# FeatureSelectionNCAClassification class

Feature selection for classification using neighborhood component analysis (NCA)

## Description

`FeatureSelectionNCAClassification`

object contains the data, fitting
information, feature weights, and other parameters of a neighborhood component analysis
(NCA) model. `fscnca`

learns the feature weights using a
diagonal adaptation of NCA and returns an instance of a
`FeatureSelectionNCAClassification`

object. The function achieves
feature selection by regularizing the feature weights.

## Construction

Create a `FeatureSelectionNCAClassification`

object using `fscnca`

.

## Properties

`NumObservations`

— Number of observations in the training data

scalar

Number of observations in the training data (`X`

and `Y`

)
after removing `NaN`

or `Inf`

values,
stored as a scalar.

**Data Types: **`double`

`ModelParameters`

— Model parameters

structure

Model parameters used for training the model, stored as a structure.

You can access the fields of `ModelParameters`

using
dot notation.

For example, for a FeatureSelectionNCAClassification object named `mdl`

,
you can access the `LossFunction`

value using `mdl.ModelParameters.LossFunction`

.

**Data Types: **`struct`

`Lambda`

— Regularization parameter

scalar

Regularization parameter used for training this model, stored
as a scalar. For *n* observations, the best `Lambda`

value
that minimizes the generalization error of the NCA model is expected
to be a multiple of 1/*n*.

**Data Types: **`double`

`FitMethod`

— Name of fitting method

`'exact'`

| `'none'`

| `'average'`

Name of the fitting method used to fit this model, stored as one of the following:

`'exact'`

— Perform fitting using all of the data.`'none'`

— No fitting. Use this option to evaluate the generalization error of the NCA model using the initial feature weights supplied in the call to`fscnca`

.`'average'`

— Divide the data into partitions (subsets), fit each partition using the`exact`

method, and return the average of the feature weights. You can specify the number of partitions using the`NumPartitions`

name-value pair argument.

`Solver`

— Name of the solver used to fit this model

`'lbfgs'`

| `'sgd'`

| `'minibatch-lbfgs'`

Name of the solver used to fit this model, stored as one of the following:

`'lbfgs'`

— Limited memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm`'sgd'`

— Stochastic gradient descent (SGD) algorithm`'minibatch-lbfgs'`

— stochastic gradient descent with LBFGS algorithm applied to mini-batches

`GradientTolerance`

— Relative convergence tolerance on gradient norm

positive scalar

Relative convergence tolerance on the gradient norm for the `'lbfgs'`

and `'minibatch-lbfgs'`

solvers,
stored as a positive scalar value.

**Data Types: **`double`

`IterationLimit`

— Maximum number of iterations for optimization

positive integer

Maximum number of iterations for optimization, stored as a positive integer value.

**Data Types: **`double`

`PassLimit`

— Maximum number of passes

positive integer

Maximum number of passes for `'sgd'`

and `'minibatch-lbfgs'`

solvers. Every
pass processes all of the observations in the data.

**Data Types: **`double`

`InitialLearningRate`

— Initial learning rate

positive real scalar

Initial learning rate for the `'sgd'`

and
`'minibatch-lbfgs'`

solvers, stored as a positive real
scalar. The
learning rate decays over iterations starting at the value specified for
`InitialLearningRate`

.

Use the `NumTuningIterations`

and
`TuningSubsetSize`

name-value pair arguments to
control the automatic tuning of initial learning rate in the call to
`fscnca`

.

**Data Types: **`double`

`Verbose`

— Verbosity level indicator

nonnegative integer

Verbosity level indicator, stored as a nonnegative integer. Possible values are:

0 — No convergence summary

1 — Convergence summary, including norm of gradient and objective function value

>1 — More convergence information, depending on the fitting algorithm. When you use the

`'minibatch-lbfgs'`

solver and verbosity level > 1, the convergence information includes the iteration log from intermediate mini-batch LBFGS fits.

**Data Types: **`double`

`InitialFeatureWeights`

— Initial feature weights

*p*-by-1 vector of positive real scalars

Initial feature weights, stored as a *p*-by-1
vector of positive real scalars, where *p* is the
number of predictors in `X`

.

**Data Types: **`double`

`FeatureWeights`

— Feature weights

numeric vector | numeric matrix

Feature weights, specified as a *p*-by-1 numeric vector
or a *p*-by-*m* numeric matrix, where
*p* is the number of predictor variables after dummy
variables are created for categorical variables (for more details, see
`ExpandedPredictorNames`

).

If `FitMethod`

is `'average'`

, then
`FeatureWeights`

is a
*p*-by-*m* matrix.
*m* is the number of partitions specified via the
`'NumPartitions'`

name-value pair argument in the call
to `fscnca`

.

The absolute value of `FeatureWeights(k)`

is a measure of
the importance of predictor `k`

. A
`FeatureWeights(k)`

value that is close to 0 indicates
that predictor `k`

does not influence the response in
`Y`

.

**Data Types: **`double`

`FitInfo`

— Fit information

structure

Fit information, stored as a structure with the following fields.

Field Name | Meaning |
---|---|

`Iteration` | Iteration index |

`Objective` | Regularized objective function for minimization |

`UnregularizedObjective` | Unregularized objective function for minimization |

`Gradient` | Gradient of regularized objective function for minimization |

For classification,

`UnregularizedObjective`

represents the negative of the leave-one-out accuracy of the NCA classifier on the training data.For regression,

`UnregularizedObjective`

represents the leave-one-out loss between the true response and the predicted response when using the NCA regression model.For the

`'lbfgs'`

solver,`Gradient`

is the final gradient. For the`'sgd'`

and`'minibatch-lbfgs'`

solvers,`Gradient`

is the final mini-batch gradient.If

`FitMethod`

is`'average'`

, then`FitInfo`

is an*m*-by-1 structure array, where*m*is the number of partitions specified via the`'NumPartitions'`

name-value pair argument.

