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Feature Selection
Jamshid Shanbehzadeh, Samaneh Yazdani
Department of Computer Engineering, Faculty Of Engineering, Khorazmi University (Tarbiat Moallem University of Teheran)
OutlineOutline
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OutlineOutline
Part 1: Dimension Reduction Dimension Feature Space Definition & Goals Curse of dimensionality Research and Application Grouping of dimension reduction methods
Part 2: Feature selection Parts of feature set Feature Selection Approach
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Part 3: Application Of Feature Selection and Software
Part 1:Dimension Reduction
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Dimension Reduction
Dimension
Dimension Reduction
Dimension
Dimension (Feature or Variable): A measurement of a certain aspect of an object
Two feature of person:• weight• hight
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Dimension Reduction
Feature Space
Dimension Reduction
Feature Space
Feature Space: An abstract space where each pattern sample is represented as point
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Large and high-dimensional data Web documents, etc… A large amount of resources are needed in
Information Retrieval Classification tasks Data Preservation etc…
Dimension Reduction
Dimension Reduction
Introduction
Dimension Reduction
Introduction
Dimension Reduction
Definition & Goals
Dimension Reduction
Definition & Goals
Dimensionality reduction: The study of methods for reducing the number of dimensions describing the object
General objectives of dimensionality reduction:
Reduce the computational cost
Improve the quality of data for efficient data-intensive processing tasks
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Height (cm)
Weight (kg)
140 150
50
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Dimension Reduction preserves information on classification of overweight and underweight as much as possible makes classification easier reduces data size ( 2 features 1 feature )
Dimension Reduction
Definition & Goals
Dimension Reduction
Definition & Goals
Class 1: overweight
Class 2: underweight
Dimension Reduction
Curse of dimensionality
Dimension Reduction
Curse of dimensionality
As the number of dimension increases, a fix data sample becomes exponentially spars
Example:
Observe that the data become more and more sparse in higher dimensions
Effective solution to the problem of “curse of dimensionality” is: Dimensionality reduction
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Dimension Reduction
Research and Application
Dimension Reduction
Research and Application
Why dimension reduction is a subject of much research recently?
Massive data of large dimensionality in:
Knowledge discovery
Text mining
Web mining
and . . .
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Dimension Reduction
Grouping of dimension reduction methods
Dimension Reduction
Grouping of dimension reduction methods
Dimensionality reduction approaches include
Feature Selection
Feature Extraction
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Dimension Reduction
Grouping of dimension reduction methods : Feature Selection
Dimension Reduction
Grouping of dimension reduction methods : Feature Selection
Dimensionality reduction approaches include
Feature Selection: the problem of choosing a small subset of features that ideally are necessary and sufficient to describe the target concept.
Example
Feature Set= {X,Y} Two Class
Goal: ClassificationGoal: Classification
Feature X Or Feature Y ? Answer: Feature X
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Feature Selection (FS) Selects feature ex.
Preserves weight
Dimension Reduction
Grouping of dimension reduction methods : Feature Selection
Dimension Reduction
Grouping of dimension reduction methods : Feature Selection
Dimension Reduction
Grouping of dimension reduction methods
Dimension Reduction
Grouping of dimension reduction methods
Dimensionality reduction approaches include
Feature Extraction: Create new feature based on transformations or combinations of the original feature set.
Original Feature {X1,X2}
New Feature
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Feature Extraction (FE) Generates feature ex.
Preserves weight / height
Dimension Reduction
Grouping of dimension reduction methods
Dimension Reduction
Grouping of dimension reduction methods
Dimension Reduction
Grouping of dimension reduction methods
Dimension Reduction
Grouping of dimension reduction methods
Dimensionality reduction approaches include
Feature Extraction: Create new feature based on transformations or combinations of the original feature set.
N: Number of original features M: Number of extracted features M<N
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Dimension Reduction
Question: Feature Selection Or Feature Extraction
Dimension Reduction
Question: Feature Selection Or Feature Extraction
Feature Selection Or Feature Extraction
It is depend on the problem. Example
Pattern recognition: problem of dimensionality reduction is to extract a small set of features that recovers most of the variability of the data.
Text mining: problem is defined as selecting a small subset of words or terms (not new features that are combination of words or terms).
