a53

University of Michigan - Ann Arbor

Convolutional networks, also known as convolutional neural networks, or CNNs, are a specialized kind of neural network for processing data that has a known grid-like topology. Examples include time-series data, which can be thought of as a 1-D grid taking samples at regular time intervals, and image data, which can be thought of as a 2-D grid of pixels. 

The network employs a mathematical operation called convolution. Convolution is a specialized kind of linear operation. Convolutional networks are simply neural networks that use convolution in place of general matrix multiplication in at least one of their layers.

The CNN gets its power from the following concepts:
- Sparse connectivity
- Parameter sharing

Convolutional Neural Network (CNN)

CNN Reference

CNNs are currently being applied to several applications, including:

 - Computer vision—medical image analysis, image recognition, face detection and video classification
 - Natural Language Processing (NLP)—semantic parsing, sentence modeling and search query retrieval
 - Drug discovery—the discovery of chemical features and prediction of medicinal benefits

Applications of Convolutional Neural Networks

CNNs and RNNs are not mutually exclusive, as both can perform classification of image and text inputs, creating an opportunity to combine the two network types for increased effectiveness. This is especially true if the input to be classified is visually complex with added temporal characteristics that a CNN alone would be unable to process.

Typically, when these two network types are combined, sometimes referred to as a CRNN, inputs are first processed by CNN layers whose outputs are then fed to RNN layers. CNN Long Short-Term Memory (LSTM) architectures are particularly promising, as they facilitate analysis of inputs over longer periods than could be achieved with lower-level RNN architecture types.

Currently, these hybrid architectures are being explored for use in applications like video scene labeling, emotion detection or gesture recognition, video identification or gait recognition, and DNA sequence prediction.

Hybrid of Convolutional and Recurrent Neural Network

- Python: conv_forward
- TensorFlow: tf.nn.conv2d
- Keras: Conv2D
- Pytorch: torch.nn.Conv2d
- Caffe: message ConvolutionParameter
- Theano: theano.tensor.nnet.conv.conv2d

Methods to Calculate Convolution in Python

CNNs are made up of three-layer types—convolutional, pooling and fully-connected (FC).

In the convolutional layers, the input matrix is passed through a set of filters that output a feature map. This output is then sent to a pooling layer, which reduces the size of the feature map. This helps reduce the processing time by condensing the map to its most essential information.

The convolutional and pooling processes are repeated several times, with the number of repeats depending on the network, after which the condensed feature map outputs are sent to a series of FC layers. These FC layers then flatten the maps together and compare the probabilities of each feature occurring in conjunction with the others, until the best classification is determined.

Convolutional Neural Networks Architecture

A 3D CNN is similar to a 2D CNN except that it differs in (non-exhaustive listing):
1- 3D Convolution Layers

2- 3D MaxPool Layers

3D Convolutional Neural Network

Visualizing and Understanding Convolutional Networks Paper

- Convolutional neural network can be used for obtaining high- dimensional images rather than being used in class prediction for logistic regression  or value prediction for regression problem

- Output of the CNN model can be a tensor S(i,j,k) which represent the pixel(j,k) of ith class, such a collaborative  effort can be used to precisely form a perfect image as the output.

Strategies to get output dimension same as the input are 

- Pooling is completely avoided or can use pooling with unit stride.

- Pixel-wise labelling involves initial guess of image pixels and refining this guess by interacting with neighboring pixels by parameter sharing.

Structured Output from CNN

A Convolutional Recurrent Neural Network (CRNN) is a combination of a Convolutional Neural Network (CNN) and a Recurrent Neural Network (RNN). 
-CNN are specialized networks for processing data that use a specialized, linear mathematical operation, also known as a convolution. 
-RNN is specialized for processing a sequence of inputs $x^{(1)}, . . . , x^{(τ)}$ and each time adds additional layers of comprehension on top of the previous inputs. 
-The goal of a CRNN is to take advantage of CNNs for local feature extraction and RNNs for temporal summarization of the extracted features.


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