You can access the fields of `FitInfo`

using
dot notation. For example, for a FeatureSelectionNCAClassificationobject named `mdl`

,
you can access the `Objective`

field using `mdl.FitInfo.Objective`

.

**Data Types: **`struct`

`Mu`

— Predictor means

*p*-by-1 vector | `[]`

Predictor means, stored as a *p*-by-1 vector
for standardized training data. In this case, the `predict`

method
centers predictor matrix `X`

by subtracting the
respective element of `Mu`

from every column.

If data is not standardized during training, then `Mu`

is
empty.

**Data Types: **`double`

`Sigma`

— Predictor standard deviations

*p*-by-1 vector | `[]`

Predictor standard deviations, stored as a *p*-by-1
vector for standardized training data. In this case, the `predict`

method
scales predictor matrix `X`

by dividing every column
by the respective element of `Sigma`

after centering
the data using `Mu`

.

If data is not standardized during training, then `Sigma`

is
empty.

**Data Types: **`double`

`X`

— Predictor values

*n*-by-*p* matrix

Predictor values used to train this model, stored as an *n*-by-*p* matrix. *n* is
the number of observations and *p* is the number
of predictor variables in the training data.

**Data Types: **`double`

`Y`

— Response values

numeric vector of size *n*

Response values used to train this model, stored as a numeric
vector of size *n*, where n is the number of observations.

**Data Types: **`double`

`W`

— Observation weights

numeric vector of size *n*

Observation weights used to train this model, stored as a numeric
vector of size *n*. The sum of observation weights
is *n*.

**Data Types: **`double`

`CategoricalPredictors`

— Categorical predictor indices

vector of positive integers | `[]`

Categorical predictor indices, specified as a vector of positive integers.
`CategoricalPredictors`

contains index values indicating that the
corresponding predictors are categorical. The index values are between 1 and
*p*, where *p* is the number of predictors used to
train the model. If none of the predictors are categorical, then this property is empty
(`[]`

).

**Data Types: **`single`

| `double`

`ResponseName`

— Response variable name

character vector

Response variable name, specified as a character vector.

**Data Types: **`char`

`PredictorNames`

— Predictor variable names

cell array of unique character vectors

Predictor variable names in order of their appearance in the predictor data, specified as a
cell array of character vectors. The length of `PredictorNames`

is
equal to the number of variables in the training data `X`

used as
predictor variables.

**Data Types: **`cell`

`ExpandedPredictorNames`

— Expanded predictor names

cell array of unique character vectors

Expanded predictor names, specified as a cell array of unique character vectors.

If the model uses encoding for categorical variables, then
`ExpandedPredictorNames`

includes the names that describe the
expanded variables. Otherwise, `ExpandedPredictorNames`

is the same as
`PredictorNames`

.

**Data Types: **`cell`

## Methods

loss | Evaluate accuracy of learned feature weights on test data |

predict | Predict responses using neighborhood component analysis (NCA) classifier |

refit | Refit neighborhood component analysis (NCA) model for classification |

## Examples

### Explore `FeatureSelectionNCAClassification`

Object

Load the sample data.

`load ionosphere`

The data set has 34 continuous predictors. The response variable is the radar returns, labeled as b (bad) or g (good).

Fit a neighborhood component analysis (NCA) model for classification to detect the relevant features.

mdl = fscnca(X,Y);

The returned NCA model, `mdl`

, is a `FeatureSelectionNCAClassification`

object. This object stores information about the training data, model, and optimization. You can access the object properties, such as the feature weights, using dot notation.

Plot the feature weights.

figure() plot(mdl.FeatureWeights,'ro') xlabel('Feature Index') ylabel('Feature Weight') grid on

The weights of the irrelevant features are zero. The `'Verbose',1`

option in the call to `fscnca`

displays the optimization information on the command line. You can also visualize the optimization process by plotting the objective function versus the iteration number.

figure plot(mdl.FitInfo.Iteration,mdl.FitInfo.Objective,'ro-') grid on xlabel('Iteration Number') ylabel('Objective')

The `ModelParameters`

property is a `struct`

that contains more information about the model. You can access the fields of this property using dot notation. For example, see if the data was standardized or not.

mdl.ModelParameters.Standardize

`ans = `*logical*
0

`0`

means that the data was not standardized before fitting the NCA model. You can standardize the predictors when they are on very different scales using the `'Standardize',1`

name-value pair argument in the call to `fscnca`

.

## Copy Semantics

Value. To learn how value classes affect copy operations, see Copying Objects.

## Version History

**Introduced in R2016b**

## Apri esempio

Si dispone di una versione modificata di questo esempio. Desideri aprire questo esempio con le tue modifiche?

## Comando MATLAB

Hai fatto clic su un collegamento che corrisponde a questo comando MATLAB:

Esegui il comando inserendolo nella finestra di comando MATLAB. I browser web non supportano i comandi MATLAB.

Select a Web Site

Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .

You can also select a web site from the following list:

## How to Get Best Site Performance

Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.

### Americas

- América Latina (Español)
- Canada (English)
- United States (English)

### Europe

- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)

- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)