# fscchi2

Univariate feature ranking for classification using chi-square tests

## Syntax

## Description

ranks features (predictors) using chi-square tests.
The table `idx`

= fscchi2(`Tbl`

,`ResponseVarName`

)`Tbl`

contains predictor variables and a response variable,
and `ResponseVarName`

is the name of the response variable in
`Tbl`

. The function returns `idx`

, which contains
the indices of predictors ordered by predictor importance, meaning
`idx(1)`

is the index of the most important predictor. You can use
`idx`

to select important predictors for classification
problems.

specifies additional options using one or more name-value pair arguments in addition to
any of the input argument combinations in the previous syntaxes. For example, you can
specify prior probabilities and observation weights.`idx`

= fscchi2(___,`Name,Value`

)

## Examples

### Rank Predictors in Matrix

Rank predictors in a numeric matrix and create a bar plot of predictor importance scores.

Load the sample data.

`load ionosphere`

`ionosphere`

contains predictor variables (`X`

) and a response variable (`Y`

).

Rank the predictors using chi-square tests.

[idx,scores] = fscchi2(X,Y);

The values in `scores`

are the negative logs of the *p*-values. If a *p*-value is smaller than `eps(0)`

, then the corresponding score value is `Inf`

. Before creating a bar plot, determine whether `scores`

includes `Inf`

values.

find(isinf(scores))

ans = 1x0 empty double row vector

`scores`

does not include `Inf`

values. If `scores`

includes `Inf`

values, you can replace `Inf`

by a large numeric number before creating a bar plot for visualization purposes. For details, see Rank Predictors in Table.

Create a bar plot of the predictor importance scores.

bar(scores(idx)) xlabel('Predictor rank') ylabel('Predictor importance score')

Select the top five most important predictors. Find the columns of these predictors in `X`

.

idx(1:5)

`ans = `*1×5*
5 7 3 8 6

The fifth column of `X`

is the most important predictor of `Y`

.

### Rank Predictors in Table

Rank predictors in a table and create a bar plot of predictor importance scores.

If your data is in a table and `fscchi2`

ranks a subset of the variables in the table, then the function indexes the variables using only the subset. Therefore, a good practice is to move the predictors that you do not want to rank to the end of the table. Move the response variable and observation weight vector as well. Then, the indexes of the output arguments are consistent with the indexes of the table.

Load the census1994 data set.

`load census1994`

The table `adultdata`

in `census1994`

contains demographic data from the US Census Bureau to predict whether an individual makes over $50,000 per year. Display the first three rows of the table.

head(adultdata,3)

`ans=`*3×15 table*
age workClass fnlwgt education education_num marital_status occupation relationship race sex capital_gain capital_loss hours_per_week native_country salary
___ ________________ __________ _________ _____________ __________________ _________________ _____________ _____ ____ ____________ ____________ ______________ ______________ ______
39 State-gov 77516 Bachelors 13 Never-married Adm-clerical Not-in-family White Male 2174 0 40 United-States <=50K
50 Self-emp-not-inc 83311 Bachelors 13 Married-civ-spouse Exec-managerial Husband White Male 0 0 13 United-States <=50K
38 Private 2.1565e+05 HS-grad 9 Divorced Handlers-cleaners Not-in-family White Male 0 0 40 United-States <=50K

In the table `adultdata`

, the third column `fnlwgt`

is the weight of the samples, and the last column `salary`

is the response variable. Move `fnlwgt`

to the left of `salary`

by using the `movevars`

function.

adultdata = movevars(adultdata,'fnlwgt','before','salary'); head(adultdata,3)

`ans=`*3×15 table*
age workClass education education_num marital_status occupation relationship race sex capital_gain capital_loss hours_per_week native_country fnlwgt salary
___ ________________ _________ _____________ __________________ _________________ _____________ _____ ____ ____________ ____________ ______________ ______________ __________ ______
39 State-gov Bachelors 13 Never-married Adm-clerical Not-in-family White Male 2174 0 40 United-States 77516 <=50K
50 Self-emp-not-inc Bachelors 13 Married-civ-spouse Exec-managerial Husband White Male 0 0 13 United-States 83311 <=50K
38 Private HS-grad 9 Divorced Handlers-cleaners Not-in-family White Male 0 0 40 United-States 2.1565e+05 <=50K

Rank the predictors in `adultdata`

. Specify the column `salary`

as a response variable, and specify the column `fnlwgt`

as observation weights.

[idx,scores] = fscchi2(adultdata,'salary','Weights','fnlwgt');

The values in `scores`

are the negative logs of the *p*-values. If a *p*-value is smaller than `eps(0)`

, then the corresponding score value is `Inf`

. Before creating a bar plot, determine whether `scores`

includes `Inf`

values.

idxInf = find(isinf(scores))

`idxInf = `*1×8*
1 3 4 5 6 7 10 12

`scores`

includes eight `Inf`

values.