Image Compression: problem is finding the best extracted features to describe the image
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Part 2:Feature selection
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Feature selectionFeature selection
Thousands to millions of low level features: select the most relevant one to build better, faster, and easier to understand learning machines.
X
n
Nm
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Three disjoint categories of features:
Irrelevant
Weakly Relevant
Strongly Relevant
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Two Class : {Lion and Deer} We use some features to classify a new instance To which class does
this animal belong
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Two Class : {Lion and Deer} We use some feature to classify a new instance
Q: Number of legs?A: 4
So, number of legs is irrelevant feature Feature 1: Number of legs
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Two Class : {Lion and Deer} We use some features to classify a new instance
Q: What is its color?A:
So, Color is an irrelevant feature Feature 1: Number of legs
Feature 2: Color
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Two Class : {Lion and Deer} We use some features to classify a new instance
Q: What does it eat?A: Grass
So, Feature 3 is a relevant feature Feature 1: Number of legs
Feature 2: Color Feature 3: Type of food
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Three Class : {Lion, Deer and Leopard} We use some features to classify a new instance To which class does
this animal belong
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Three Class : {Lion, Deer and Leopard} We use some features to classify a new instance
Q: Number of legs?A: 4
So, number of legs is an irrelevant feature Feature 1: Number of legs
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Three Class : {Lion, Deer and Leopard} We use some features to classify a new instance
So, Color is a relevant feature
Q: What is its color?A:
Feature 1: Number of legs Feature 2: Color
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Three Class : {Lion and Deer and Leopard} We use some features to classify a new instance
So, Feature 3 is a relevant feature
Q: What does it eat?A: meat
Feature 1: Number of legs Feature 2: Color Feature3: Type of food
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Goal: Classification
Three Class : {Lion and Deer and Leopard} We use some feature to classify a new instance
Feature 1: Number of legs Feature 2: Color Feature3: Type of food
Add new feature: FelidaeIt is weakly relevant feature Optimal set: {Color, Type of food} Or {Color, Felidae}
Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Traditionally, feature selection research has focused on searching for relevant features.
Irrelevant Relevant
Feature set
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Data setFive Boolean featuresC = F1∨F2
F3 = ┐F2 , F5 = ┐F4
Optimal subset: {F1, F2} or {F1, F3}
Feature selection Parts of feature set
Irrelevant OR Relevant: An Example for the Problem
Feature selection Parts of feature set
Irrelevant OR Relevant: An Example for the Problem
F1 F2 F3 F4 F5 C
0 0 1 0 1 0
0 1 0 0 1 1
1 0 1 0 1 1
1 1 0 0 1 1
0 0 1 1 0 0
0 1 0 1 0 1
1 0 1 1 0 1
1 1 0 1 0 1
Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Formal Definition 1 (Irrelevance) :
Irrelevance indicates that the feature is not necessary at all.
In previous Example:
F4, F5 irrelevance
F4 and F5 Relevant
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Definition1(Irrelevance) A feature Fi is irrelevant if
Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
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Irrelevance indicates that the feature is not necessary at all
F be a full set of features
Fi a feature
Si = F −{Fi}.
Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Categories of relevant features:
Strongly Relevant
Weakly Relevant
StronglyIrrelevant WeaklyRelevant
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Data setFive Boolean featuresC = F1∨F2
F3 = ┐F2 , F5 = ┐F4
Feature selection Parts of feature set
Irrelevant OR Relevant: An Example for the Problem
Feature selection Parts of feature set
Irrelevant OR Relevant: An Example for the Problem
F1 F2 F3 F4 F5 C
0 0 1 0 1 0
0 1 0 0 1 1
1 0 1 0 1 1
1 1 0 0 1 1
0 0 1 1 0 0
0 1 0 1 0 1
1 0 1 1 0 1
1 1 0 1 0 1
Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Formal Definition2 (Strong relevance) :
Strong relevance of a feature indicates that the feature is always necessary for an optimal subset
It cannot be removed without affecting the original conditional class distribution.
