From 3ba006417ca0b66db7c42647398a94b05c4bf99c Mon Sep 17 00:00:00 2001 From: iABn0rma1 Date: Thu, 30 May 2024 17:30:59 +0530 Subject: [PATCH 1/7] understanding cnn from scratch --- contrib/machine-learning/IntroToCNNs.md | 453 ++++++++++++++++++++++++ contrib/machine-learning/index.md | 1 + 2 files changed, 454 insertions(+) create mode 100644 contrib/machine-learning/IntroToCNNs.md diff --git a/contrib/machine-learning/IntroToCNNs.md b/contrib/machine-learning/IntroToCNNs.md new file mode 100644 index 00000000..5f81ace5 --- /dev/null +++ b/contrib/machine-learning/IntroToCNNs.md @@ -0,0 +1,453 @@ +# Understanding Convolutional Neural Networks (CNN) + +## Table of Contents +
+Click to expand + +- [Introduction](#introduction) +- [CNN Architecture](#cnn-architecture) + -
+ Convolutional Layer + + - [Input Shape](#input-shape) + - [Stride](#strides) + - [Padding](#padding) + - [Filter](#filters) + - [Output](#output) + +
+ +- [Pooling Layer](#pooling-layer) +- [Flatten Layer](#flatten-layer) +- [Dropout Layer](#dropout-layer) + +- [Implementation](#implementation) + +
+ +## Introduction + +Convolutional Neural Networks (CNNs) are a specialized type of artificial neural network designed primarily for processing structured grid data like images. CNNs are particularly powerful for tasks involving image recognition, classification, and computer vision. They have revolutionized these fields, outperforming traditional neural networks by leveraging their unique architecture to capture spatial hierarchies in images. + +### Why CNNs are Superior to Traditional Neural Networks + +1. **Localized Receptive Fields**: + - CNNs use convolutional layers that apply filters to local regions of the input image. This localized connectivity ensures that the network learns spatial hierarchies and patterns, such as edges and textures, which are essential for image recognition tasks. + +2. **Parameter Sharing**: + - In CNNs, the same filter (set of weights) is used across different parts of the input, significantly reducing the number of parameters compared to fully connected layers in traditional neural networks. This not only lowers the computational cost but also mitigates the risk of overfitting. + +3. **Translation Invariance**: + - Due to the shared weights and pooling operations, CNNs are inherently invariant to translations of the input image. This means that they can recognize objects even when they appear in different locations within the image. + +4. **Hierarchical Feature Learning**: + - CNNs automatically learn a hierarchy of features from low-level features like edges to high-level features like shapes and objects. Traditional neural networks, on the other hand, require manual feature extraction which is less effective and more time-consuming. + +### Use Cases of CNNs + +- **Image Classification**: Identifying objects within an image (e.g., classifying a picture as containing a cat or a dog). +- **Object Detection**: Detecting and locating objects within an image (e.g., finding faces in a photo). +- **Image Segmentation**: Partitioning an image into segments or regions (e.g., dividing an image into different objects and background). +- **Medical Imaging**: Analyzing medical scans like MRI, CT, and X-rays for diagnosis. + +> This guide will walk you through the fundamentals of CNNs and their implementation in Python. We'll build a simple CNN from scratch, explaining each component to help you understand how CNNs process images and extract features. + +### Let's start by understanding the basic architecture of CNNs. + +## CNN Architecture + +Convolution layers, pooling layers, and fully connected layers are just a few of the many building blocks that CNNs use to automatically and adaptively learn spatial hierarchies of information through backpropagation. + +### Convolutional Layer +The convolutional layer is the core building block of a CNN. The layer's parameters consist of a set of learnable filters (or kernels), which have a small receptive field but extend through the full depth of the input volume. + +#### Input Shape +The dimensions of the input image, including the number of channels (e.g., 3 for RGB images & 1 for Grayscale images). +
+ + + + + + + + + + + +
1 and 0
10111
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+ + + + + + + + + + + +
9
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+
+ +- The input matrix represents a simplified binary image of handwritten digits, +where '1' denotes the presence of ink and '0' represents the absence of ink. + +- The first matrix shows the represnetation of 1 and 0, which can be depicted as a vertical line and a closed loop. + +- The second matrix represents 9, combining the loop and line. + +
+ +#### Strides +The step size with which the filter moves across the input image. +
+ + + + + + + + + + + +
3
011 + 10
010 + 10
01110
00010
000 + 10
000 + 10
00010
+ + + + + + + + + + + +
2
01 + 110
01 + 010
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00 + 010
00 + 010
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+
