6811067.ppt6811067.ppt6811067.ppt6811067.ppt

Feature Selection
1. Overview
2. Perspectives
3. Aspects
4. Most Representative Methods
5. Related and Advanced Topics
6. Experimental Comparative Analyses

Overview
• Why we need FS:
1. to improve performance (in terms of speed,
predictive power, simplicity of the model).
2. to visualize the data for model selection.
3. To reduce dimensionality and remove noise.
• Feature Selection is a process that chooses an
optimal subset of features according to a
certain criterion.

Overview
• Reasons for performing FS may include:
– removing irrelevant data.
– increasing predictive accuracy of learned models.
– reducing the cost of the data.
– improving learning efficiency, such as reducing
storage requirements and computational cost.
– reducing the complexity of the resulting model
description, improving the understanding of the
data and the model.

Perspectives
1. searching for the best subset of features.
2. criteria for evaluating different subsets.
3. principle for selecting, adding, removing or
changing new features during the search.

Perspectives:
Search of a Subset of Features
• FS can be considered as a search problem, where
each state of the search space corresponds to a
concrete subset of features selected.
• The selection can be represented as a binary
array, with each element corresponding to the
value 1, if the feature is currently selected by the
algorithm and 0, if it does not occur.
• There should be a total of 2M
subsets where M is
the number of features of a data set.

Perspectives:
Search
Space:

Perspectives:
• Search Directions:
– Sequential Forward Generation (SFG): It starts with an empty set of
features S. As the search starts, features are added into S according to
some criterion that distinguish the best feature from the others. S grows
until it reaches a full set of original features. The stopping criteria can be a
threshold for the number of relevant features m or simply the generation
of all possible subsets in brute force mode.
– Sequential Backward Generation (SBG): It starts with a full set of features
and,iteratively, they are removed one at a time. Here, the criterion must
point out the worst or least important feature. By the end, the subset is
only composed of a unique feature, which is considered to be the most
informative of the whole set. As in the previous case, different stopping
criteria can be used.

Perspectives:

Perspectives:
– Bidirectional Generation (BG): Begins the search in both directions,
performing SFG and SBG concurrently. They stop in two cases: (1)
when one search finds the best subset comprised of m features before
it reaches the exact middle, or (2) both searches achieve the middle of
the search space. It takes advantage of both SFG and SBG.
– Random Generation (RG): It starts the search in a random direction.
The choice of adding or removing a features is a random decision.
RGtries to avoid the stagnation into a local optima by not following a
fixed way for subset generation. Unlike SFG or SBG, the size of the
subset of features cannot be stipulated.

Perspectives:
• Search Strategies:
– Exhaustive Search: It corresponds to explore all possible subsets to find the
optimal ones. As we said before, the space complexity is O(2M
). If we
establish a threshold m of minimum features to be selected and the
direction of search, the search space is, independent of the forward or
backward generation. Only exhaustive search can guarantee the optimality.
Nevertheless, they are also impractical in real data sets with a high M.
– Heuristic Search: It employs heuristics to carry out the search. Thus, it
prevents brute force search, but it will surely find a non-optimal subset of
features. It draws a path connecting the beginning and the end of the
previous Figure, such in a way of a depth-first search. The maximum length
of this path is M and the number of subsets generated is O(M). The choice
of the heuristic is crucial to find a closer optimal subset of features in a
faster operation.

Perspectives:
• Search Strategies:
– Nondeterministic Search: Complementary combination of
the previous two. It is also known as random search
strategy and can generate best subsets constantly and
keep improving the quality of selected features as time
goes by. In each step, the next subset is obtained at
random.
• it is unnecessary to wait until the search ends.
• we do not know when the optimal set is obtained, although we
know which one is better than the previous one and which one is
the best at the moment.

Perspectives:
Selection Criteria
– Information Measures.
• Information serves to measure the uncertainty of the
receiver when she/he receives a message.
• Shannon’s Entropy:
• Information gain:

Perspectives:
Selection Criteria
– Distance Measures.
• Measures of separability, discrimination or divergence
measures . The most typical is derived from distance
between the class conditional density functions.

Perspectives:
Selection Criteria
– Dependence Measures.
• known as measures of association or correlation.
• Its main goal is to quantify how strongly two variables
are correlated or present some association with each
other, in such way that knowing the value of one of
them, we can derive the value for the other.
• Pearson correlation coefficient:

Perspectives:
Selection Criteria
– Consistency Measures.
• They attempt to find a minimum number of features that
separate classes as the full set of features can.
• They aim to achieve P(C|FullSet) = P(C|SubSet).
• An inconsistency is defined as the case of two examples with
the same inputs (same feature values) but with different
output feature values (classes in classification).

Perspectives:
Selection Criteria
– Accuracy Measures.
• This form of evaluation relies on the classifier or learner. Among
various possible subsets of features, the subset which yields the
best predictive accuracy is chosen

Perspectives
• Filters:
– measuring uncertainty, distances, dependence or
consistency is usually cheaper than measuring the
accuracy of a learning process. Thus, filter methods are
usually faster.
– it does not rely on a particular learning bias, in such a way
that the selected features can be used to learn different
models from different DM techniques.
– it can handle larger sized data, due to the simplicity and
low time complexity of the evaluation measures.

Perspectives
• Wrappers:
– can achieve the purpose of improving the particular
learner’s predictive performance.
– usage of internal statistical validation to control the
overfitting, ensembles of learners and
hybridizations with heuristic learning like Bayesian
classifiers or Decision Tree induction.
– filter models cannot allow a learning algorithm to
fully exploit its bias, whereas wrapper methods do.