In previous Example:
Feature F1 is strongly relevant
F4 and F5Weakly F1
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Definition 2 (Strong relevance) A feature Fi is strongly relevant if
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Strong relevance of a feature cannot be removed without affecting the original conditional class distribution
Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Formal Definition 3 (Weak relevance) :
Weak relevance suggests that the feature is not always necessary but may become necessary for an optimal subset at certain conditions.
In previous Example:
F2, F3 weakly relevant
F4 and F5F1F2 and F3
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Feature selection Parts of feature set
Irrelevant OR Relevant
Feature selection Parts of feature set
Irrelevant OR Relevant
Definition 3 (Weak relevance) A feature Fi is weakly relevant if
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Weak relevance suggests that the feature is not always necessary but may become necessary for an optimal subset at certain conditions.
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Example:
In order to determine the target concept (C=g(F1, F2)):
F1 is indispensable
One of F2 and F3 can be disposed
Both F4 and F5 can be discarded.
optimal subset: Either {F1, F2} or {F1, F3}
The goal of feature selection is to find either of them.
Feature selection Parts of feature set
Optimal Feature Subset
Feature selection Parts of feature set
Optimal Feature Subset
Feature selection Parts of feature set
Optimal Feature Subset
Feature selection Parts of feature set
Optimal Feature Subset
Conclusion
An optimal subset should include all strongly relevant features, none of irrelevant features, and a subset of weakly relevant features.
optimal subset: Either {F1, F2} or {F1, F3}
which of weakly relevant features should be selected and which of them removed
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Feature selection Parts of feature set
Redundancy
Feature selection Parts of feature set
Redundancy
Solution
Defining Feature Redundancy
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Redundancy
It is widely accepted that two features are redundant to each other if their values are completely correlated
Feature selection Parts of feature set
Redundancy
Feature selection Parts of feature set
Redundancy
32 FF
In previous Example:
F2, F3 ( )
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Feature selection Parts of feature set
Redundancy
Feature selection Parts of feature set
Redundancy
Markov blanket
It used when one feature is correlated with a set of features.
Given a feature Fi, let ,Mi is said to be a Markov blanket for Fi if)( iii MFFM
The Markov blanket condition requires that Mi subsume not only the information that Fi has about C, but also about all of the other features.
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Feature selection Parts of feature set
Redundancy
Feature selection Parts of feature set
Redundancy
Redundancy definition further divides weakly relevant features into redundant and non-redundant ones.
StronglyIrrelevant Weakly IIIII
II : Weakly relevant and redundant features
III: Weakly relevant but non-redundant features
Optimal Subset: Strongly relevant features +Weakly relevant but non-redundant features
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Feature selection Approaches
Feature selection Approaches
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Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Framework of feature selection via subset evaluation
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Generation Evaluation
Stopping Criterion Validation
OriginalFeature Set Subset
Goodness of the subset
No Yes
1 2
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Generates subset of features for evaluation
Can start with:
•no features
•all features
•random subset of features
Subset Generation
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Examine all combinations of feature subset.
Example:
{f1,f2,f3} => { {f1},{f2},{f3},{f1,f2},{f1,f3},{f2,f3},{f1,f2,f3} }
Order of the search space O(2d), d - # feature.
Optimal subset is achievable.
Too expensive if feature space is large.
Subset search method -Exhaustive Search Example
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Generation Evaluation
Stopping Criterion Validation
OriginalFeature Set Subset
Goodness of the subset
No Yes
1 2
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Measures the goodness of the subset
Compares with the previous best subset
if found better, then replaces the previous best subset
Subset Evaluation
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Each feature and feature subset needs to be evaluated based on importance by a criterion.
The existing feature selection algorithms, based on criterion functions used in searching for informative features can be generally categorized as:
Filter model
Wrapper model
Embedded methods
Note: Different criteria may select different features.
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Subset Evaluation
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Filter
The filter approach utilizes the data alone to decide which features should be kept, without running the learning algorithm.
The filter approach basically pre-selects the features, and then applies the selected feature subset to the clustering algorithm.
Evaluation function <> Classifier Ignored effect of selected subset on the performance of classifier.
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Filter (1)- Independent Criterion
Some popular independent criteria are
Distance measures (Euclidean distance measure).
Information measures (Entropy, Information gain, etc.)
