This document provides an introduction to support vector machines (SVM). It discusses the history and development of SVM, including its introduction in 1992 and popularity due to success in handwritten digit recognition. The document then covers key concepts of SVM, including linear classifiers, maximum margin classification, soft margins, kernels, and nonlinear decision boundaries. Examples are provided to illustrate SVM classification and parameter selection.
This document provides an introduction to support vector machines (SVM). It discusses the history and key concepts of SVM, including how SVM finds the optimal separating hyperplane with maximum margin between classes to perform linear classification. It also describes how SVM can learn nonlinear decision boundaries using kernel tricks to implicitly map inputs to high-dimensional feature spaces. The document gives examples of commonly used kernel functions and outlines the steps to perform classification with SVM.
This document provides an overview of support vector machines (SVMs) presented by Eric Xing at CMU. It discusses how SVMs find the optimal decision boundary between two classes by maximizing the margin between them. It introduces the concepts of support vectors, which are the data points that define the decision boundary, and the kernel trick, which allows SVMs to implicitly perform computations in higher-dimensional feature spaces without explicitly computing the feature mappings.
This document summarizes support vector machines (SVMs), a machine learning technique for classification and regression. SVMs find the optimal separating hyperplane that maximizes the margin between positive and negative examples in the training data. This is achieved by solving a convex optimization problem that minimizes a quadratic function under linear constraints. SVMs can perform non-linear classification by implicitly mapping inputs into a higher-dimensional feature space using kernel functions. They have applications in areas like text categorization due to their ability to handle high-dimensional sparse data.
2.6 support vector machines and associative classifiers revisedKrish_ver2
Support vector machines (SVMs) are a type of supervised machine learning model that can be used for both classification and regression analysis. SVMs work by finding a hyperplane in a multidimensional space that best separates clusters of data points. Nonlinear kernels can be used to transform input data into a higher dimensional space to allow for the detection of complex patterns. Associative classification is an alternative approach that uses association rule mining to generate rules describing attribute relationships that can then be used for classification.
This document provides an overview of linear classifiers and support vector machines (SVMs) for text classification. It explains that SVMs find the optimal separating hyperplane between classes by maximizing the margin between the hyperplane and the closest data points of each class. The document discusses how SVMs can be extended to non-linear classification through kernel methods and feature spaces. It also provides details on solving the SVM optimization problem and using SVMs for classification.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
This document provides an introduction to support vector machines (SVM). It discusses the history and key concepts of SVM, including how SVM finds the optimal separating hyperplane with maximum margin between classes to perform linear classification. It also describes how SVM can learn nonlinear decision boundaries using kernel tricks to implicitly map inputs to high-dimensional feature spaces. The document gives examples of commonly used kernel functions and outlines the steps to perform classification with SVM.
This document provides an overview of support vector machines (SVMs) presented by Eric Xing at CMU. It discusses how SVMs find the optimal decision boundary between two classes by maximizing the margin between them. It introduces the concepts of support vectors, which are the data points that define the decision boundary, and the kernel trick, which allows SVMs to implicitly perform computations in higher-dimensional feature spaces without explicitly computing the feature mappings.
This document summarizes support vector machines (SVMs), a machine learning technique for classification and regression. SVMs find the optimal separating hyperplane that maximizes the margin between positive and negative examples in the training data. This is achieved by solving a convex optimization problem that minimizes a quadratic function under linear constraints. SVMs can perform non-linear classification by implicitly mapping inputs into a higher-dimensional feature space using kernel functions. They have applications in areas like text categorization due to their ability to handle high-dimensional sparse data.
2.6 support vector machines and associative classifiers revisedKrish_ver2
Support vector machines (SVMs) are a type of supervised machine learning model that can be used for both classification and regression analysis. SVMs work by finding a hyperplane in a multidimensional space that best separates clusters of data points. Nonlinear kernels can be used to transform input data into a higher dimensional space to allow for the detection of complex patterns. Associative classification is an alternative approach that uses association rule mining to generate rules describing attribute relationships that can then be used for classification.
This document provides an overview of linear classifiers and support vector machines (SVMs) for text classification. It explains that SVMs find the optimal separating hyperplane between classes by maximizing the margin between the hyperplane and the closest data points of each class. The document discusses how SVMs can be extended to non-linear classification through kernel methods and feature spaces. It also provides details on solving the SVM optimization problem and using SVMs for classification.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
This document provides an overview of Support Vector Machines (SVMs). It discusses how SVMs find the optimal separating hyperplane between two classes that maximizes the margin between them. It describes how SVMs can handle non-linearly separable data using kernels to project the data into higher dimensions where it may be linearly separable. The document also discusses multi-class classification approaches for SVMs and how they can be used for anomaly detection.