+ +- This visualization will help you understand how the filter (kernel) moves acroos the input matrix with stride values of 3 and 2. + +- A stride of 1 means the filter moves one step at a time, ensuring it covers the entire input matrix. + +- However, with larger strides (like 3 or 2 in this example), the filter may not cover all elements, potentially missing some information. + +- While this might seem like a drawback, higher strides are often used to reduce computational cost and decrease the output size, which can be beneficial in speeding up the training process and preventing overfitting. + +
+ +#### Padding +Determines whether the output size is the same as the input size ('same') or reduced ('valid'). +
+ + + + + + + + + + + + + +
padding='same'
0000000
0011100
0010100
0011100
0000100
0000100
0000100
0000100
0000000
+ + + + + + + + + + + +
padding='valid'
01110
01010
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+
+ +- `Same` padding is preferred in earlier layers to preserve spatial and edge information, as it can help the network learn more detailed features. + +- Choose `valid` padding when focusing on the central input region or requiring specific output dimensions. + +
+ +#### Filters +Small matrices that slide over the input data to extract features. +
+ + + + + + + +
closed loop
111
101
111
+ + + + + + + +
vertical line
010
010
010
+ + + + + + + +
both diagonals
101
010
101
+
+ +- The first filter aims to detect closed loops within the input image, being highly relevant for recognizing digits with circular or oval shapes, such as '0', '6', '8', or '9'. + +- The next filter helps in detecting vertical lines, crucial for identifying digits like '1', '4', '7', and parts of other digits that contain vertical strokes. + +- The last filter shows how to detect diagonal lines in the input image, useful for identifying the slashes present in digits like '1', '7', or parts of '4' and '9'. + +
+ +#### Output +A set of feature maps that represent the presence of different features in the input. +
+ + + + + + + + + +
('valid', 1)
404
25-3
25-3
032
032
+ + + + + + + + + + + +
('same', 1)
22422
34843
22533
12533
00323
00323
00212
+ + + + + + + +
('valid', 2)
44
23
02
+
+ +- With no padding and a stride of 1, the 3x3 filter moves one step at a time across the 7x5 input matrix. The filter can only move within the original boundaries of the input, resulting in a smaller 5x3 output matrix. This configuration is useful when you want to reduce the spatial dimensions of the feature map while preserving the exact spatial relationships between features. + +- By adding zero padding to the input matrix, it is expanded to 9x7, allowing the 3x3 filter to "fit" fully on the edges and corners. With a stride of 1, the filter still moves one step at a time, but now the output matrix is the same size (7x5) as the original input. Same padding is often preferred in early layers of a CNN to preserve spatial information and avoid rapid feature map shrinkage. + +- Without padding, the 3x3 filter operates within the original input matrix boundaries, but now it moves two steps at a time (stride 2). This significantly reduces the output matrix size to 3x2. Larger strides are employed to decrease computational cost and the output size, which can be beneficial in speeding up the training process and preventing overfitting. However, they might miss some finer details due to the larger jumps. + +
+ +### Pooling Layer +Pooling layers reduce the dimensionality of each feature map while retaining the most critical information. The most common form of pooling is max pooling. +- **Input Shape:** The dimensions of the feature map from the convolutional layer. +- **Pooling Size:** The size of the pooling window (e.g., 2x2). +- **Strides:** The step size for the pooling operation. +- **Output:** A reduced feature map highlighting the most important features. +
+ + + + + + + + + + +
((2,2), 1)
4884
4884
2553
2553
0333
0333
+ + + + + + + +
((3,3) 2)
88
55
33
+
+ +- The high values (8) indicate that the "closed loop" filter found a strong match in those regions. + +- First matrix of size 6x4 represents a downsampled version of the input. + +- While the second matrix with 3x2, resulting in more aggressive downsampling. + + +
+ +### Flatten Layer +The flatten layer converts the 2D matrix data to a 1D vector, which can be fed into a fully connected (dense) layer. +- **Input Shape:** The 2D feature maps from the previous layer. +- **Output:** A 1D vector that represents the same data in a flattened format. +
+ + + + + + + + + + +
After max pooling (with kernel size = 3 and stride = 1)
888888555555333
+
+ +
+ +### Dropout Layer +Dropout is a regularization technique to prevent overfitting in neural networks by randomly setting a fraction of input units to zero at each update during training time. +- **Input Shape:** The data from the previous layer. +- **Dropout Rate:** The fraction of units to drop (e.g., 0.5 for 50% dropout). +- **Output:** The same shape as the input, with some units set to zero. +
+ + + + + +
dropout rate = 0.3
880800 505055 033
+