Dependency measures (Correlation coefficient)
Consistency measures
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Wrappers In wrapper methods, the performance of a learning algorithm is used to evaluate the
goodness of selected feature subsets.
Evaluation function = classifier Take classifier into account.
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Wrappers (2)
Wrappers utilize a learning machine as a “black box” to score subsets of features according to their predictive power.
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Filters Advantages
Fast execution: Filters generally involve a non-iterative computation on the dataset, which can execute much faster than a classifier training session
Generality: Since filters evaluate the intrinsic properties of the data, rather than their interactions with a particular classifier, their results exhibit more generality: the solution will be “good” for a larger family of classifiers
Disadvantages The main disadvantage of the filter approach is that it totally ignores the effects of the selected feature subset on the performance of the induction algorithm
Filters vs. Wrappers
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Filters vs. Wrappers
Wrappers Advantages
Accuracy: wrappers generally achieve better recognition rates than filters since they are tuned to the specific interactions between the classifier and the dataset
Disadvantages
Slow execution: since the wrapper must train a classifier for each feature subset (or several classifiers if cross-validation is used), the method can become infeasible for computationally intensive methods
Lack of generality: the solution lacks generality since it is tied to the bias of the classifier used in the evaluation function.
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Yes, stop!
All features Eliminate
uselessfeature(s)
Train SVM
Eliminateuseless
feature(s)
Train SVM
Performancedegradation?
Train SVM
Eliminateuseless
feature(s)
Train SVM
Train SVM
Eliminateuseless
feature(s)
Eliminateuseless
feature(s)
No, continue…
Recursive Feature Elimination (RFE) SVM. Guyon-Weston, 2000. US patent 7,117,188
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Embedded methods
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Generation Evaluation
Stopping Criterion Validation
OriginalFeature Set
Subset
Goodness of the subset
No Yes
1 2
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Based on Generation rcdure:
•Pre-defined number of features
•Pre-defined number of iterations
Based on Evaluation Function:
•whether addition or deletion of a
feature does not produce a better
subset•whether optimal subset based on
some evaluation function is achieved
Stopping Criterion
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Generation Evaluation
Stopping Criterion Validation
OriginalFeature Set Subset
Goodness of the subset
No Yes
1 2
3 4
Basically not part of the feature selection process itself
- compare results with already established results or results from competing feature selection methods
Result Validation
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
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Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
A feature subset selected by this approach approximates the optimal subset:
Subset Evaluation: Advantage
StronglyIrrelevant Weakly IIIII
II : Weakly relevant and redundant features
III: Weakly relevant but non-redundant features
Optimal Subset: Strongly relevant features +Weakly relevant but non-redundant features
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Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Feature selection Approaches : Subset Evaluation (Feature Subset Selection )
Subset Evaluation: Disadvantages
High computational cost of the subset search makes subset evaluation approach inefficient for high dimensional data.
Feature selection Approaches
Feature selection Approaches
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Individual method (Feature Ranking / Feature weighting)
Individual methods evaluate each feature individually according to a criterion.
They then select features, which either satisfy a condition or are top-ranked.
Exhaustive, greedy and random searches are subset search methods because they evaluate each candidate subset.
Feature selection Approaches : Individual Evaluation (Feature Weighting/Ranking)
Feature selection Approaches : Individual Evaluation (Feature Weighting/Ranking)
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linear time complexity in terms of dimensionality N.
Individual method is efficient for high-dimensional data.
Individual Evaluation: Advantage
Feature selection Approaches : Individual Evaluation (Feature Weighting/Ranking)
Feature selection Approaches : Individual Evaluation (Feature Weighting/Ranking)
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Individual Evaluation: Disadvantages
Feature selection Approaches : Individual Evaluation (Feature Weighting/Ranking)
Feature selection Approaches : Individual Evaluation (Feature Weighting/Ranking)
It is incapable of removing redundant features.
For high-dimensional data which may contain a large number of redundant features, this approach may produce results far from optimal.
StronglyIrrelevant Weakly IIIII
Select= Weakly + Strongly
Feature selection Approaches
Feature selection Approaches
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Feature selection New Framework
Feature selection New Framework
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New framework of feature selection composed of two steps:
First Step (Relevance analysis): determines the subset of relevant features by removing irrelevant ones.
