Introduction to Algorithms: Bellman-Ford

Introduction to Algorithms: Bellman-Ford

This lecture introduces a single source shortest path algorithm that works for general graphs. The process, correctness, and running time of the Bellman-Ford algorithm is discussed.

Course Description

This course is an introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. It emphasizes the relationship between algorithms and programming and introduces basic performance measures and analysis techniques for these problems.

#algorithms #datastructures 

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Introduction to Random Forest Algorithm: Functions, Applications & Benefits

Random Forest is a mainstream AI algorithm that has a place with the regulated learning strategy. It might be used for both Classification and Regression issues in ML. It depends on the idea of ensemble learning, which is a cycle of joining numerous classifiers to tackle an intricate issue and to improve the presentation of the model.

As the name proposes, “Random Forest is a classifier that contains different decision trees on various subsets of the given dataset and takes the typical to improve the perceptive precision of that dataset.”

Instead of relying upon one decision tree, the random forest takes the figure from each tree and subject it to the larger part votes of desires, and it predicts the last yield. The more noticeable number of trees in the forest prompts higher exactness and forestalls the issue of overfitting.

**Presumptions for Random Forest **

Since the random forest consolidates various trees to anticipate the class of the dataset, it is conceivable that some choice trees may foresee the right yield, while others may not. Yet, together, all the trees anticipate the right yield. In this way, beneath are two presumptions for a superior random forest classifier:

• There should be some real qualities in the component variable of a dataset with a goal that the classifier can foresee precise outcomes as opposed to a speculated result.
• The forecasts from each tree must have low connections.

#artificial intelligence #random forest #introduction to random forest algorithm #random forest algorithm #algorithm

Introduction to Genetic Algorithm

What is Optimization?

• Making something better.
• Increase efficiency.

Optimization problem

• A problem in which we have to find the values of inputs (also called solutions or decision variables) from all possible inputs in such a way that we get the “best” output values.
• Definition of “best”- Finding the values of inputs that result in a maximum or minimum of a function called the objective function.
• There can be multiple objective functions as well (depends on the problem).

Optimization algorithm

An algorithm used to solve an optimization problem is called an optimization algorithm.

Evolutionary Algorithms

Algorithms that simulate physical and/or biological behavior in nature to solve optimization problems.

Genetic Algorithm (GA)

• It is a subset of evolutionary algorithms that simulates/models Genetics and Evolution (biological behavior) to optimize a highly complex function.
• A highly complex function can be:
• 1. Very difficult to model mathematically.
• 2. Computationally expensive to solve. Eg. NP-hard problems.
• 3. Involves a large number of parameters.

Background of GA

• Introduced by Prof. John Holland in 1965.
• The first article on GA was published in 1975.
• GA is based on two fundamental biological processes:
• 1. Genetics (by G.J. Mendel in 1865): It is the branch of biology that deals with the study of genes, gene variation, and heredity.
• 2. Evolution (by C. Darwin in 1875): It is the process by which the population of organisms changes over generations.

Natural selection in Evolution

1. A population of individuals exists in an environment with limited resources.
2. Competition for those resources causes the selection of those fitter individuals that are better adapted to the environment.
3. These individuals act as seeds for the generation of new individuals through recombination and mutation.
4. Evolved new individuals act as initial population and Steps 1 to 3 are repeated.

Nature-GA Analogy

Structure of GA

GA vs Traditional Algorithms

Applications of GA

• 1. Acoustics
• 2. Aerospace Engineering
• 3. Financial Markets
• 4. Geophysics
• 5. Materials Engineering
• 6. Routing and Scheduling
• 7. Systems Engineering

Problems with GA

• 1. Population Selection Problem
• 2. Defining Fitness Function
• 3. Premature or rapid convergence of GA
• 4. Convergence to Local Optima

#evolutionary-algorithms #data-science #genetic-algorithm #algorithm

Introduction to Algorithms: Bellman-Ford

Introduction to Algorithms: Bellman-Ford

This lecture introduces a single source shortest path algorithm that works for general graphs. The process, correctness, and running time of the Bellman-Ford algorithm is discussed.

Course Description

This course is an introduction to mathematical modeling of computational problems, as well as common algorithms, algorithmic paradigms, and data structures used to solve these problems. It emphasizes the relationship between algorithms and programming and introduces basic performance measures and analysis techniques for these problems.

#algorithms #datastructures 

Introductions to Algorithms and Computation

The goal of this introductions to algorithms class is to teach you to solve computation problems and communication that your solutions are correct and efficient. Models of computation, data structures, and algorithms are introduced.

#algorithm #datastructures #algorithms 

A greedy algorithm is a simple

The Greedy Method is an approach for solving certain types of optimization problems. The greedy algorithm chooses the optimum result at each stage. While this works the majority of the times, there are numerous examples where the greedy approach is not the correct approach. For example, let’s say that you’re taking the greedy algorithm approach to earning money at a certain point in your life. You graduate high school and have two options:

#computer-science #algorithms #developer #programming #greedy-algorithms #algorithms