UNIT 5
Genetic Algorithms
GA stimulates the natural selection process which means only species who can adapt to changes in their environment can survive and reproduce and pass on to the next generation.
In simple words, they follow the principle of “survival of the fittest” among individuals of consecutive generations for solving a problem.
Each generation consist of a population of individuals and each individual represents a point in search space and possible solution. Each individual is represented as a string of bits (character/integer/float). This string is analogous to the Chromosome.
Principle of Genetic Algorithm
Genetic algorithms are based on an analogy with the genetic structure and behavior of chromosomes of the population. Following is the foundation of GAs based on this analogy –
illustrative example
Figure.1. GA basic execution flow
The hypothesis method is not the same as other methods presented till far. It is neither general-to-specific nor simple-to-complex. Search is performed genetic algorithms takes place in a quick and undetermined way, replacing a parent hypothesis by an offspring which is radically different so this method is less likely to fall into some local minimum
Practical difficulty: crowding
Some individuals that fit better than others reproduce quickly so that copies and very similar offspring take over a large fraction of the population ⇒ reduced diversity of population ⇒ slower progress of the genetic algorithms
Hypotheses are often represented as bit strings so that they can easily be modified by genetic operators. The represented hypotheses can be quite complex as each attribute can be represented as a substring with a no. of positions. And as there are possible values to obtain a fixed-length bit string, each attribute has to be considered, even in the most general case.
Ex:
(Outlook = Overcast ∨ Rain ) ∧ (Wind = Strong ) is represented as: Outlook 011, Wind 10 ⇒ 01110
Genetic programming (GP) is an evolutionary approach that exploits genetic algorithms to allow the exploration of the space of computer programs. GP works by defining a goal in the form of a quality criterion also known as fitness) and then using this criterion to evolve a set (or population) of candidate solutions by using the basic principles of Darwinian evolution. GP reproduces the solutions to problems using an iterative process involving the probabilistic selection of the fittest solutions and their variation through a set of genetic operators, usually crossover and mutation. GP has been successfully applied to some challenging real-world problem domains.
Its operations and behaviour are now reasonably well-understood thanks to a variety of powerful theoretical results
Advantages of GAs
GAs have various advantages that have made them immensely popular. These include −
Limitations of GAs
KEY TAKEAWAYS
1. Individual in population compete for resources and mate
2. Those individuals who are successful (fittest) then mate to create more offspring than others
3. Genes from “fittest” parent propagate throughout the generation, that is sometimes parents create offspring which is better than either parent.
4. Thus each successive generation is more suited for their environment.
During an individual’s lifetime, biological and social processes allow a species to adapt over a time frame of many generations, Individual organisms learn to adapt significantly.
Lamarckian Evolution: | Baldwin Effect: |
the proposition that evolution over many generations was directly influenced by the experiences of individual organisms | a species in a changing environment underlies evolutionary pressure that favors individuals with the ability to learn |
during their lifetime direct influence of the genetic makeup of the offspring | such individuals perform a small local search to maximize their fitness |
completely contradicted by science | additionally, such individuals rely less on genetic code |
Lamarckian processes can sometimes improve the effectiveness of genetic algorithms | thus, they support a more diverse gene pool, relying on individual learning to overcome “missing” or “not quite well” traits |
| ⇒ the indirect influence of evolutionary adaption for the entire population |
5.2.1 Learning first-order rules-sequential covering algorithms
Propositional logic allows the expression of individual propositions and their truth-functional combination.
Ex: Ram is a man or All men are mortal can be represented by single proposition letters P or Q– Truth functional combinations are built up using connectives, such as ∧, ∨, ¬, → – e.g. P∧Q
First-Order Logic:
All expressions in first-order logic are composed of the following attributes:
Term: It can be defined as any constant, variable, or function applied to any term. e.g. height(ram)
Literal: It can be defined as any predicate or negated predicate applied to any terms. e.g. girl(sita), father(I, J)
It has 3 types:
First-order logic is much more expressive than propositional logic – i.e. it allows a finer-grain of specification and reasoning when representing knowledge
While in machine learning, consider learning a relational concept daughter(x, y) defined over pairs of person x, y, where – persons are represented by attributes: (Name, Mother, Father, Male, Female)
5.2.2 General to specific beam search-FOIL
FOIL learns first-order rules which are similar to Horn clauses with two exceptions:
Like SEQUENTIAL-COVERING, FOIL learns one rule at a time and removes positive examples covered by the learned rule before attempting to learn a further rule.
