Deciphering SVMs: A Comprehensive Guide to Support Vector Machines

June 28, 2023

Support Vector Machines (SVMs) are highly effective and extensively utilized models in  machine learning for classification and regression tasks. They have proven effective in various domains, including image recognition, text classification, and bioinformatics. This article will dive into the concepts behind SVMs, their mathematical formulation, and their practical implementation.

Introduction to SVMs

Support Vector Machines are supervised learning models used for binary classification tasks, where the goal is to separate data points belonging to different classes using a hyperplane. The key idea behind SVMs is to find the hyperplane that maximizes the margin between the classes, leading to better generalization and robustness.

Linear SVMs

Let's start by understanding linear SVMs, which work with linearly separable data. Given a training dataset consisting of input vectors X and corresponding binary labels y (-1 or 1), the goal of a linear SVM is to find the optimal hyperplane that separates the two classes with the most significant possible margin.

The margin is the distance between the hyperplane and the nearest data points from each class, called support vectors. The equation represents the hyperplane:

w^T * x + b = 0

Here, w is the weight vector perpendicular to the hyperplane, and b is the bias term. The decision function of the SVM is given by:

f(x) = sign(w^T * x + b)

The sign function returns -1 or 1, depending on which side of the hyperplane the data point lies.

Soft Margin SVMs

In real-world scenarios, data may not be perfectly separable by a hyperplane. Soft Margin SVMs address this issue by allowing some misclassification errors. The soft margin formulation introduces slack variables ξ to relax the constraints and permits misclassifications. The objective of a soft margin SVM is to minimize the misclassification errors while maximizing the margin.

The optimization problem for soft-margin SVMs can be formulated as :

minimize: (1/2) * ||w||^2 + C * Σ ξ_i

subject to: y_i * (w^T * x_i + b) ≥ 1 - ξ_i

            ξ_i ≥ 0

Here, C is a hyperparameter that controls the trade-off between maximizing the margin and minimizing the misclassifications. A considerable C value enforces a stricter margin and reduces misclassification tolerance.

Non-Linear SVMs

Linear SVMs are limited to linearly separable data. However, SVMs can handle non-linear data by using the kernel trick. The kernel trick involves mapping the input vectors into a higher-dimensional feature space where the data becomes linearly separable.

The kernel function K(x, x') computes the inner product of the mapped feature vectors. The SVM algorithm only requires the dot product between feature vectors, which is computationally efficient. Kernel functions commonly employed in machine learning encompass the linear, polynomial, and radial basis function (RBF) kernels.

Here's an example code snippet demonstrating how to use non-linear SVMs with different kernel functions:

from sklearn import svm
from sklearn.datasets import make_circles

# Generate non-linearly separable data
X, y = make_circles(n_samples=100, noise=0.1, factor=0.5, random_state=42)

# Create an SVM classifier with a polynomial kernel
poly_svm = svm.SVC(kernel='poly', degree=3), y)

# Create an SVM classifier with an RBF kernel
rbf_svm = svm.SVC(kernel='rbf', gamma='scale'), y)

# Create an SVM classifier with a linear kernel
linear_svm = svm.SVC(kernel='linear'), y)

# New data point for prediction
new_data = [[0.2, 0.2]]

# Predict the class using the trained models
poly_prediction = poly_svm.predict(new_data)
rbf_prediction = rbf_svm.predict(new_data)
linear_prediction = linear_svm.predict(new_data)

# Print the predictions
print("Poly SVM:", poly_prediction)
print("RBF SVM:", rbf_prediction)
print("Linear SVM:", linear_prediction)

In this example, we use the make_circles function from sklearn.datasets module to generate a synthetic dataset with non-linearly separable data points. We then create three SVM classifiers with different kernel functions: a polynomial kernel of degree 3, an RBF kernel, and a linear kernel.

Next, we train each SVM classifier using the generated data. Finally, we use the trained models to predict the class of a new data point (new_data) and print the predictions.

Training SVMs

We need to solve the optimization problem discussed earlier to train an SVM. This optimization problem is convex, and various optimization algorithms can be used, such as the Sequential Minimal Optimization (SMO) algorithm or gradient descent methods.

Once the optimization problem is solved, we obtain the optimal weight vector w and bias term b. These parameters can then predict unseen data by evaluating the f(x) decision function.

Here's an example code snippet demonstrating how to train an SVM classifier using the Sequential Minimal Optimization (SMO) algorithm and make predictions on unseen data:

from sklearn import svm
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# Load the Iris dataset
iris = load_iris()
X =
y =

# Split the data into training and testing sets
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

# Create an SVM classifier with the SMO algorithm
svm_classifier = svm.SVC(kernel='linear')

# Train the SVM classifier, y_train)

# Make predictions on the test set
y_pred = svm_classifier.predict(X_test)

# Calculate the accuracy of the classifier
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)

In this example, we use the Iris dataset from the sklearn.datasets module. We split the data into training and testing sets using the train_test_split function from the sklearn.model_selection module.