This document provides an introduction and overview of support vector machines (SVMs) for text classification. It discusses how SVMs find an optimal separating hyperplane between classes that maximizes the margin between the classes. It explains how SVMs can handle non-linear classification through the use of kernels to map data into higher-dimensional feature spaces. The document also discusses evaluation metrics like precision, recall, and accuracy for text classification and the differences between micro-averaging and macro-averaging of these metrics.
For more info visit us at: http://www.siliconmentor.com/
Support vector machines are widely used binary classifiers known for its ability to handle high dimensional data that classifies data by separating classes with a hyper-plane that maximizes the margin between them. The data points that are closest to hyper-plane are known as support vectors. Thus the selected decision boundary will be the one that minimizes the generalization error (by maximizing the margin between classes).
Linear Discrimination Centering on Support Vector Machinesbutest
Support vector machines learn hyperplanes that maximize the margin between two classes of data points. They introduce slack variables to handle non-linearly separable data, trying to maximize margins while minimizing errors. Popular SVMs use kernel functions to map data into higher dimensions, finding good linear separators in this space. SVMs find optimal hyperplanes by solving a convex optimization problem, but can be slow for large datasets. SVMs generally achieve high accuracy compared to other methods.
Support Vector Machine topic of machine learning.pptxCodingChamp1
Support Vector Machines (SVM) find the optimal separating hyperplane that maximizes the margin between two classes of data points. The hyperplane is chosen such that it maximizes the distance from itself to the nearest data points of each class. When data is not linearly separable, the kernel trick can be used to project the data into a higher dimensional space where it may be linearly separable. Common kernel functions include linear, polynomial, radial basis function (RBF), and sigmoid kernels. Soft margin SVMs introduce slack variables to allow some misclassification and better handle non-separable data. The C parameter controls the tradeoff between margin maximization and misclassification.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document provides an introduction to support vector machines (SVMs). It discusses how SVMs can be used for binary classification, regression, and multi-class problems. SVMs find the optimal separating hyperplane that maximizes the margin between classes. Soft margins allow for misclassified points by introducing slack variables. Kernels are discussed for mapping data into higher dimensional feature spaces to perform linear separation. The document outlines the formulation of SVMs for classification and regression and discusses model selection and different kernel functions.
Support Vector Machines (SVMs) were proposed in 1963 and took shape in the late 1970s as part of statistical learning theory. They became popular in the last decade for classification, regression, and optimization tasks. SVMs find the optimal separating hyperplane that maximizes the margin between positive and negative examples by solving a quadratic programming optimization with linear constraints. This is done efficiently using kernel methods that implicitly map inputs to high-dimensional feature spaces without explicitly computing the mappings. Empirically, SVMs have been shown to generalize well and are among the best performing classifiers.
Support Vector Machines in MapReduce presented an overview of support vector machines (SVMs) and how to implement them in a MapReduce framework to handle large datasets. The document discussed the theory behind basic linear SVMs and generalized multi-classification SVMs. It explained how to parallelize SVM training using stochastic gradient descent and randomly distributing samples across mappers and reducers. The document also addressed handling non-linear SVMs using kernel methods and approximations that allow SVMs to be treated as a linear problem in MapReduce. Finally, examples were given of large companies using SVMs trained on MapReduce to perform customer segmentation and improve inventory value.
This document provides an overview of various machine learning classification techniques including decision trees, k-nearest neighbors, decision lists, naive Bayes, artificial neural networks, and support vector machines. For each technique, it discusses the basic approach, how models are trained and tested, and potential issues that may arise such as overfitting, parameter selection, and handling different data types.
The document provides an overview of various machine learning classification algorithms including decision trees, lazy learners like K-nearest neighbors, decision lists, naive Bayes, artificial neural networks, and support vector machines. It also discusses evaluating and combining classifiers, as well as preprocessing techniques like feature selection and dimensionality reduction.
This document provides an overview of various machine learning algorithms and concepts, including supervised learning techniques like linear regression, logistic regression, decision trees, random forests, and support vector machines. It also discusses unsupervised learning methods like principal component analysis and kernel-based PCA. Key aspects of linear regression, logistic regression, and random forests are summarized, such as cost functions, gradient descent, sigmoid functions, and bagging. Kernel methods are also introduced, explaining how the kernel trick can allow solving non-linear problems by mapping data to a higher-dimensional feature space.
This document provides an introduction to support vector machines (SVMs) for text classification. It discusses how SVMs find an optimal separating hyperplane that maximizes the margin between classes. SVMs can handle non-linear classification through the use of kernels, which map data into a higher-dimensional feature space. The document outlines the mathematical formulations of linear and soft-margin SVMs, explains how the kernel trick allows evaluating inner products implicitly in that feature space, and summarizes how SVMs are used for classification tasks.