Perspectives
• Embedded FS:
– similar to the wrapper approach in the sense that
the features are specifically selected for a certain
learning algorithm, but in this approach, the
features are selected during the learning process.
– they could take advantage of the available data by
not requiring to split the training data into a
training and validation set; they could achieve a
faster solution by avoiding the re-training of a
predictor for each feature subset explored.

Aspects:
Output of Feature Selection
• Feature Ranking Techniques:
– we expect as the output a ranked list of features
which are ordered according to evaluation
measures.
– they return the relevance of the features.
– For performing actual FS, the simplest way is to
choose the first m features for the task at hand,
whenever we know the most appropriate m value.

Aspects:
• Feature Ranking Techniques:

Aspects:
• Minimum Subset Techniques:
– The number of relevant features is a parameter
that is often not known by the practitioner.
– There must be a second category of techniques
focused on obtaining the minimum possible
subset without ordering the features.
– whatever is relevant within the subset, is
otherwise irrelevant.

Aspects:
• Minimum Subset Techniques:

Aspects:
Evaluation
• Goals:
– Inferability: For predictive tasks, considered as an
improvement of the prediction of unseen examples with
respect to the direct usage of the raw training data.
– Interpretability: Given the incomprehension of raw data
by humans, DM is also used for generating more
understandable structure representation that can explain
the behavior of the data.
– Data Reduction: It is better and simpler to handle data
with lower dimensions in terms of efficiency and
interpretability.

Aspects:
Evaluation
• We can derive three assessment measures
from these three goals:
– Accuracy
– Complexity
– Number of Features Selected
– Speed of the FS method
– Generality of the features selected

Aspects:
Drawbacks
• The resulted subsets of many models of FS are strongly dependent
on the training set size.
• It is not true that a large dimensionality input can always be
reduced to a small subset of features because the objective
feature is actually related with many input features and the
removal of any of them will seriously effect the learning
performance.
• A backward removal strategy is very slow when working with
large-scale data sets. This is because in the firsts stages of the
algorithm, it has to make decisions funded on huge quantities of
data.
• In some cases, the FS outcome will still be left with a relatively
large number of relevant features which even inhibit the use of
complex learning methods.

Aspects:
Using Decision Trees for FS
• Decision trees can be used to implement a
trade-off between the performance of the
selected features and the computation time
which is required to find a subset.
• Decision tree inducers can be considered as
anytime algorithms for FS, due to the fact that
they gradually improve the performance and
can be stopped at any time, providing sub-
optimal feature subsets.

Most Representative Methods
• Three major components to categorize
combinations:
– Search Direction
– Search Strategy
– Evaluation Measure

Exhaustive Methods
• Cover the whole search space.
• Six Combinations (C1-C6).
– Focus method: C2.
– Automatic Branch and Bound (ABB): C5.
– Best First Search (BFS): C1.
– Beam Search: C3.
– Branch and Bound (BB): C4.

Exhaustive Methods

Heuristic Methods
• They do not have any expectations of finding
an optimal subset with a rapid solution.
• Nine Combinations (C7-C15).
– Use a DM algorithm for FS: C12.
– Wrapper Sequential Forward Selection: C9.
– SetCover: C8.
– Heuristic search algorithm and in each sub-search
space: C13-C15.
– MIFS: C10.

Heuristic Methods

Nondeterministic Methods
• They add or remove features to and from a
subset without a sequential order.
• Three Combinations (C16-C18).
– Simulated Annealing / Genetic Algorithms are the
most common techniques.
– LVF: C17.
– LVW: C18.

Nondeterministic Methods

Feature Weighting Methods
• Provide weights to features, also can be used
for FS.
• Relief (binary) and ReliefF (multipe classes).

Related and Advanced Topics
Leading and Recent FS Techniques
• The related literature is huge, quite chaotic
and difficult to understand or categorize the
differences among the hundreds of algorithms
published.
• Focus attention on the main ideas that lead to
updates and improvements.

• Modifications of classical FS:
– MIFS-U, MIFS based on Parzen window, mRMR,
NMIFS.
– Several Relief modifications: Iterative-RELIEF.
• Separability and Similarity:
– Kernel class separability.
– Common subspace measure and Fisher subspace
measure combination.
– The redundancy-constrained FS (RCFS).
– Many more…

• Use of meta-heuristics:
– Genetic algorithms.
– Tabu search.
– Hybridizations between genetic algorithms and
local searches.
• Rough Sets theory:
– evaluation criteria based onn reducts and
approximations.
– Fuzzy Rough FS (FRFS).

• Fusion of filters and wrappers:
– Evaluation criteria merging dependency,
coefficients of correlations and error estimation
by KNN.
– GAMIFS: genetic algorithm to form an hybrid
filter/wrapper.
• Extremely high-dimensional data:
– Reduction of the FS task to a quadratic
optimization problem: QPFS.
– Big Data solutions.

Feature Extraction
• Find new features that are calculated as a
function of the original features.
• Dimensionality Reduction is done by mapping
a multidimensional space into a space of
fewer dimensions.
• It is another name given to Space
Transformations.

Feature Construction
• Attach to the algorithms some mechanism to
compound new features from the original
ones endeavouring to improve accuracy and
the decrease in model complexity.
• They have been extensively applied on
separate-and-conquer predictive learning
approaches.

Feature Construction
• Constructive operators:
– Product, inequality, maximum, minimum, average,
addition, substraction, division, count, …

Experimental Comparative
Analyses
• Summary of some major studies:
– With 1-NN, the main conclusions point to the use of the
bidirectional approaches for small and medium scale data
sets.
– Regarding evaluation measures, the inconsistency
criterion was emphasized in several aspects.
– Evaluation measure + stopping criterion: information
theory based functions obtain better accuracy results; no
cutting criterion can be generally recommended.
– On synthetic data, ReliefF turned out to be the best option
independent of the particulars of the data.

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