+ +- The updated 0 values represents the dropped units. + +## Implementation + +Below is the implementation of a simple CNN in Python. Each function within the `CNN` class corresponds to a layer in the network. + +```python +import numpy as np + +class CNN: + def __init__(self): + pass + + def convLayer(self, input_shape, channels, strides, padding, filter_size): + height, width = input_shape + input_shape_with_channels = (height, width, channels) + print("Input Shape (with channels):", input_shape_with_channels) + + # Generate random input and filter matrices + input_matrix = np.random.randint(0, 10, size=input_shape_with_channels) + filter_matrix = np.random.randint(0, 5, size=(filter_size[0], filter_size[1], channels)) + + print("\nInput Matrix:\n", input_matrix[:, :, 0]) + print("\nFilter Matrix:\n", filter_matrix[:, :, 0]) + + padding = padding.lower() + + if padding == 'same': + # Calculate padding needed for each dimension + pad_height = filter_size[0] // 2 + pad_width = filter_size[1] // 2 + + # Apply padding to the input matrix + input_matrix = np.pad(input_matrix, ((pad_height, pad_height), (pad_width, pad_width), (0, 0)), mode='constant') + + # Adjust height and width to consider the padding + height += 2 * pad_height + width += 2 * pad_width + + elif padding == 'valid': + pass + + else: + return "Invalid Padding!!" + + # Output dimensions + conv_height = (height - filter_size[0]) // strides[0] + 1 + conv_width = (width - filter_size[1]) // strides[1] + 1 + + output_matrix = np.zeros((conv_height, conv_width, channels)) + + # Convolution Operation + for i in range(0, height - filter_size[0] + 1, strides[0]): + for j in range(0, width - filter_size[1] + 1, strides[1]): + receptive_field = input_matrix[i:i + filter_size[0], j:j + filter_size[1], :] + output_matrix[i // strides[0], j // strides[1], :] = np.sum(receptive_field * filter_matrix, axis=(0, 1, 2)) + + return output_matrix + + def maxPooling(self, input_matrix, pool_size=(2, 2), strides_pooling=(2, 2)): + input_height, input_width, input_channels = input_matrix.shape + pool_height, pool_width = pool_size + stride_height, stride_width = strides_pooling + + # Calculate output dimensions + pooled_height = (input_height - pool_height) // stride_height + 1 + pooled_width = (input_width - pool_width) // stride_width + 1 + + # Initialize output + pooled_matrix = np.zeros((pooled_height, pooled_width, input_channels)) + + # Perform max pooling + for c in range(input_channels): + for i in range(0, input_height - pool_height + 1, stride_height): + for j in range(0, input_width - pool_width + 1, stride_width): + patch = input_matrix[i:i + pool_height, j:j + pool_width, c] + pooled_matrix[i // stride_height, j // stride_width, c] = np.max(patch) + + return pooled_matrix + + def flatten(self, input_matrix): + return input_matrix.flatten() + + def dropout(self, input_matrix, dropout_rate=0.5): + assert 0 <= dropout_rate < 1, "Dropout rate must be in [0, 1)." + dropout_mask = np.random.binomial(1, 1 - dropout_rate, size=input_matrix.shape) + return input_matrix * dropout_mask +``` + +Run the below command to generate output, based on random input and filter matrices. + +```python +input_shape = (5, 5) +channels = 1 +strides = (1, 1) +padding = 'valid' +filter_size = (3, 3) + +cnn_model = CNN() + +conv_output = cnn_model.convLayer(input_shape, channels, strides, padding, filter_size) +print("\nConvolution Output:\n", conv_output[:, :, 0]) + +pool_size = (2, 2) +strides_pooling = (1, 1) + +maxPool_output = cnn_model.maxPooling(conv_output, pool_size, strides_pooling) +print("\nMax Pooling Output:\n", maxPool_output[:, :, 0]) + +flattened_output = cnn_model.flatten(maxPool_output) +print("\nFlattened Output:\n", flattened_output) + +dropout_output = cnn_model.dropout(flattened_output, dropout_rate=0.3) +print("\nDropout Output:\n", dropout_output) +``` + +Feel free to play around with the parameters! \ No newline at end of file diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md index 94ca1e2f..ea8b5cb3 100644 --- a/contrib/machine-learning/index.md +++ b/contrib/machine-learning/index.md @@ -9,3 +9,4 @@ - [TensorFlow.md](tensorFlow.md) - [PyTorch.md](pytorch.md) - [Types of optimizers](Types_of_optimizers.md) +- [Introduction To Convolutional Neural Networks (CNNs)](IntroToCNNs.md) From f89ffbd58c0082f8533064aa864483799a9c1751 Mon Sep 17 00:00:00 2001 From: Aman Barthwal Date: Thu, 30 May 2024 17:41:16 +0530 Subject: [PATCH 2/7] Update IntroToCNNs.md --- contrib/machine-learning/IntroToCNNs.md | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/contrib/machine-learning/IntroToCNNs.md b/contrib/machine-learning/IntroToCNNs.md index 5f81ace5..7c0812f4 100644 --- a/contrib/machine-learning/IntroToCNNs.md +++ b/contrib/machine-learning/IntroToCNNs.md @@ -63,7 +63,8 @@ The convolutional layer is the core building block of a CNN. The layer's paramet #### Input Shape The dimensions of the input image, including the number of channels (e.g., 3 for RGB images & 1 for Grayscale images). -
+
+

@@ -76,6 +77,8 @@ The dimensions of the input image, including the number of channels (e.g., 3 for