The proposed method uses an online weighted ensemble of one-class SVMs for feature selection in background/foreground separation. It automatically selects the best features for different image regions. Multiple base classifiers are generated using weighted random subspaces. The best base classifiers are selected and combined based on error rates. Feature importance is computed adaptively based on classifier responses. The background model is updated incrementally using a heuristic approach. Experimental results on the MSVS dataset show the proposed method achieves higher precision, recall, and F-score than other methods compared.
Support vector machine is a powerful machine learning method in data classification. Using it for applied researches is easy but comprehending it for further development requires a lot of efforts. This report is a tutorial on support vector machine with full of mathematical proofs and example, which help researchers to understand it by the fastest way from theory to practice. The report focuses on theory of optimization which is the base of support vector machine.
This document summarizes support vector machines (SVMs). It explains that SVMs find the optimal separating hyperplane that maximizes the margin between two classes of data points. The hyperplane is determined by support vectors, which are the data points closest to the hyperplane. SVMs can be solved as a quadratic programming problem. The document also discusses how kernels can map data into higher dimensional spaces to make non-separable problems separable by SVMs.
SVM is a supervised learning method that finds a hyperplane with maximum margin to separate classes. It uses kernels to map data to higher dimensions to allow for nonlinear separation. The objective is to minimize training error and model complexity by maximizing the margin between classes. SVMs solve a convex optimization problem that finds support vectors and determines the separating hyperplane using kernels, slack variables, and a cost parameter C to balance margin and errors. Parameter selection, like the kernel and its parameters, affects performance and is typically done through grid search and cross-validation.
Anomaly detection using deep one class classifier홍배 김
The document discusses anomaly detection techniques using deep one-class classifiers and generative adversarial networks (GANs). It proposes using an autoencoder to extract features from normal images, training a GAN on those features to model the distribution, and using a one-class support vector machine (SVM) to determine if new images are within the normal distribution. The method detects and localizes anomalies by generating a binary mask for abnormal regions. It also discusses Gaussian mixture models and the expectation-maximization algorithm for modeling multiple distributions in data.
The document discusses classification algorithms in machine learning. It introduces classification problems using the Iris flower dataset as an example, which contains measurements of Iris flowers to classify them into three species. It then discusses two classic classification algorithms - logistic regression and Gaussian discriminant analysis. Logistic regression uses a sigmoid function to generate predictions, while Gaussian discriminant analysis assumes a Gaussian distribution of the data. The document also demonstrates an application of these algorithms to classify handwritten digits.
This document provides an overview of support vector machines and related pattern recognition techniques:
- SVMs find the optimal separating hyperplane between classes by maximizing the margin between classes using support vectors.
- Nonlinear decision surfaces can be achieved by transforming data into a higher-dimensional feature space using kernel functions.
- Soft margin classifiers allow some misclassified points by introducing slack variables to improve generalization.
- Relevance vector machines take a Bayesian approach, placing a sparsity-inducing prior over weights to provide a probabilistic interpretation.
Orchestrating the Future: Navigating Today's Data Workflow Challenges with Ai...Kaxil Naik
Navigating today's data landscape isn't just about managing workflows; it's about strategically propelling your business forward. Apache Airflow has stood out as the benchmark in this arena, driving data orchestration forward since its early days. As we dive into the complexities of our current data-rich environment, where the sheer volume of information and its timely, accurate processing are crucial for AI and ML applications, the role of Airflow has never been more critical.
In my journey as the Senior Engineering Director and a pivotal member of Apache Airflow's Project Management Committee (PMC), I've witnessed Airflow transform data handling, making agility and insight the norm in an ever-evolving digital space. At Astronomer, our collaboration with leading AI & ML teams worldwide has not only tested but also proven Airflow's mettle in delivering data reliably and efficiently—data that now powers not just insights but core business functions.
This session is a deep dive into the essence of Airflow's success. We'll trace its evolution from a budding project to the backbone of data orchestration it is today, constantly adapting to meet the next wave of data challenges, including those brought on by Generative AI. It's this forward-thinking adaptability that keeps Airflow at the forefront of innovation, ready for whatever comes next.
The ever-growing demands of AI and ML applications have ushered in an era where sophisticated data management isn't a luxury—it's a necessity. Airflow's innate flexibility and scalability are what makes it indispensable in managing the intricate workflows of today, especially those involving Large Language Models (LLMs).
This talk isn't just a rundown of Airflow's features; it's about harnessing these capabilities to turn your data workflows into a strategic asset. Together, we'll explore how Airflow remains at the cutting edge of data orchestration, ensuring your organization is not just keeping pace but setting the pace in a data-driven future.