Next, we create an SVM classifier with the svm.SVC class and specify the kernel parameter as 'linear' to indicate using a linear kernel. The SMO algorithm is the default optimization algorithm used by svm.SVC for linear SVMs.

We then train the SVM classifier using the training data by calling the appropriate method, passing in X_train and y_train.

After training, we make predictions on the test set (X_test) using the trained SVM classifier's predict method and store the predicted labels in y_pred.

Finally, we calculate the accuracy of the classifier by comparing the predicted labels (y_pred) with the accurate labels (y_test) using the accuracy_score function from the sklearn.metrics module and print the accuracy.

Pros and Cons of SVMs

Support Vector Machines offer several advantages that contribute to their popularity:

1. Effective in high-dimensional spaces: SVMs perform well even when the number of features is larger than the number of samples, making them suitable for high-dimensional datasets.

2. Robust against overfitting: SVMs aim to maximize the margin, encouraging better generalization and reducing the risk of overfitting.

3. Versatile through kernel functions: SVMs can handle complex non-linear data patterns using different kernel functions.

However, SVMs also have some limitations:

1. Computationally expensive: Training an SVM can be computationally expensive, especially for large datasets. The runtime complexity of training an SVM is approximately O(n^3), where n is the number of training samples.

2. Difficult to interpret: SVMs provide accurate predictions, but the resulting models can be challenging to interpret and understand compared to other algorithms like decision trees.


When it comes to classification and regression tasks, Support Vector Machines prove to be the best option. They leverage the concept of finding an optimal hyperplane that maximizes the margin between classes, resulting in robust and accurate predictions. With the kernel trick, SVMs can handle non-linear data patterns efficiently. While SVMs have certain limitations, their effectiveness in various domains makes them a valuable tool in the machine learning toolkit.

By understanding the underlying concepts of SVMs and their mathematical formulation, you can leverage these models to tackle a wide range of real-world problems and achieve high performance in classification and regression tasks.

Latest Blogs
This is a decorative image for: A Complete Guide To Customer Acquisition For Startups
October 18, 2022

A Complete Guide To Customer Acquisition For Startups

Any business is enlivened by its customers. Therefore, a strategy to constantly bring in new clients is an ongoing requirement. In this regard, having a proper customer acquisition strategy can be of great importance.

So, if you are just starting your business, or planning to expand it, read on to learn more about this concept.

The problem with customer acquisition

As an organization, when working in a diverse and competitive market like India, you need to have a well-defined customer acquisition strategy to attain success. However, this is where most startups struggle. Now, you may have a great product or service, but if you are not in the right place targeting the right demographic, you are not likely to get the results you want.

To resolve this, typically, companies invest, but if that is not channelized properly, it will be futile.

So, the best way out of this dilemma is to have a clear customer acquisition strategy in place.

How can you create the ideal customer acquisition strategy for your business?

  • Define what your goals are

You need to define your goals so that you can meet the revenue expectations you have for the current fiscal year. You need to find a value for the metrics –

  • MRR – Monthly recurring revenue, which tells you all the income that can be generated from all your income channels.
  • CLV – Customer lifetime value tells you how much a customer is willing to spend on your business during your mutual relationship duration.  
  • CAC – Customer acquisition costs, which tells how much your organization needs to spend to acquire customers constantly.
  • Churn rate – It tells you the rate at which customers stop doing business.

All these metrics tell you how well you will be able to grow your business and revenue.

  • Identify your ideal customers

You need to understand who your current customers are and who your target customers are. Once you are aware of your customer base, you can focus your energies in that direction and get the maximum sale of your products or services. You can also understand what your customers require through various analytics and markers and address them to leverage your products/services towards them.

  • Choose your channels for customer acquisition

How will you acquire customers who will eventually tell at what scale and at what rate you need to expand your business? You could market and sell your products on social media channels like Instagram, Facebook and YouTube, or invest in paid marketing like Google Ads. You need to develop a unique strategy for each of these channels. 

  • Communicate with your customers

If you know exactly what your customers have in mind, then you will be able to develop your customer strategy with a clear perspective in mind. You can do it through surveys or customer opinion forms, email contact forms, blog posts and social media posts. After that, you just need to measure the analytics, clearly understand the insights, and improve your strategy accordingly.

Combining these strategies with your long-term business plan will bring results. However, there will be challenges on the way, where you need to adapt as per the requirements to make the most of it. At the same time, introducing new technologies like AI and ML can also solve such issues easily. To learn more about the use of AI and ML and how they are transforming businesses, keep referring to the blog section of E2E Networks.