1 and 0
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+

@@ -88,6 +91,7 @@ The dimensions of the input image, including the number of channels (e.g., 3 for
9
00010
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- The input matrix represents a simplified binary image of handwritten digits, @@ -450,4 +454,4 @@ dropout_output = cnn_model.dropout(flattened_output, dropout_rate=0.3) print("\nDropout Output:\n", dropout_output) ``` -Feel free to play around with the parameters! \ No newline at end of file +Feel free to play around with the parameters! From d9ab12136329bf485af34a2dbf31fa8e933a9ebe Mon Sep 17 00:00:00 2001 From: Aman Barthwal Date: Thu, 30 May 2024 17:42:51 +0530 Subject: [PATCH 3/7] Update IntroToCNNs.md --- contrib/machine-learning/IntroToCNNs.md | 16 ++++++++++++++++ 1 file changed, 16 insertions(+) diff --git a/contrib/machine-learning/IntroToCNNs.md b/contrib/machine-learning/IntroToCNNs.md index 7c0812f4..802cfdb8 100644 --- a/contrib/machine-learning/IntroToCNNs.md +++ b/contrib/machine-learning/IntroToCNNs.md @@ -25,6 +25,22 @@ + + +
Table 1 Heading 1 Table 1 Heading 2
+ +|Table 1| Middle | Table 2| +|--|--|--| +|a| not b|and c | + + + +|b|1|2|3| +|--|--|--|--| +|a|s|d|f| + +
+ ## Introduction Convolutional Neural Networks (CNNs) are a specialized type of artificial neural network designed primarily for processing structured grid data like images. CNNs are particularly powerful for tasks involving image recognition, classification, and computer vision. They have revolutionized these fields, outperforming traditional neural networks by leveraging their unique architecture to capture spatial hierarchies in images. From 1d01704f40d48be974079d84a7511d281caab497 Mon Sep 17 00:00:00 2001 From: iABn0rma1 Date: Thu, 30 May 2024 23:59:27 +0530 Subject: [PATCH 4/7] replaced tables with images --- contrib/machine-learning/IntroToCNNs.md | 230 ++---------------- .../machine-learning/assets/cnn-dropout.png | Bin 0 -> 28288 bytes .../machine-learning/assets/cnn-filters.png | Bin 0 -> 38260 bytes .../machine-learning/assets/cnn-flattened.png | Bin 0 -> 33305 bytes .../assets/cnn-input_shape.png | Bin 0 -> 54890 bytes .../machine-learning/assets/cnn-ouputs.png | Bin 0 -> 94050 bytes .../machine-learning/assets/cnn-padding.png | Bin 0 -> 98306 bytes .../machine-learning/assets/cnn-pooling.png | Bin 0 -> 79460 bytes .../machine-learning/assets/cnn-strides.png | Bin 0 -> 75501 bytes 9 files changed, 19 insertions(+), 211 deletions(-) create mode 100644 contrib/machine-learning/assets/cnn-dropout.png create mode 100644 contrib/machine-learning/assets/cnn-filters.png create mode 100644 contrib/machine-learning/assets/cnn-flattened.png create mode 100644 contrib/machine-learning/assets/cnn-input_shape.png create mode 100644 contrib/machine-learning/assets/cnn-ouputs.png create mode 100644 contrib/machine-learning/assets/cnn-padding.png create mode 100644 contrib/machine-learning/assets/cnn-pooling.png create mode 100644 contrib/machine-learning/assets/cnn-strides.png diff --git a/contrib/machine-learning/IntroToCNNs.md b/contrib/machine-learning/IntroToCNNs.md index 802cfdb8..f8329804 100644 --- a/contrib/machine-learning/IntroToCNNs.md +++ b/contrib/machine-learning/IntroToCNNs.md @@ -25,22 +25,6 @@ - - -
Table 1 Heading 1 Table 1 Heading 2
- -|Table 1| Middle | Table 2| -|--|--|--| -|a| not b|and c | - - - -|b|1|2|3| -|--|--|--|--| -|a|s|d|f| - -
- ## Introduction Convolutional Neural Networks (CNNs) are a specialized type of artificial neural network designed primarily for processing structured grid data like images. CNNs are particularly powerful for tasks involving image recognition, classification, and computer vision. They have revolutionized these fields, outperforming traditional neural networks by leveraging their unique architecture to capture spatial hierarchies in images. @@ -79,35 +63,8 @@ The convolutional layer is the core building block of a CNN. The layer's paramet #### Input Shape The dimensions of the input image, including the number of channels (e.g., 3 for RGB images & 1 for Grayscale images). -
-

- - - - - - - - - - - -
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-

- - - - - - - - - - - -
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+
+
- The input matrix represents a simplified binary image of handwritten digits, @@ -121,39 +78,8 @@ where '1' denotes the presence of ink and '0' represents the absence of ink. #### Strides The step size with which the filter moves across the input image. -
- - - - - - - - - - - -
3
011 - 10
010 - 10
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000 - 10
000 - 10
00010
- - - - - - - - - - - -
2
01 - 110
01 - 010
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00 - 010
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00010
+
+
- This visualization will help you understand how the filter (kernel) moves acroos the input matrix with stride values of 3 and 2. @@ -168,33 +94,8 @@ The step size with which the filter moves across the input image. #### Padding Determines whether the output size is the same as the input size ('same') or reduced ('valid'). -