Unlike SEQUENTIAL-COVERING and LEARN-ONE-RULE, FOIL
FOIL searches its hypothesis space via two nested loops:
• The outer loop at each iteration adds a new rule to an overall disjunctive hypothesis (i.e. rule1 ∨ rule2 ∨...)
This loop may be viewed as a specific-to-general search
The inner loop works out the detail of each specific rule, adding conjunctive constraints to the rule precondition on each iteration.
This loop may be viewed as a general-to-specific search
Figure.3 FOIL ALGORITHM
5.2.3 REINFORCEMENT LEARNING - The Learning Task, Q Learning.
Reinforcement learning (RL) solves a particular kind of problem where decision making is sequential, and the goal is long-term, such as game playing, robotics, resource management, or logistics.
RL is an area of Machine Learning which is related to taking suitable action to maximize reward in a particular situation. It is employed by various software and machines to find the best possible behaviour or path. RL differs from supervised learning in a way that the training data has the answer key with it so the model is trained with the correct answer itself whereas in reinforcement learning, there is no answer but the reinforcement agent decides what to do to perform the given task. In the absence of a training dataset, it is bound to learn from its experience.
Example:
For a robot, an environment is a place where it has been put to use. Remember this robot is itself the agent. For example, a textile factory where a robot is used to move materials from one place to another.
These tasks have a property in common:
- these tasks involve an environment and expect the agents to learn from that environment. This is where traditional machine learning fails and hence the need for reinforcement learning.
q-learning
Q-learning is another type of reinforcement learning algorithm that seeks to find the best action to take given the current state. It’s considered as the off-policy because the q-learning function learns from actions that are outside the current policy, such as taking random actions, and therefore a policy isn’t needed.
More specifically, q-learning seeks to learn a policy that maximizes the total reward.
Role of ‘Q’
The ‘q’ in q-learning stands for quality. Quality in this case represents how useful a given action is in gaining some future reward.
Create a q-table
When q-learning is performed we create what’s called a q-table or matrix that follows the shape of [state, action] and we initialize our values to zero. We then update and store our q-values after an episode. This q-table becomes a reference table for our agent to select the best action based on the q-value.
Updating the q-table
The updates occur after each step or action and end when an episode is done. Done in this case means reaching some terminal point by the agent. A terminal state for example can be anything like landing on a checkout page, reaching the end of some game, completing some desired objective, etc. The agent will not learn much after a single episode, but eventually, with enough exploring (steps and episodes) it will converge and learn the optimal q-values or q-star (Q∗).
Here are the 3 basic steps:
Resources and links used :
Great RL and q-learning example using the OpenAI Gym taxi environment
Reinforcement Learning: An Introduction (free book by Sutton)
Quora Q-learning
Wikipedia Q-learning
David Silver’s lectures on RL
R. S. Sutton, A. G. Barto: Reinforcement Learning: An Introduction. MIT Press, 1998
KEY TAKEAWAYS
References:
1. Tom M. Mitchell, ―Machine Learning, McGraw-Hill Education (India) Private Limited, 2013.
2. Ethem Alpaydin, ―Introduction to Machine Learning (Adaptive Computation And Machine Learning), The MIT Press 2004.
3. Stephen Marsland, ―Machine Learning: An Algorithmic Perspective, CRC Press, 2009.
4. Bishop, C., Pattern Recognition, and Machine Learning. Berlin: Springer-Verlag.
UNIT 5
Genetic Algorithms
GA stimulates the natural selection process which means only species who can adapt to changes in their environment can survive and reproduce and pass on to the next generation.
In simple words, they follow the principle of “survival of the fittest” among individuals of consecutive generations for solving a problem.
Each generation consist of a population of individuals and each individual represents a point in search space and possible solution. Each individual is represented as a string of bits (character/integer/float). This string is analogous to the Chromosome.