Session in https://budapestdata.hu/2024/04/kaxil-naik-astronomer-io/ | https://dataml24.sessionize.com/session/667627
This document provides an overview of Support Vector Machines (SVMs). It discusses how SVMs find the optimal separating hyperplane between two classes that maximizes the margin between them. It describes how SVMs can handle non-linearly separable data using kernels to project the data into higher dimensions where it may be linearly separable. The document also discusses multi-class classification approaches for SVMs and how they can be used for anomaly detection.
This document provides an introduction and overview of support vector machines (SVMs) for text classification. It discusses how SVMs find an optimal separating hyperplane between classes that maximizes the margin between the classes. It explains how SVMs can handle non-linear classification through the use of kernels to map data into higher-dimensional feature spaces. The document also discusses evaluation metrics like precision, recall, and accuracy for text classification and the differences between micro-averaging and macro-averaging of these metrics.
For more info visit us at: http://www.siliconmentor.com/
Support vector machines are widely used binary classifiers known for its ability to handle high dimensional data that classifies data by separating classes with a hyper-plane that maximizes the margin between them. The data points that are closest to hyper-plane are known as support vectors. Thus the selected decision boundary will be the one that minimizes the generalization error (by maximizing the margin between classes).
Linear Discrimination Centering on Support Vector Machinesbutest
Support vector machines learn hyperplanes that maximize the margin between two classes of data points. They introduce slack variables to handle non-linearly separable data, trying to maximize margins while minimizing errors. Popular SVMs use kernel functions to map data into higher dimensions, finding good linear separators in this space. SVMs find optimal hyperplanes by solving a convex optimization problem, but can be slow for large datasets. SVMs generally achieve high accuracy compared to other methods.
Support Vector Machine topic of machine learning.pptxCodingChamp1
Support Vector Machines (SVM) find the optimal separating hyperplane that maximizes the margin between two classes of data points. The hyperplane is chosen such that it maximizes the distance from itself to the nearest data points of each class. When data is not linearly separable, the kernel trick can be used to project the data into a higher dimensional space where it may be linearly separable. Common kernel functions include linear, polynomial, radial basis function (RBF), and sigmoid kernels. Soft margin SVMs introduce slack variables to allow some misclassification and better handle non-separable data. The C parameter controls the tradeoff between margin maximization and misclassification.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
This document provides an introduction to support vector machines (SVMs). It discusses how SVMs can be used for binary classification, regression, and multi-class problems. SVMs find the optimal separating hyperplane that maximizes the margin between classes. Soft margins allow for misclassified points by introducing slack variables. Kernels are discussed for mapping data into higher dimensional feature spaces to perform linear separation. The document outlines the formulation of SVMs for classification and regression and discusses model selection and different kernel functions.
Support Vector Machines (SVMs) were proposed in 1963 and took shape in the late 1970s as part of statistical learning theory. They became popular in the last decade for classification, regression, and optimization tasks. SVMs find the optimal separating hyperplane that maximizes the margin between positive and negative examples by solving a quadratic programming optimization with linear constraints. This is done efficiently using kernel methods that implicitly map inputs to high-dimensional feature spaces without explicitly computing the mappings. Empirically, SVMs have been shown to generalize well and are among the best performing classifiers.
Support Vector Machines in MapReduce presented an overview of support vector machines (SVMs) and how to implement them in a MapReduce framework to handle large datasets. The document discussed the theory behind basic linear SVMs and generalized multi-classification SVMs. It explained how to parallelize SVM training using stochastic gradient descent and randomly distributing samples across mappers and reducers. The document also addressed handling non-linear SVMs using kernel methods and approximations that allow SVMs to be treated as a linear problem in MapReduce. Finally, examples were given of large companies using SVMs trained on MapReduce to perform customer segmentation and improve inventory value.
This document provides an overview of various machine learning classification techniques including decision trees, k-nearest neighbors, decision lists, naive Bayes, artificial neural networks, and support vector machines. For each technique, it discusses the basic approach, how models are trained and tested, and potential issues that may arise such as overfitting, parameter selection, and handling different data types.
The document provides an overview of various machine learning classification algorithms including decision trees, lazy learners like K-nearest neighbors, decision lists, naive Bayes, artificial neural networks, and support vector machines. It also discusses evaluating and combining classifiers, as well as preprocessing techniques like feature selection and dimensionality reduction.
This document provides an overview of various machine learning algorithms and concepts, including supervised learning techniques like linear regression, logistic regression, decision trees, random forests, and support vector machines. It also discusses unsupervised learning methods like principal component analysis and kernel-based PCA. Key aspects of linear regression, logistic regression, and random forests are summarized, such as cost functions, gradient descent, sigmoid functions, and bagging. Kernel methods are also introduced, explaining how the kernel trick can allow solving non-linear problems by mapping data to a higher-dimensional feature space.