- - - - - - - - - - - - - -
padding='same'
0000000
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- - - - - - - - - - - -
padding='valid'
01110
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+
- `Same` padding is preferred in earlier layers to preserve spatial and edge information, as it can help the network learn more detailed features. @@ -205,31 +106,8 @@ Determines whether the output size is the same as the input size ('same') or red #### Filters Small matrices that slide over the input data to extract features. -
- - - - - - - -
closed loop
111
101
111
- - - - - - - -
vertical line
010
010
010
- - - - - - - -
both diagonals
101
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+
+
- The first filter aims to detect closed loops within the input image, being highly relevant for recognizing digits with circular or oval shapes, such as '0', '6', '8', or '9'. @@ -242,37 +120,8 @@ Small matrices that slide over the input data to extract features. #### Output A set of feature maps that represent the presence of different features in the input. -
- - - - - - - - - -
('valid', 1)
404
25-3
25-3
032
032
- - - - - - - - - - - -
('same', 1)
22422
34843
22533
12533
00323
00323
00212
- - - - - - - -
('valid', 2)
44
23
02
+
+
- With no padding and a stride of 1, the 3x3 filter moves one step at a time across the 7x5 input matrix. The filter can only move within the original boundaries of the input, resulting in a smaller 5x3 output matrix. This configuration is useful when you want to reduce the spatial dimensions of the feature map while preserving the exact spatial relationships between features. @@ -289,69 +138,29 @@ Pooling layers reduce the dimensionality of each feature map while retaining the - **Pooling Size:** The size of the pooling window (e.g., 2x2). - **Strides:** The step size for the pooling operation. - **Output:** A reduced feature map highlighting the most important features. -
- - - - - - - - - - -
((2,2), 1)
4884
4884
2553
2553
0333
0333
- - - - - - - -
((3,3) 2)
88
55
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+
+
- The high values (8) indicate that the "closed loop" filter found a strong match in those regions. - - First matrix of size 6x4 represents a downsampled version of the input. - - While the second matrix with 3x2, resulting in more aggressive downsampling. - -
- ### Flatten Layer The flatten layer converts the 2D matrix data to a 1D vector, which can be fed into a fully connected (dense) layer. - **Input Shape:** The 2D feature maps from the previous layer. - **Output:** A 1D vector that represents the same data in a flattened format. -
- - - - - - - - - - -
After max pooling (with kernel size = 3 and stride = 1)
888888555555333
+
+
-
- ### Dropout Layer Dropout is a regularization technique to prevent overfitting in neural networks by randomly setting a fraction of input units to zero at each update during training time. - **Input Shape:** The data from the previous layer. - **Dropout Rate:** The fraction of units to drop (e.g., 0.5 for 50% dropout). - **Output:** The same shape as the input, with some units set to zero. -
- - - - - -
dropout rate = 0.3
880800 505055 033
+
+
- The updated 0 values represents the dropped units. @@ -402,9 +211,8 @@ class CNN: # Output dimensions conv_height = (height - filter_size[0]) // strides[0] + 1 conv_width = (width - filter_size[1]) // strides[1] + 1 - output_matrix = np.zeros((conv_height, conv_width, channels)) - + # Convolution Operation for i in range(0, height - filter_size[0] + 1, strides[0]): for j in range(0, width - filter_size[1] + 1, strides[1]): @@ -443,7 +251,7 @@ class CNN: return input_matrix * dropout_mask ``` -Run the below command to generate output, based on random input and filter matrices. +Run the below command to generate output with random input and filter matrices, depending on the given size. ```python input_shape = (5, 5) @@ -470,4 +278,4 @@ dropout_output = cnn_model.dropout(flattened_output, dropout_rate=0.3) print("\nDropout Output:\n", dropout_output) ``` -Feel free to play around with the parameters! +Feel free to play around with the parameters! \ No newline at end of file diff --git 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b/contrib/machine-learning/IntroToCNNs.md @@ -26,25 +26,15 @@ ## Introduction - Convolutional Neural Networks (CNNs) are a specialized type of artificial neural network designed primarily for processing structured grid data like images. CNNs are particularly powerful for tasks involving image recognition, classification, and computer vision. They have revolutionized these fields, outperforming traditional neural networks by leveraging their unique architecture to capture spatial hierarchies in images. ### Why CNNs are Superior to Traditional Neural Networks - -1. **Localized Receptive Fields**: - - CNNs use convolutional layers that apply filters to local regions of the input image. This localized connectivity ensures that the network learns spatial hierarchies and patterns, such as edges and