Second Step (redundancy analysis): determines and eliminates redundant features from relevant ones and thus produces the final subset.
New Framework
Part 3:Applications of Feature Selection
AndSoftware
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Feature selection Applications of Feature Selection
Feature selection Applications of Feature Selection
Internet
Information explosive 80% information stored in text documents: journals, web pages, emails... Difficult to extract special information Current technologies...
Feature selection Applications of Feature Selection
Text categorization: Importance
Feature selection Applications of Feature Selection
Text categorization: Importance
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Feature selection Applications of Feature Selection
Text categorization
Feature selection Applications of Feature Selection
Text categorization
Assigning documents to a fixed set of categories
Newsarticle categorizer
sports
cultures
health
politics
economics
vacations
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Text-Categorization
Documents are represented by a vector of dimension the size of the vocabulary containing word frequency counts
Vocabulary ~ 15.000 words (i.e. each document is represented by a 15.000-dimensional vector)
Typical tasks: - Automatic sorting of documents into web-directories- Detection of spam-email
Feature selection Applications of Feature Selection
Text categorization
Feature selection Applications of Feature Selection
Text categorization
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Feature selection Applications of Feature Selection
Text categorization
Feature selection Applications of Feature Selection
Text categorization
Major characteristic, or difficulty of text categorization:
High dimensionality of the feature space
Goal: Reduce the original feature space without sacrificing categorization accuracy
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Feature selection Applications of Feature Selection
Image retrieval
Feature selection Applications of Feature Selection
Image retrieval
Importance: Rapid increase of the size and amount of image collections from both civilian and military equipments
Problem: Cannot access to or make use of the information unless it is organized.
Content-based image retrieval: Instead of being manually annotated bytext-based keywords, images would be indexed by their own visual contents (features), such as color, texture, shape, etc.
One of the biggest problems to make content-based image retrieval trulyscalable to large size image collections is still the “curse of dimensionality
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Paper: ReliefF Based Feature Selection In Content-Based Image Retrieval
A. sarrafzadeh, Habibollah Agh Atabay, Mir Mosen Pedram, Jamshid Shanbehzadeh
Feature selection Applications of Feature Selection
Image retrieval
Feature selection Applications of Feature Selection
Image retrieval
Image dataset: Coil-20 contains :
1440 grayscale pictures from 20 classes of objects.
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Feature selection Applications of Feature Selection
Image retrieval
Feature selection Applications of Feature Selection
Image retrieval
In this paper They use :
Legendre moments to extract features ReliefF algorithm to select the most relevant and non-redundant features Support vector machine to classify images.
The effects of features on classification accuracy
Weka is a piece of software, written in Java, that provides an array of machine learning tools, many of which can be used for data mining
Pre-processing data Features selection Features extraction Regression Classify data Clustering data Associate rules
More functions Create random data set Connect data sets in other formats Visualize data …….
Feature selection Weka Software: What we can do with ?
Feature selection Weka Software: What we can do with ?
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ReferencesReferences
[1] M. Dash and H.Liu, “Dimensionality Reduction, in Encyclopedia of ComputerScience and Engineering,” John Wiley & Sons, Inc 2,958-966, 2009.
[2]H. Liu and L. Yu, "Toward Integrating Feature Selection Algorithms for Classification and Clustering", presented at IEEE Trans. Knowl. Data Eng, vol. 17, no.4, pp.491-502, 2005.
[3]I.Guyon and A.Elisseeff, "An introduction to variable and feature selection", Journal of Machine Learning Research 3, 1157–1182, 2003.
[4] L. Yu and H. Liu, “Efficient Feature Selection via Analysis of Relevance and Redundancy", presented at Journal of Machine Learning Research, vol. 5, pp.1205-1224, 2004.
[5] H. Liu, and H. Motoda, "Computational methods of feature selection", Chapman and Hall/CRC Press, 2007.
[6] I.Guyon, Lecture 2: Introduction to Feature Selection.
[7] M.Dash and H.liu, Feature selection for classification.
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ReferencesReferences
[8] Makoto Miwa, A Survey on Incremental Feature Extraction
[9] Lei Yu, Feature Selection and Its Application in Genomic Data Analysis