Principle of Genetic Algorithm
Genetic algorithms are based on an analogy with the genetic structure and behavior of chromosomes of the population. Following is the foundation of GAs based on this analogy –
illustrative example
Figure.1. GA basic execution flow
The hypothesis method is not the same as other methods presented till far. It is neither general-to-specific nor simple-to-complex. Search is performed genetic algorithms takes place in a quick and undetermined way, replacing a parent hypothesis by an offspring which is radically different so this method is less likely to fall into some local minimum
Practical difficulty: crowding
Some individuals that fit better than others reproduce quickly so that copies and very similar offspring take over a large fraction of the population ⇒ reduced diversity of population ⇒ slower progress of the genetic algorithms
Hypotheses are often represented as bit strings so that they can easily be modified by genetic operators. The represented hypotheses can be quite complex as each attribute can be represented as a substring with a no. of positions. And as there are possible values to obtain a fixed-length bit string, each attribute has to be considered, even in the most general case.
Ex:
(Outlook = Overcast ∨ Rain ) ∧ (Wind = Strong ) is represented as: Outlook 011, Wind 10 ⇒ 01110
Genetic programming (GP) is an evolutionary approach that exploits genetic algorithms to allow the exploration of the space of computer programs. GP works by defining a goal in the form of a quality criterion also known as fitness) and then using this criterion to evolve a set (or population) of candidate solutions by using the basic principles of Darwinian evolution. GP reproduces the solutions to problems using an iterative process involving the probabilistic selection of the fittest solutions and their variation through a set of genetic operators, usually crossover and mutation. GP has been successfully applied to some challenging real-world problem domains.
Its operations and behaviour are now reasonably well-understood thanks to a variety of powerful theoretical results
Advantages of GAs
GAs have various advantages that have made them immensely popular. These include −
Limitations of GAs
KEY TAKEAWAYS
1. Individual in population compete for resources and mate
2. Those individuals who are successful (fittest) then mate to create more offspring than others
3. Genes from “fittest” parent propagate throughout the generation, that is sometimes parents create offspring which is better than either parent.
4. Thus each successive generation is more suited for their environment.
During an individual’s lifetime, biological and social processes allow a species to adapt over a time frame of many generations, Individual organisms learn to adapt significantly.
Lamarckian Evolution: | Baldwin Effect: |
the proposition that evolution over many generations was directly influenced by the experiences of individual organisms | a species in a changing environment underlies evolutionary pressure that favors individuals with the ability to learn |
during their lifetime direct influence of the genetic makeup of the offspring | such individuals perform a small local search to maximize their fitness |
completely contradicted by science | additionally, such individuals rely less on genetic code |
Lamarckian processes can sometimes improve the effectiveness of genetic algorithms | thus, they support a more diverse gene pool, relying on individual learning to overcome “missing” or “not quite well” traits |
| ⇒ the indirect influence of evolutionary adaption for the entire population |
5.2.1 Learning first-order rules-sequential covering algorithms
Propositional logic allows the expression of individual propositions and their truth-functional combination.
Ex: Ram is a man or All men are mortal can be represented by single proposition letters P or Q– Truth functional combinations are built up using connectives, such as ∧, ∨, ¬, → – e.g. P∧Q
First-Order Logic:
All expressions in first-order logic are composed of the following attributes:
Term: It can be defined as any constant, variable, or function applied to any term. e.g. height(ram)
Literal: It can be defined as any predicate or negated predicate applied to any terms. e.g. girl(sita), father(I, J)
It has 3 types:
First-order logic is much more expressive than propositional logic – i.e. it allows a finer-grain of specification and reasoning when representing knowledge
While in machine learning, consider learning a relational concept daughter(x, y) defined over pairs of person x, y, where – persons are represented by attributes: (Name, Mother, Father, Male, Female)
5.2.2 General to specific beam search-FOIL
FOIL learns first-order rules which are similar to Horn clauses with two exceptions:
Like SEQUENTIAL-COVERING, FOIL learns one rule at a time and removes positive examples covered by the learned rule before attempting to learn a further rule.
Unlike SEQUENTIAL-COVERING and LEARN-ONE-RULE, FOIL
FOIL searches its hypothesis space via two nested loops:
• The outer loop at each iteration adds a new rule to an overall disjunctive hypothesis (i.e. rule1 ∨ rule2 ∨...)
This loop may be viewed as a specific-to-general search
The inner loop works out the detail of each specific rule, adding conjunctive constraints to the rule precondition on each iteration.
This loop may be viewed as a general-to-specific search
Figure.3 FOIL ALGORITHM
5.2.3 REINFORCEMENT LEARNING - The Learning Task, Q Learning.
Reinforcement learning (RL) solves a particular kind of problem where decision making is sequential, and the goal is long-term, such as game playing, robotics, resource management, or logistics.