This document provides an introduction to support vector machines (SVMs) for text classification. It discusses how SVMs find an optimal separating hyperplane that maximizes the margin between classes. SVMs can handle non-linear classification through the use of kernels, which map data into a higher-dimensional feature space. The document outlines the mathematical formulations of linear and soft-margin SVMs, explains how the kernel trick allows evaluating inner products implicitly in that feature space, and summarizes how SVMs are used for classification tasks.
The proposed method uses an online weighted ensemble of one-class SVMs for feature selection in background/foreground separation. It automatically selects the best features for different image regions. Multiple base classifiers are generated using weighted random subspaces. The best base classifiers are selected and combined based on error rates. Feature importance is computed adaptively based on classifier responses. The background model is updated incrementally using a heuristic approach. Experimental results on the MSVS dataset show the proposed method achieves higher precision, recall, and F-score than other methods compared.
Support vector machine is a powerful machine learning method in data classification. Using it for applied researches is easy but comprehending it for further development requires a lot of efforts. This report is a tutorial on support vector machine with full of mathematical proofs and example, which help researchers to understand it by the fastest way from theory to practice. The report focuses on theory of optimization which is the base of support vector machine.
This document summarizes support vector machines (SVMs). It explains that SVMs find the optimal separating hyperplane that maximizes the margin between two classes of data points. The hyperplane is determined by support vectors, which are the data points closest to the hyperplane. SVMs can be solved as a quadratic programming problem. The document also discusses how kernels can map data into higher dimensional spaces to make non-separable problems separable by SVMs.
SVM is a supervised learning method that finds a hyperplane with maximum margin to separate classes. It uses kernels to map data to higher dimensions to allow for nonlinear separation. The objective is to minimize training error and model complexity by maximizing the margin between classes. SVMs solve a convex optimization problem that finds support vectors and determines the separating hyperplane using kernels, slack variables, and a cost parameter C to balance margin and errors. Parameter selection, like the kernel and its parameters, affects performance and is typically done through grid search and cross-validation.
Anomaly detection using deep one class classifier홍배 김
The document discusses anomaly detection techniques using deep one-class classifiers and generative adversarial networks (GANs). It proposes using an autoencoder to extract features from normal images, training a GAN on those features to model the distribution, and using a one-class support vector machine (SVM) to determine if new images are within the normal distribution. The method detects and localizes anomalies by generating a binary mask for abnormal regions. It also discusses Gaussian mixture models and the expectation-maximization algorithm for modeling multiple distributions in data.
The document discusses classification algorithms in machine learning. It introduces classification problems using the Iris flower dataset as an example, which contains measurements of Iris flowers to classify them into three species. It then discusses two classic classification algorithms - logistic regression and Gaussian discriminant analysis. Logistic regression uses a sigmoid function to generate predictions, while Gaussian discriminant analysis assumes a Gaussian distribution of the data. The document also demonstrates an application of these algorithms to classify handwritten digits.
This document provides an overview of support vector machines and related pattern recognition techniques:
- SVMs find the optimal separating hyperplane between classes by maximizing the margin between classes using support vectors.
- Nonlinear decision surfaces can be achieved by transforming data into a higher-dimensional feature space using kernel functions.
- Soft margin classifiers allow some misclassified points by introducing slack variables to improve generalization.
- Relevance vector machines take a Bayesian approach, placing a sparsity-inducing prior over weights to provide a probabilistic interpretation.
Orchestrating the Future: Navigating Today's Data Workflow Challenges with Ai...Kaxil Naik
Navigating today's data landscape isn't just about managing workflows; it's about strategically propelling your business forward. Apache Airflow has stood out as the benchmark in this arena, driving data orchestration forward since its early days. As we dive into the complexities of our current data-rich environment, where the sheer volume of information and its timely, accurate processing are crucial for AI and ML applications, the role of Airflow has never been more critical.
In my journey as the Senior Engineering Director and a pivotal member of Apache Airflow's Project Management Committee (PMC), I've witnessed Airflow transform data handling, making agility and insight the norm in an ever-evolving digital space. At Astronomer, our collaboration with leading AI & ML teams worldwide has not only tested but also proven Airflow's mettle in delivering data reliably and efficiently—data that now powers not just insights but core business functions.
This session is a deep dive into the essence of Airflow's success. We'll trace its evolution from a budding project to the backbone of data orchestration it is today, constantly adapting to meet the next wave of data challenges, including those brought on by Generative AI. It's this forward-thinking adaptability that keeps Airflow at the forefront of innovation, ready for whatever comes next.