textures, which are essential for image recognition tasks. - -2. **Parameter Sharing**: - - In CNNs, the same filter (set of weights) is used across different parts of the input, significantly reducing the number of parameters compared to fully connected layers in traditional neural networks. This not only lowers the computational cost but also mitigates the risk of overfitting. - -3. **Translation Invariance**: - - Due to the shared weights and pooling operations, CNNs are inherently invariant to translations of the input image. This means that they can recognize objects even when they appear in different locations within the image. - -4. **Hierarchical Feature Learning**: - - CNNs automatically learn a hierarchy of features from low-level features like edges to high-level features like shapes and objects. Traditional neural networks, on the other hand, require manual feature extraction which is less effective and more time-consuming. +1. **Localized Receptive Fields**: CNNs use convolutional layers that apply filters to local regions of the input image. This localized connectivity ensures that the network learns spatial hierarchies and patterns, such as edges and textures, which are essential for image recognition tasks. +2. **Parameter Sharing**: In CNNs, the same filter (set of weights) is used across different parts of the input, significantly reducing the number of parameters compared to fully connected layers in traditional neural networks. This not only lowers the computational cost but also mitigates the risk of overfitting. +3. **Translation Invariance**: Due to the shared weights and pooling operations, CNNs are inherently invariant to translations of the input image. This means that they can recognize objects even when they appear in different locations within the image. +4. **Hierarchical Feature Learning**: CNNs automatically learn a hierarchy of features from low-level features like edges to high-level features like shapes and objects. Traditional neural networks, on the other hand, require manual feature extraction which is less effective and more time-consuming. ### Use Cases of CNNs - - **Image Classification**: Identifying objects within an image (e.g., classifying a picture as containing a cat or a dog). - **Object Detection**: Detecting and locating objects within an image (e.g., finding faces in a photo). - **Image Segmentation**: Partitioning an image into segments or regions (e.g., dividing an image into different objects and background). @@ -55,7 +45,6 @@ Convolutional Neural Networks (CNNs) are a specialized type of artificial neural ### Let's start by understanding the basic architecture of CNNs. ## CNN Architecture - Convolution layers, pooling layers, and fully connected layers are just a few of the many building blocks that CNNs use to automatically and adaptively learn spatial hierarchies of information through backpropagation. ### Convolutional Layer @@ -67,31 +56,22 @@ The dimensions of the input image, including the number of channels (e.g., 3 for

-- The input matrix represents a simplified binary image of handwritten digits, -where '1' denotes the presence of ink and '0' represents the absence of ink. - +- The input matrix is a binary image of handwritten digits, +where '1' marks the pixels containing the digit (ink/grayscale area) and '0' marks the background pixels (empty space). - The first matrix shows the represnetation of 1 and 0, which can be depicted as a vertical line and a closed loop. - - The second matrix represents 9, combining the loop and line. -
- #### Strides The step size with which the filter moves across the input image.
-- This visualization will help you understand how the filter (kernel) moves acroos the input matrix with stride values of 3 and 2. - +- This visualization will help you understand how the filter (kernel) moves acroos the input matrix with stride values of (3,3) and (2,2). - A stride of 1 means the filter moves one step at a time, ensuring it covers the entire input matrix. - - However, with larger strides (like 3 or 2 in this example), the filter may not cover all elements, potentially missing some information. - - While this might seem like a drawback, higher strides are often used to reduce computational cost and decrease the output size, which can be beneficial in speeding up the training process and preventing overfitting. -
- #### Padding Determines whether the output size is the same as the input size ('same') or reduced ('valid').
@@ -99,10 +79,8 @@ Determines whether the output size is the same as the input size ('same') or red
- `Same` padding is preferred in earlier layers to preserve spatial and edge information, as it can help the network learn more detailed features. - - Choose `valid` padding when focusing on the central input region or requiring specific output dimensions. - -
+- Padding value can be determined by $ ( f - 1 ) \over 2 $, where f isfilter size #### Filters Small matrices that slide over the input data to extract features. @@ -111,9 +89,7 @@ Small matrices that slide over the input data to extract features.