RL is an area of Machine Learning which is related to taking suitable action to maximize reward in a particular situation. It is employed by various software and machines to find the best possible behaviour or path. RL differs from supervised learning in a way that the training data has the answer key with it so the model is trained with the correct answer itself whereas in reinforcement learning, there is no answer but the reinforcement agent decides what to do to perform the given task. In the absence of a training dataset, it is bound to learn from its experience.
Example:
For a robot, an environment is a place where it has been put to use. Remember this robot is itself the agent. For example, a textile factory where a robot is used to move materials from one place to another.
These tasks have a property in common:
- these tasks involve an environment and expect the agents to learn from that environment. This is where traditional machine learning fails and hence the need for reinforcement learning.
q-learning
Q-learning is another type of reinforcement learning algorithm that seeks to find the best action to take given the current state. It’s considered as the off-policy because the q-learning function learns from actions that are outside the current policy, such as taking random actions, and therefore a policy isn’t needed.
More specifically, q-learning seeks to learn a policy that maximizes the total reward.
Role of ‘Q’
The ‘q’ in q-learning stands for quality. Quality in this case represents how useful a given action is in gaining some future reward.
Create a q-table
When q-learning is performed we create what’s called a q-table or matrix that follows the shape of [state, action] and we initialize our values to zero. We then update and store our q-values after an episode. This q-table becomes a reference table for our agent to select the best action based on the q-value.
Updating the q-table
The updates occur after each step or action and end when an episode is done. Done in this case means reaching some terminal point by the agent. A terminal state for example can be anything like landing on a checkout page, reaching the end of some game, completing some desired objective, etc. The agent will not learn much after a single episode, but eventually, with enough exploring (steps and episodes) it will converge and learn the optimal q-values or q-star (Q∗).
Here are the 3 basic steps:
Resources and links used :
Great RL and q-learning example using the OpenAI Gym taxi environment
Reinforcement Learning: An Introduction (free book by Sutton)
Quora Q-learning
Wikipedia Q-learning
David Silver’s lectures on RL
R. S. Sutton, A. G. Barto: Reinforcement Learning: An Introduction. MIT Press, 1998
KEY TAKEAWAYS
References:
1. Tom M. Mitchell, ―Machine Learning, McGraw-Hill Education (India) Private Limited, 2013.
2. Ethem Alpaydin, ―Introduction to Machine Learning (Adaptive Computation And Machine Learning), The MIT Press 2004.
3. Stephen Marsland, ―Machine Learning: An Algorithmic Perspective, CRC Press, 2009.
4. Bishop, C., Pattern Recognition, and Machine Learning. Berlin: Springer-Verlag.
UNIT 5
Genetic Algorithms
GA stimulates the natural selection process which means only species who can adapt to changes in their environment can survive and reproduce and pass on to the next generation.
In simple words, they follow the principle of “survival of the fittest” among individuals of consecutive generations for solving a problem.
Each generation consist of a population of individuals and each individual represents a point in search space and possible solution. Each individual is represented as a string of bits (character/integer/float). This string is analogous to the Chromosome.
Principle of Genetic Algorithm
Genetic algorithms are based on an analogy with the genetic structure and behavior of chromosomes of the population. Following is the foundation of GAs based on this analogy –
illustrative example
Figure.1. GA basic execution flow
The hypothesis method is not the same as other methods presented till far. It is neither general-to-specific nor simple-to-complex. Search is performed genetic algorithms takes place in a quick and undetermined way, replacing a parent hypothesis by an offspring which is radically different so this method is less likely to fall into some local minimum
Practical difficulty: crowding
Some individuals that fit better than others reproduce quickly so that copies and very similar offspring take over a large fraction of the population ⇒ reduced diversity of population ⇒ slower progress of the genetic algorithms
Hypotheses are often represented as bit strings so that they can easily be modified by genetic operators. The represented hypotheses can be quite complex as each attribute can be represented as a substring with a no. of positions. And as there are possible values to obtain a fixed-length bit string, each attribute has to be considered, even in the most general case.