The ever-growing demands of AI and ML applications have ushered in an era where sophisticated data management isn't a luxury—it's a necessity. Airflow's innate flexibility and scalability are what makes it indispensable in managing the intricate workflows of today, especially those involving Large Language Models (LLMs).
This talk isn't just a rundown of Airflow's features; it's about harnessing these capabilities to turn your data workflows into a strategic asset. Together, we'll explore how Airflow remains at the cutting edge of data orchestration, ensuring your organization is not just keeping pace but setting the pace in a data-driven future.
Session in https://budapestdata.hu/2024/04/kaxil-naik-astronomer-io/ | https://dataml24.sessionize.com/session/667627
Predictably Improve Your B2B Tech Company's Performance by Leveraging DataKiwi Creative
Harness the power of AI-backed reports, benchmarking and data analysis to predict trends and detect anomalies in your marketing efforts.
Peter Caputa, CEO at Databox, reveals how you can discover the strategies and tools to increase your growth rate (and margins!).
From metrics to track to data habits to pick up, enhance your reporting for powerful insights to improve your B2B tech company's marketing.
- - -
This is the webinar recording from the June 2024 HubSpot User Group (HUG) for B2B Technology USA.
Watch the video recording at https://youtu.be/5vjwGfPN9lw
Sign up for future HUG events at https://events.hubspot.com/b2b-technology-usa/
Open Source Contributions to Postgres: The Basics POSETTE 2024ElizabethGarrettChri
Postgres is the most advanced open-source database in the world and it's supported by a community, not a single company. So how does this work? How does code actually get into Postgres? I recently had a patch submitted and committed and I want to share what I learned in that process. I’ll give you an overview of Postgres versions and how the underlying project codebase functions. I’ll also show you the process for submitting a patch and getting that tested and committed.
Introduction to Jio Cinema**:
- Brief overview of Jio Cinema as a streaming platform.
- Its significance in the Indian market.
- Introduction to retention and engagement strategies in the streaming industry.
2. **Understanding Retention and Engagement**:
- Define retention and engagement in the context of streaming platforms.
- Importance of retaining users in a competitive market.
- Key metrics used to measure retention and engagement.
3. **Jio Cinema's Content Strategy**:
- Analysis of the content library offered by Jio Cinema.
- Focus on exclusive content, originals, and partnerships.
- Catering to diverse audience preferences (regional, genre-specific, etc.).
- User-generated content and interactive features.
4. **Personalization and Recommendation Algorithms**:
- How Jio Cinema leverages user data for personalized recommendations.
- Algorithmic strategies for suggesting content based on user preferences, viewing history, and behavior.
- Dynamic content curation to keep users engaged.
5. **User Experience and Interface Design**:
- Evaluation of Jio Cinema's user interface (UI) and user experience (UX).
- Accessibility features and device compatibility.
- Seamless navigation and search functionality.
- Integration with other Jio services.
6. **Community Building and Social Features**:
- Strategies for fostering a sense of community among users.
- User reviews, ratings, and comments.
- Social sharing and engagement features.
- Interactive events and campaigns.
7. **Retention through Loyalty Programs and Incentives**:
- Overview of loyalty programs and rewards offered by Jio Cinema.
- Subscription plans and benefits.
- Promotional offers, discounts, and partnerships.
- Gamification elements to encourage continued usage.
8. **Customer Support and Feedback Mechanisms**:
- Analysis of Jio Cinema's customer support infrastructure.
- Channels for user feedback and suggestions.
- Handling of user complaints and queries.
- Continuous improvement based on user feedback.
9. **Multichannel Engagement Strategies**:
- Utilization of multiple channels for user engagement (email, push notifications, SMS, etc.).
- Targeted marketing campaigns and promotions.
- Cross-promotion with other Jio services and partnerships.
- Integration with social media platforms.
10. **Data Analytics and Iterative Improvement**:
- Role of data analytics in understanding user behavior and preferences.
- A/B testing and experimentation to optimize engagement strategies.
- Iterative improvement based on data-driven insights.
1. Introduction to Support
Vector Machines
Note to other teachers and users of
these slides. Andrew would be delighted
if you found this source material useful in
giving your own lectures. Feel free to use
these slides verbatim, or to modify them
to fit your own needs. PowerPoint
originals are available. If you make use
of a significant portion of these slides in
your own lecture, please include this
message, or the following link to the
source repository of Andrew’s tutorials:
http://www.cs.cmu.edu/~awm/tutorials .
Comments and corrections gratefully
received.
Thanks:
Andrew Moore
CMU
And
Martin Law
Michigan State University
2. 2023/3/6 2
History of SVM
SVM is related to statistical learning theory [3]
SVM was first introduced in 1992 [1]
SVM becomes popular because of its success in
handwritten digit recognition
1.1% test error rate for SVM. This is the same as the error
rates of a carefully constructed neural network, LeNet 4.