- The first filter aims to detect closed loops within the input image, being highly relevant for recognizing digits with circular or oval shapes, such as '0', '6', '8', or '9'. - - The next filter helps in detecting vertical lines, crucial for identifying digits like '1', '4', '7', and parts of other digits that contain vertical strokes. - - The last filter shows how to detect diagonal lines in the input image, useful for identifying the slashes present in digits like '1', '7', or parts of '4' and '9'.
@@ -125,12 +101,21 @@ A set of feature maps that represent the presence of different features in the i
- With no padding and a stride of 1, the 3x3 filter moves one step at a time across the 7x5 input matrix. The filter can only move within the original boundaries of the input, resulting in a smaller 5x3 output matrix. This configuration is useful when you want to reduce the spatial dimensions of the feature map while preserving the exact spatial relationships between features. - - By adding zero padding to the input matrix, it is expanded to 9x7, allowing the 3x3 filter to "fit" fully on the edges and corners. With a stride of 1, the filter still moves one step at a time, but now the output matrix is the same size (7x5) as the original input. Same padding is often preferred in early layers of a CNN to preserve spatial information and avoid rapid feature map shrinkage. - - Without padding, the 3x3 filter operates within the original input matrix boundaries, but now it moves two steps at a time (stride 2). This significantly reduces the output matrix size to 3x2. Larger strides are employed to decrease computational cost and the output size, which can be beneficial in speeding up the training process and preventing overfitting. However, they might miss some finer details due to the larger jumps. - -
+- The output dimension of a CNN model is given by, $$ n_{out} = { n_{in} + (2 \cdot p) - k \over s } $$ +where,
+ nin = number of input features
+ p = padding
+ k = kernel size
+ s = stride + +- Also, the number of trainable parameters for each layer is given by, $ (n_c \cdot [k \cdot k] \cdot f) + f $ +
where,
+ nc = number of input channels
+ k x k = kernel size
+ f = number of filters
+ an additional f is added for bias ### Pooling Layer Pooling layers reduce the dimensionality of each feature map while retaining the most critical information. The most common form of pooling is max pooling. From 03a168d202babc9839e00b9b9563dc49f39bed39 Mon Sep 17 00:00:00 2001 From: Ankit Mahato Date: Sun, 2 Jun 2024 03:11:03 +0530 Subject: [PATCH 6/7] Update and rename IntroToCNNs.md to intro-to-cnn.md --- .../{IntroToCNNs.md => intro-to-cnn.md} | 75 +++++-------------- 1 file changed, 17 insertions(+), 58 deletions(-) rename contrib/machine-learning/{IntroToCNNs.md => intro-to-cnn.md} (89%) diff --git a/contrib/machine-learning/IntroToCNNs.md b/contrib/machine-learning/intro-to-cnn.md similarity index 89% rename from contrib/machine-learning/IntroToCNNs.md rename to contrib/machine-learning/intro-to-cnn.md index fb9027a5..0221ca10 100644 --- a/contrib/machine-learning/IntroToCNNs.md +++ b/contrib/machine-learning/intro-to-cnn.md @@ -1,30 +1,5 @@ # Understanding Convolutional Neural Networks (CNN) -## Table of Contents -
-Click to expand - -- [Introduction](#introduction) -- [CNN Architecture](#cnn-architecture) - -
- Convolutional Layer - - - [Input Shape](#input-shape) - - [Stride](#strides) - - [Padding](#padding) - - [Filter](#filters) - - [Output](#output) - -
- -- [Pooling Layer](#pooling-layer) -- [Flatten Layer](#flatten-layer) -- [Dropout Layer](#dropout-layer) - -- [Implementation](#implementation) - -
- ## Introduction Convolutional Neural Networks (CNNs) are a specialized type of artificial neural network designed primarily for processing structured grid data like images. CNNs are particularly powerful for tasks involving image recognition, classification, and computer vision. They have revolutionized these fields, outperforming traditional neural networks by leveraging their unique architecture to capture spatial hierarchies in images. @@ -52,9 +27,7 @@ The convolutional layer is the core building block of a CNN. The layer's paramet #### Input Shape The dimensions of the input image, including the number of channels (e.g., 3 for RGB images & 1 for Grayscale images). -
- -
+![image](assets/cnn-input_shape.png) - The input matrix is a binary image of handwritten digits, where '1' marks the pixels containing the digit (ink/grayscale area) and '0' marks the background pixels (empty space). @@ -63,9 +36,7 @@ where '1' marks the pixels containing the digit (ink/grayscale area) and '0' mar #### Strides The step size with which the filter moves across the input image. -
- -
+![image](assets/cnn-strides.png) - This visualization will help you understand how the filter (kernel) moves acroos the input matrix with stride values of (3,3) and (2,2). - A stride of 1 means the filter moves one step at a time, ensuring it covers the entire input matrix. @@ -74,9 +45,7 @@ The step size with which the filter moves across the input image. #### Padding Determines whether the output size is the same as the input size ('same') or reduced ('valid'). -