Ex:
(Outlook = Overcast ∨ Rain ) ∧ (Wind = Strong ) is represented as: Outlook 011, Wind 10 ⇒ 01110
Genetic programming (GP) is an evolutionary approach that exploits genetic algorithms to allow the exploration of the space of computer programs. GP works by defining a goal in the form of a quality criterion also known as fitness) and then using this criterion to evolve a set (or population) of candidate solutions by using the basic principles of Darwinian evolution. GP reproduces the solutions to problems using an iterative process involving the probabilistic selection of the fittest solutions and their variation through a set of genetic operators, usually crossover and mutation. GP has been successfully applied to some challenging real-world problem domains.
Its operations and behaviour are now reasonably well-understood thanks to a variety of powerful theoretical results
Advantages of GAs
GAs have various advantages that have made them immensely popular. These include −
Limitations of GAs
KEY TAKEAWAYS
1. Individual in population compete for resources and mate
2. Those individuals who are successful (fittest) then mate to create more offspring than others
3. Genes from “fittest” parent propagate throughout the generation, that is sometimes parents create offspring which is better than either parent.
4. Thus each successive generation is more suited for their environment.
UNIT 5
Genetic Algorithms
GA stimulates the natural selection process which means only species who can adapt to changes in their environment can survive and reproduce and pass on to the next generation.
In simple words, they follow the principle of “survival of the fittest” among individuals of consecutive generations for solving a problem.
Each generation consist of a population of individuals and each individual represents a point in search space and possible solution. Each individual is represented as a string of bits (character/integer/float). This string is analogous to the Chromosome.
Principle of Genetic Algorithm
Genetic algorithms are based on an analogy with the genetic structure and behavior of chromosomes of the population. Following is the foundation of GAs based on this analogy –
illustrative example
Figure.1. GA basic execution flow
The hypothesis method is not the same as other methods presented till far. It is neither general-to-specific nor simple-to-complex. Search is performed genetic algorithms takes place in a quick and undetermined way, replacing a parent hypothesis by an offspring which is radically different so this method is less likely to fall into some local minimum
Practical difficulty: crowding
Some individuals that fit better than others reproduce quickly so that copies and very similar offspring take over a large fraction of the population ⇒ reduced diversity of population ⇒ slower progress of the genetic algorithms
Hypotheses are often represented as bit strings so that they can easily be modified by genetic operators. The represented hypotheses can be quite complex as each attribute can be represented as a substring with a no. of positions. And as there are possible values to obtain a fixed-length bit string, each attribute has to be considered, even in the most general case.
Ex:
(Outlook = Overcast ∨ Rain ) ∧ (Wind = Strong ) is represented as: Outlook 011, Wind 10 ⇒ 01110
Genetic programming (GP) is an evolutionary approach that exploits genetic algorithms to allow the exploration of the space of computer programs. GP works by defining a goal in the form of a quality criterion also known as fitness) and then using this criterion to evolve a set (or population) of candidate solutions by using the basic principles of Darwinian evolution. GP reproduces the solutions to problems using an iterative process involving the probabilistic selection of the fittest solutions and their variation through a set of genetic operators, usually crossover and mutation. GP has been successfully applied to some challenging real-world problem domains.
Its operations and behaviour are now reasonably well-understood thanks to a variety of powerful theoretical results
Advantages of GAs
GAs have various advantages that have made them immensely popular. These include −
Limitations of GAs
KEY TAKEAWAYS
1. Individual in population compete for resources and mate
2. Those individuals who are successful (fittest) then mate to create more offspring than others
3. Genes from “fittest” parent propagate throughout the generation, that is sometimes parents create offspring which is better than either parent.
4. Thus each successive generation is more suited for their environment.
During an individual’s lifetime, biological and social processes allow a species to adapt over a time frame of many generations, Individual organisms learn to adapt significantly.
Lamarckian Evolution: | Baldwin Effect: |
the proposition that evolution over many generations was directly influenced by the experiences of individual organisms | a species in a changing environment underlies evolutionary pressure that favors individuals with the ability to learn |
during their lifetime direct influence of the genetic makeup of the offspring | such individuals perform a small local search to maximize their fitness |
completely contradicted by science | additionally, such individuals rely less on genetic code |
Lamarckian processes can sometimes improve the effectiveness of genetic algorithms | thus, they support a more diverse gene pool, relying on individual learning to overcome “missing” or “not quite well” traits |
| ⇒ the indirect influence of evolutionary adaption for the entire population |
5.2.1 Learning first-order rules-sequential covering algorithms
Propositional logic allows the expression of individual propositions and their truth-functional combination.