See Section 5.11 in [2] or the discussion in [3] for details
SVM is now regarded as an important example of “kernel
methods”, one of the key area in machine learning
Note: the meaning of “kernel” is different from the “kernel”
function for Parzen windows
[1] B.E. Boser et al. A Training Algorithm for Optimal Margin Classifiers. Proceedings of the Fifth Annual Workshop on
Computational Learning Theory 5 144-152, Pittsburgh, 1992.
[2] L. Bottou et al. Comparison of classifier methods: a case study in handwritten digit recognition. Proceedings of the 12th
IAPR International Conference on Pattern Recognition, vol. 2, pp. 77-82.
[3] V. Vapnik. The Nature of Statistical Learning Theory. 2nd edition, Springer, 1999.
3. 2023/3/6 3
Linear Classifiers
f
x yest
denotes +1
denotes -1
f(x,w,b) = sign(w. x - b)
How would you
classify this data?
Estimation:
w: weight vector
x: data vector
8. 2023/3/6 8
Classifier Margin
f
x
a
yest
denotes +1
denotes -1
f(x,w,b) = sign(w. x - b)
Define the margin
of a linear
classifier as the
width that the
boundary could be
increased by
before hitting a
datapoint.
9. 2023/3/6 9
Maximum Margin
f
x
a
yest
denotes +1
denotes -1
f(x,w,b) = sign(w. x - b)
The maximum
margin linear
classifier is the
linear classifier
with the, um,
maximum margin.
This is the
simplest kind of
SVM (Called an
LSVM)
Linear SVM
10. 2023/3/6 10
Maximum Margin
f
x
a
yest
denotes +1
denotes -1
f(x,w,b) = sign(w. x + b)
The maximum
margin linear
classifier is the
linear classifier
with the, um,
maximum margin.
This is the
simplest kind of
SVM (Called an
LSVM)
Support Vectors
are those
datapoints that
the margin
pushes up
against
Linear SVM
11. 2023/3/6 11
Why Maximum Margin?
denotes +1
denotes -1
f(x,w,b) = sign(w. x - b)
The maximum
margin linear
classifier is the
linear classifier
with the, um,
maximum margin.
This is the
simplest kind of
SVM (Called an
LSVM)
Support Vectors
are those
datapoints that
the margin
pushes up
against
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How to calculate the distance from a point
to a line?
http://mathworld.wolfram.com/Point-LineDistance2-
Dimensional.html
In our case, w1*x1+w2*x2+b=0,
thus, w=(w1,w2), x=(x1,x2)
denotes +1
denotes -1 x
wx +b = 0
X – Vector
W – Normal Vector
b – Scale Value
W
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Estimate the Margin
What is the distance expression for a point x to a line
wx+b= 0?
denotes +1
denotes -1 x
wx +b = 0
2 2
1
2
( )
d
i
i
b b
d
w
x w x w
x
w
X – Vector
W – Normal Vector
b – Scale Value
W
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Large-margin Decision Boundary
The decision boundary should be as far away from the
data of both classes as possible
We should maximize the margin, m
Distance between the origin and the line wtx=-b is b/||w||
Class 1
Class 2
m
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Finding the Decision Boundary
Let {x1, ..., xn} be our data set and let yi {1,-1} be
the class label of xi
The decision boundary should classify all points correctly
To see this: when y=-1, we wish (wx+b)<1, when y=1,
we wish (wx+b)>1. For support vectors, we wish
y(wx+b)=1.
The decision boundary can be found by solving the
following constrained optimization problem
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Next step… Optional
Converting SVM to a form we can solve
Dual form
Allowing a few errors
Soft margin
Allowing nonlinear boundary
Kernel functions
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The Dual Problem (we ignore the derivation)
The new objective function is in terms of ai only
It is known as the dual problem: if we know w, we
know all ai; if we know all ai, we know w
The original problem is known as the primal problem
The objective function of the dual problem needs to be
maximized!
The dual problem is therefore:
Properties of ai when we introduce
the Lagrange multipliers
The result when we differentiate the
original Lagrangian w.r.t. b
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The Dual Problem
This is a quadratic programming (QP) problem
A global maximum of ai can always be found
w can be recovered by
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Characteristics of the Solution
Many of the ai are zero (see next page for example)
w is a linear combination of a small number of data points
This “sparse” representation can be viewed as data
compression as in the construction of knn classifier
xi with non-zero ai are called support vectors (SV)
The decision boundary is determined only by the SV
Let tj (j=1, ..., s) be the indices of the s support vectors. We
can write
For testing with a new data z
Compute and
classify z as class 1 if the sum is positive, and class 2
otherwise
Note: w need not be formed explicitly
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Allowing errors in our solutions
We allow “error” xi in classification; it is based on the
output of the discriminant function wTx+b
xi approximates the number of misclassified samples
Class 1
Class 2
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Soft Margin Hyperplane
If we minimize ixi, xi can be computed by
xi are “slack variables” in optimization
Note that xi=0 if there is no error for xi
xi is an upper bound of the number of errors
We want to minimize
C : tradeoff parameter between error and margin
The optimization problem becomes
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Extension to Non-linear Decision Boundary
So far, we have only considered large-
margin classifier with a linear decision
boundary
How to generalize it to become nonlinear?