- -
+![image](assets/cnn-padding.png) - `Same` padding is preferred in earlier layers to preserve spatial and edge information, as it can help the network learn more detailed features. - Choose `valid` padding when focusing on the central input region or requiring specific output dimensions. @@ -84,37 +53,31 @@ Determines whether the output size is the same as the input size ('same') or red #### Filters Small matrices that slide over the input data to extract features. -
- -
+![image](assets/cnn-filters.png) - The first filter aims to detect closed loops within the input image, being highly relevant for recognizing digits with circular or oval shapes, such as '0', '6', '8', or '9'. - The next filter helps in detecting vertical lines, crucial for identifying digits like '1', '4', '7', and parts of other digits that contain vertical strokes. - The last filter shows how to detect diagonal lines in the input image, useful for identifying the slashes present in digits like '1', '7', or parts of '4' and '9'. -
- #### Output A set of feature maps that represent the presence of different features in the input. -
- -
+![image](assets/cnn-ouputs.png) - With no padding and a stride of 1, the 3x3 filter moves one step at a time across the 7x5 input matrix. The filter can only move within the original boundaries of the input, resulting in a smaller 5x3 output matrix. This configuration is useful when you want to reduce the spatial dimensions of the feature map while preserving the exact spatial relationships between features. - By adding zero padding to the input matrix, it is expanded to 9x7, allowing the 3x3 filter to "fit" fully on the edges and corners. With a stride of 1, the filter still moves one step at a time, but now the output matrix is the same size (7x5) as the original input. Same padding is often preferred in early layers of a CNN to preserve spatial information and avoid rapid feature map shrinkage. - Without padding, the 3x3 filter operates within the original input matrix boundaries, but now it moves two steps at a time (stride 2). This significantly reduces the output matrix size to 3x2. Larger strides are employed to decrease computational cost and the output size, which can be beneficial in speeding up the training process and preventing overfitting. However, they might miss some finer details due to the larger jumps. - The output dimension of a CNN model is given by, $$ n_{out} = { n_{in} + (2 \cdot p) - k \over s } $$ -where,
- nin = number of input features
- p = padding
- k = kernel size
+where, + nin = number of input features + p = padding + k = kernel size s = stride -- Also, the number of trainable parameters for each layer is given by, $ (n_c \cdot [k \cdot k] \cdot f) + f $ -
where,
- nc = number of input channels
- k x k = kernel size
- f = number of filters
+- Also, the number of trainable parameters for each layer is given by, $ (n_c \cdot [k \cdot k] \cdot f) + f $ +where, + nc = number of input channels + k x k = kernel size + f = number of filters an additional f is added for bias ### Pooling Layer @@ -135,18 +98,14 @@ Pooling layers reduce the dimensionality of each feature map while retaining the The flatten layer converts the 2D matrix data to a 1D vector, which can be fed into a fully connected (dense) layer. - **Input Shape:** The 2D feature maps from the previous layer. - **Output:** A 1D vector that represents the same data in a flattened format. -
- -
+![image](assets/cnn-flattened.png) ### Dropout Layer Dropout is a regularization technique to prevent overfitting in neural networks by randomly setting a fraction of input units to zero at each update during training time. - **Input Shape:** The data from the previous layer. - **Dropout Rate:** The fraction of units to drop (e.g., 0.5 for 50% dropout). - **Output:** The same shape as the input, with some units set to zero. -
- -
+![image](assets/cnn-dropout.png) - The updated 0 values represents the dropped units. @@ -263,4 +222,4 @@ dropout_output = cnn_model.dropout(flattened_output, dropout_rate=0.3) print("\nDropout Output:\n", dropout_output) ``` -Feel free to play around with the parameters! \ No newline at end of file +Feel free to play around with the parameters! From e4dd80f1ce9e18679d00ba97bbe99a337a15b73e Mon Sep 17 00:00:00 2001 From: Ankit Mahato Date: Sun, 2 Jun 2024 03:11:26 +0530 Subject: [PATCH 7/7] Update index.md --- contrib/machine-learning/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/contrib/machine-learning/index.md b/contrib/machine-learning/index.md index ea8b5cb3..988a27f8 100644 --- a/contrib/machine-learning/index.md +++ b/contrib/machine-learning/index.md @@ -9,4 +9,4 @@ - [TensorFlow.md](tensorFlow.md) - [PyTorch.md](pytorch.md) - [Types of optimizers](Types_of_optimizers.md) -- [Introduction To Convolutional Neural Networks (CNNs)](IntroToCNNs.md) +- [Introduction To Convolutional Neural Networks (CNNs)](intro-to-cnn.md)