Ex: Ram is a man or All men are mortal can be represented by single proposition letters P or Q– Truth functional combinations are built up using connectives, such as ∧, ∨, ¬, → – e.g. P∧Q
First-Order Logic:
All expressions in first-order logic are composed of the following attributes:
Term: It can be defined as any constant, variable, or function applied to any term. e.g. height(ram)
Literal: It can be defined as any predicate or negated predicate applied to any terms. e.g. girl(sita), father(I, J)
It has 3 types:
First-order logic is much more expressive than propositional logic – i.e. it allows a finer-grain of specification and reasoning when representing knowledge
While in machine learning, consider learning a relational concept daughter(x, y) defined over pairs of person x, y, where – persons are represented by attributes: (Name, Mother, Father, Male, Female)
5.2.2 General to specific beam search-FOIL
FOIL learns first-order rules which are similar to Horn clauses with two exceptions:
Like SEQUENTIAL-COVERING, FOIL learns one rule at a time and removes positive examples covered by the learned rule before attempting to learn a further rule.
Unlike SEQUENTIAL-COVERING and LEARN-ONE-RULE, FOIL
FOIL searches its hypothesis space via two nested loops:
• The outer loop at each iteration adds a new rule to an overall disjunctive hypothesis (i.e. rule1 ∨ rule2 ∨...)
This loop may be viewed as a specific-to-general search
The inner loop works out the detail of each specific rule, adding conjunctive constraints to the rule precondition on each iteration.
This loop may be viewed as a general-to-specific search
Figure.3 FOIL ALGORITHM
5.2.3 REINFORCEMENT LEARNING - The Learning Task, Q Learning.
Reinforcement learning (RL) solves a particular kind of problem where decision making is sequential, and the goal is long-term, such as game playing, robotics, resource management, or logistics.
RL is an area of Machine Learning which is related to taking suitable action to maximize reward in a particular situation. It is employed by various software and machines to find the best possible behaviour or path. RL differs from supervised learning in a way that the training data has the answer key with it so the model is trained with the correct answer itself whereas in reinforcement learning, there is no answer but the reinforcement agent decides what to do to perform the given task. In the absence of a training dataset, it is bound to learn from its experience.
Example:
For a robot, an environment is a place where it has been put to use. Remember this robot is itself the agent. For example, a textile factory where a robot is used to move materials from one place to another.
These tasks have a property in common:
- these tasks involve an environment and expect the agents to learn from that environment. This is where traditional machine learning fails and hence the need for reinforcement learning.
q-learning
Q-learning is another type of reinforcement learning algorithm that seeks to find the best action to take given the current state. It’s considered as the off-policy because the q-learning function learns from actions that are outside the current policy, such as taking random actions, and therefore a policy isn’t needed.
More specifically, q-learning seeks to learn a policy that maximizes the total reward.
Role of ‘Q’
The ‘q’ in q-learning stands for quality. Quality in this case represents how useful a given action is in gaining some future reward.
Create a q-table
When q-learning is performed we create what’s called a q-table or matrix that follows the shape of [state, action] and we initialize our values to zero. We then update and store our q-values after an episode. This q-table becomes a reference table for our agent to select the best action based on the q-value.
Updating the q-table
The updates occur after each step or action and end when an episode is done. Done in this case means reaching some terminal point by the agent. A terminal state for example can be anything like landing on a checkout page, reaching the end of some game, completing some desired objective, etc. The agent will not learn much after a single episode, but eventually, with enough exploring (steps and episodes) it will converge and learn the optimal q-values or q-star (Q∗).
Here are the 3 basic steps:
Resources and links used :
Great RL and q-learning example using the OpenAI Gym taxi environment
Reinforcement Learning: An Introduction (free book by Sutton)
Quora Q-learning
Wikipedia Q-learning
David Silver’s lectures on RL
R. S. Sutton, A. G. Barto: Reinforcement Learning: An Introduction. MIT Press, 1998
KEY TAKEAWAYS
References:
1. Tom M. Mitchell, ―Machine Learning, McGraw-Hill Education (India) Private Limited, 2013.
2. Ethem Alpaydin, ―Introduction to Machine Learning (Adaptive Computation And Machine Learning), The MIT Press 2004.
3. Stephen Marsland, ―Machine Learning: An Algorithmic Perspective, CRC Press, 2009.
4. Bishop, C., Pattern Recognition, and Machine Learning. Berlin: Springer-Verlag.