Reference Links

This is a decorative image for: Constructing 3D objects through Deep Learning
October 18, 2022

Image-based 3D Object Reconstruction State-of-the-Art and trends in the Deep Learning Era

3D reconstruction is one of the most complex issues of deep learning systems. There have been multiple types of research in this field, and almost everything has been tried on it — computer vision, computer graphics and machine learning, but to no avail. However, that has resulted in CNN or convolutional neural networks foraying into this field, which has yielded some success.

The Main Objective of the 3D Object Reconstruction

Developing this deep learning technology aims to infer the shape of 3D objects from 2D images. So, to conduct the experiment, you need the following:

  • Highly calibrated cameras that take a photograph of the image from various angles.
  • Large training datasets can predict the geometry of the object whose 3D image reconstruction needs to be done. These datasets can be collected from a database of images, or they can be collected and sampled from a video.

By using the apparatus and datasets, you will be able to proceed with the 3D reconstruction from 2D datasets.

State-of-the-art Technology Used by the Datasets for the Reconstruction of 3D Objects

The technology used for this purpose needs to stick to the following parameters:

  • Input

Training with the help of one or multiple RGB images, where the segmentation of the 3D ground truth needs to be done. It could be one image, multiple images or even a video stream.

The testing will also be done on the same parameters, which will also help to create a uniform, cluttered background, or both.

  • Output

The volumetric output will be done in both high and low resolution, and the surface output will be generated through parameterisation, template deformation and point cloud. Moreover, the direct and intermediate outputs will be calculated this way.

  • Network architecture used

The architecture used in training is 3D-VAE-GAN, which has an encoder and a decoder, with TL-Net and conditional GAN. At the same time, the testing architecture is 3D-VAE, which has an encoder and a decoder.

  • Training used

The degree of supervision used in 2D vs 3D supervision, weak supervision along with loss functions have to be included in this system. The training procedure is adversarial training with joint 2D and 3D embeddings. Also, the network architecture is extremely important for the speed and processing quality of the output images.

  • Practical applications and use cases

Volumetric representations and surface representations can do the reconstruction. Powerful computer systems need to be used for reconstruction.

Given below are some of the places where 3D Object Reconstruction Deep Learning Systems are used:

  • 3D reconstruction technology can be used in the Police Department for drawing the faces of criminals whose images have been procured from a crime site where their faces are not completely revealed.
  • It can be used for re-modelling ruins at ancient architectural sites. The rubble or the debris stubs of structures can be used to recreate the entire building structure and get an idea of how it looked in the past.
  • They can be used in plastic surgery where the organs, face, limbs or any other portion of the body has been damaged and needs to be rebuilt.
  • It can be used in airport security, where concealed shapes can be used for guessing whether a person is armed or is carrying explosives or not.
  • It can also help in completing DNA sequences.

So, if you are planning to implement this technology, then you can rent the required infrastructure from E2E Networks and avoid investing in it. And if you plan to learn more about such topics, then keep a tab on the blog section of the website

Reference Links

This is a decorative image for: Comprehensive Guide to Deep Q-Learning for Data Science Enthusiasts
October 18, 2022

A Comprehensive Guide To Deep Q-Learning For Data Science Enthusiasts

For all data science enthusiasts who would love to dig deep, we have composed a write-up about Q-Learning specifically for you all. Deep Q-Learning and Reinforcement learning (RL) are extremely popular these days. These two data science methodologies use Python libraries like TensorFlow 2 and openAI’s Gym environment.

So, read on to know more.

What is Deep Q-Learning?

Deep Q-Learning utilizes the principles of Q-learning, but instead of using the Q-table, it uses the neural network. The algorithm of deep Q-Learning uses the states as input and the optimal Q-value of every action possible as the output. The agent gathers and stores all the previous experiences in the memory of the trained tuple in the following order:

State> Next state> Action> Reward

The neural network training stability increases using a random batch of previous data by using the experience replay. Experience replay also means the previous experiences stocking, and the target network uses it for training and calculation of the Q-network and the predicted Q-Value. This neural network uses openAI Gym, which is provided by taxi-v3 environments.

Now, any understanding of Deep Q-Learning   is incomplete without talking about Reinforcement Learning.

What is Reinforcement Learning?

Reinforcement is a subsection of ML. This part of ML is related to the action in which an environmental agent participates in a reward-based system and uses Reinforcement Learning to maximize the rewards. Reinforcement Learning is a different technique from unsupervised learning or supervised learning because it does not require a supervised input/output pair. The number of corrections is also less, so it is a highly efficient technique.