Key idea: transform xi to a higher
dimensional space to “make life easier”
Input space: the space the point xi are
located
Feature space: the space of f(xi) after
transformation
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Transforming the Data (c.f. DHS Ch. 5)
Computation in the feature space can be costly because it is
high dimensional
The feature space is typically infinite-dimensional!
The kernel trick comes to rescue
f( )
f( )
f( )
f( )
f( )
f( )
f( )
f( )
f(.)
f( )
f( )
f( )
f( )
f( )
f( )
f( )
f( )
f( )
f( )
Feature space
Input space
Note: feature space is of higher dimension
than the input space in practice
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The Kernel Trick
Recall the SVM optimization problem
The data points only appear as inner product
As long as we can calculate the inner product in the
feature space, we do not need the mapping explicitly
Many common geometric operations (angles, distances)
can be expressed by inner products
Define the kernel function K by
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An Example for f(.) and K(.,.)
Suppose f(.) is given as follows
An inner product in the feature space is
So, if we define the kernel function as follows, there is
no need to carry out f(.) explicitly
This use of kernel function to avoid carrying out f(.)
explicitly is known as the kernel trick
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More on Kernel Functions
Not all similarity measures can be used as kernel
function, however
The kernel function needs to satisfy the Mercer function,
i.e., the function is “positive-definite”
This implies that
the n by n kernel matrix,
in which the (i,j)-th entry is the K(xi, xj), is always positive
definite
This also means that optimization problem can be solved
in polynomial time!
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Examples of Kernel Functions
Polynomial kernel with degree d
Radial basis function kernel with width s
Closely related to radial basis function neural networks
The feature space is infinite-dimensional
Sigmoid with parameter k and q
It does not satisfy the Mercer condition on all k and q
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Non-linear SVMs: Feature spaces
General idea: the original input space can always be mapped to
some higher-dimensional feature space where the training set is
separable:
Φ: x → φ(x)
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Example
Suppose we have 5 one-dimensional data points
x1=1, x2=2, x3=4, x4=5, x5=6, with 1, 2, 6 as class 1 and 4,
5 as class 2 y1=1, y2=1, y3=-1, y4=-1, y5=1
We use the polynomial kernel of degree 2
K(x,y) = (xy+1)2
C is set to 100
We first find ai (i=1, …, 5) by
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Example
By using a QP solver, we get
a1=0, a2=2.5, a3=0, a4=7.333, a5=4.833
Note that the constraints are indeed satisfied
The support vectors are {x2=2, x4=5, x5=6}
The discriminant function is
b is recovered by solving f(2)=1 or by f(5)=-1 or by f(6)=1,
as x2 and x5 lie on the line and x4
lies on the line
All three give b=9
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Software
A list of SVM implementation can be found at
http://www.kernel-machines.org/software.html
Some implementation (such as LIBSVM) can handle
multi-class classification
SVMLight is among one of the earliest implementation of
SVM
Several Matlab toolboxes for SVM are also available
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Summary: Steps for Classification
Prepare the pattern matrix
Select the kernel function to use
Select the parameter of the kernel function and the
value of C
You can use the values suggested by the SVM software, or
you can set apart a validation set to determine the values
of the parameter
Execute the training algorithm and obtain the ai
Unseen data can be classified using the ai and the
support vectors
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Conclusion
SVM is a useful alternative to neural networks
Two key concepts of SVM: maximize the margin and the
kernel trick
Many SVM implementations are available on the web for
you to try on your data set!
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Appendix: Distance from a point to a line
Equation for the line: let u be a variable, then any point
on the line can be described as:
P = P1 + u (P2 - P1)
Let the intersect point be u,
Then, u can be determined by:
The two vectors (P2-P1) is orthogonal to P3-u:
That is,
(P3-P) dot (P2-P1) =0
P=P1+u(P2-P1)
P1=(x1,y1),P2=(x2,y2),P3=(x3,y3) P1
P2
P3
P
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Distance and margin
x = x1 + u (x2 - x1)
y = y1 + u (y2 - y1)
The distance therefore between the point P3 and the
line is the distance between P=(x,y) above and P3
Thus,
d= |(P3-P)|=