Now, the understanding of reinforcement learning is incomplete without knowing about Markov Decision Process (MDP). MDP is involved with each state that has been presented in the results of the environment, derived from the state previously there. The information which composes both states is gathered and transferred to the decision process. The task of the chosen agent is to maximize the awards. The MDP optimizes the actions and helps construct the optimal policy.

For developing the MDP, you need to follow the Q-Learning Algorithm, which is an extremely important part of data science and machine learning.

What is Q-Learning Algorithm?

The process of Q-Learning is important for understanding the data from scratch. It involves defining the parameters, choosing the actions from the current state and also choosing the actions from the previous state and then developing a Q-table for maximizing the results or output rewards.

The 4 steps that are involved in Q-Learning:

  1. Initializing parameters – The RL (reinforcement learning) model learns the set of actions that the agent requires in the state, environment and time.
  2. Identifying current state – The model stores the prior records for optimal action definition for maximizing the results. For acting in the present state, the state needs to be identified and perform an action combination for it.
  3. Choosing the optimal action set and gaining the relevant experience – A Q-table is generated from the data with a set of specific states and actions, and the weight of this data is calculated for updating the Q-Table to the following step.
  4. Updating Q-table rewards and next state determination – After the relevant experience is gained and agents start getting environmental records. The reward amplitude helps to present the subsequent step.  

In case the Q-table size is huge, then the generation of the model is a time-consuming process. This situation requires Deep Q-learning.

Hopefully, this write-up has provided an outline of Deep Q-Learning and its related concepts. If you wish to learn more about such topics, then keep a tab on the blog section of the E2E Networks website.

Reference Links

This is a decorative image for: GAUDI: A Neural Architect for Immersive 3D Scene Generation
October 13, 2022

GAUDI: A Neural Architect for Immersive 3D Scene Generation

The evolution of artificial intelligence in the past decade has been staggering, and now the focus is shifting towards AI and ML systems to understand and generate 3D spaces. As a result, there has been extensive research on manipulating 3D generative models. In this regard, Apple’s AI and ML scientists have developed GAUDI, a method specifically for this job.

An introduction to GAUDI

The GAUDI 3D immersive technique founders named it after the famous architect Antoni Gaudi. This AI model takes the help of a camera pose decoder, which enables it to guess the possible camera angles of a scene. Hence, the decoder then makes it possible to predict the 3D canvas from almost every angle.

What does GAUDI do?

GAUDI can perform multiple functions –

  • The extensions of these generative models have a tremendous effect on ML and computer vision. Pragmatically, such models are highly useful. They are applied in model-based reinforcement learning and planning world models, SLAM is s, or 3D content creation.
  • Generative modelling for 3D objects has been used for generating scenes using graf, pigan, and gsn, which incorporate a GAN (Generative Adversarial Network). The generator codes radiance fields exclusively. Using the 3D space in the scene along with the camera pose generates the 3D image from that point. This point has a density scalar and RGB value for that specific point in 3D space. This can be done from a 2D camera view. It does this by imposing 3D datasets on those 2D shots. It isolates various objects and scenes and combines them to render a new scene altogether.
  • GAUDI also removes GANs pathologies like mode collapse and improved GAN.
  • GAUDI also uses this to train data on a canonical coordinate system. You can compare it by looking at the trajectory of the scenes.

How is GAUDI applied to the content?

The steps of application for GAUDI have been given below:

  • Each trajectory is created, which consists of a sequence of posed images (These images are from a 3D scene) encoded into a latent representation. This representation which has a radiance field or what we refer to as the 3D scene and the camera path is created in a disentangled way. The results are interpreted as free parameters. The problem is optimized by and formulation of a reconstruction objective.
  • This simple training process is then scaled to trajectories, thousands of them creating a large number of views. The model samples the radiance fields totally from the previous distribution that the model has learned.
  • The scenes are thus synthesized by interpolation within the hidden space.
  • The scaling of 3D scenes generates many scenes that contain thousands of images. During training, there is no issue related to canonical orientation or mode collapse.
  • A novel de-noising optimization technique is used to find hidden representations that collaborate in modelling the camera poses and the radiance field to create multiple datasets with state-of-the-art performance in generating 3D scenes by building a setup that uses images and text.

To conclude, GAUDI has more capabilities and can also be used for sampling various images and video datasets. Furthermore, this will make a foray into AR (augmented reality) and VR (virtual reality). With GAUDI in hand, the sky is only the limit in the field of media creation. So, if you enjoy reading about the latest development in the field of AI and ML, then keep a tab on the blog section of the E2E Networks website.

Reference Links

Build on the most powerful infrastructure cloud

A vector illustration of a tech city using latest cloud technologies & infrastructure