Create a bar plot of predictor importance scores. Use the predictor names for the *x*-axis tick labels.

figure bar(scores(idx)) xlabel('Predictor rank') ylabel('Predictor importance score') xticklabels(strrep(adultdata.Properties.VariableNames(idx),'_','\_')) xtickangle(45)

The `bar`

function does not plot any bars for the `Inf`

values. For the `Inf`

values, plot bars that have the same length as the largest finite score.

hold on bar(scores(idx(length(idxInf)+1))*ones(length(idxInf),1)) legend('Finite Scores','Inf Scores') hold off

The bar graph displays finite scores and Inf scores using different colors.

## Input Arguments

`Tbl`

— Sample data

table

Sample data, specified as a table. Multicolumn variables and cell arrays other than cell arrays of character vectors are not allowed.

Each row of `Tbl`

corresponds to one observation, and each column corresponds
to one predictor variable. Optionally, `Tbl`

can contain additional
columns for a response variable and observation weights.

A response variable can be a categorical, character, or string array, logical or numeric vector, or cell array of character vectors. If the response variable is a character array, then each element of the response variable must correspond to one row of the array.

If

`Tbl`

contains the response variable, and you want to use all remaining variables in`Tbl`

as predictors, then specify the response variable by using`ResponseVarName`

. If`Tbl`

also contains the observation weights, then you can specify the weights by using`Weights`

.If

`Tbl`

contains the response variable, and you want to use only a subset of the remaining variables in`Tbl`

as predictors, then specify the subset of variables by using`formula`

.If

`Tbl`

does not contain the response variable, then specify a response variable by using`Y`

. The response variable and`Tbl`

must have the same number of rows.

If `fscchi2`

uses a subset of variables in `Tbl`

as
predictors, then the function indexes the predictors using only the subset. The values
in the `'CategoricalPredictors'`

name-value pair argument and the
output argument `idx`

do not count the predictors that the function
does not rank.

`fscchi2`

considers `NaN`

, `''`

(empty character vector), `""`

(empty string),
`<missing>`

, and `<undefined>`

values
in `Tbl`

for a response variable to be missing values.
`fscchi2`

does not use observations with missing values for a
response variable.

**Data Types: **`table`

`ResponseVarName`

— Response variable name

character vector or string scalar containing name of variable in
`Tbl`

Response variable name, specified as a character vector or string scalar containing the name of a variable in `Tbl`

.

For example, if a response variable is the column `Y`

of
`Tbl`

(`Tbl.Y`

), then specify
`ResponseVarName`

as ```
'Y'
```

.

**Data Types: **`char`

| `string`

`formula`

— Explanatory model of response variable and subset of predictor variables

character vector | string scalar

Explanatory model of the response variable and a subset of the predictor variables, specified
as a character vector or string scalar in the form ```
'Y ~ x1 + x2 +
x3'
```

. In this form, `Y`

represents the response variable, and
`x1`

, `x2`

, and `x3`

represent
the predictor variables.

To specify a subset of variables in `Tbl`

as predictors, use a formula. If
you specify a formula, then `fscchi2`

does not rank any variables
in `Tbl`

that do not appear in `formula`

.

The variable names in the formula must be both variable names in
`Tbl`

(`Tbl.Properties.VariableNames`

) and valid
MATLAB^{®} identifiers. You can verify the variable names in `Tbl`

by using the `isvarname`

function. If the variable
names are not valid, then you can convert them by using the `matlab.lang.makeValidName`

function.

**Data Types: **`char`

| `string`

`Y`

— Response variable

numeric vector | categorical vector | logical vector | character array | string array | cell array of character vectors

Response variable, specified as a numeric, categorical, or logical vector, a character or
string array, or a cell array of character vectors. Each row of `Y`

represents the labels of the corresponding row of `X`

.

`fscchi2`

considers `NaN`

, `''`

(empty character vector), `""`

(empty string),
`<missing>`

, and `<undefined>`

values
in `Y`

to be missing values. `fscchi2`

does
not use observations with missing values for `Y`

.

**Data Types: **`single`

| `double`

| `categorical`

| `logical`

| `char`

| `string`

| `cell`

`X`

— Predictor data

numeric matrix

Predictor data, specified as a numeric matrix. Each row of `X`

corresponds to one observation, and each column corresponds to one predictor variable.

**Data Types: **`single`

| `double`

### Name-Value Arguments

Specify optional
comma-separated pairs of `Name,Value`

arguments. `Name`

is
the argument name and `Value`

is the corresponding value.
`Name`

must appear inside quotes. You can specify several name and value
pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

**Example:**

`'NumBins',20,'UseMissing',true`

sets the number of bins as 20
and specifies to use missing values in predictors for ranking.`CategoricalPredictors`

— List of categorical predictors

vector of positive integers | logical vector | character matrix | string array | cell array of character vectors | `'all'`

List of categorical predictors, specified as one of the values in this table.

Value | Description |
---|---|

Vector of positive integers |
Each entry in the vector is an index value indicating that the corresponding predictor is
categorical. The index values are between 1 and If |

Logical vector |
A |

Character matrix | Each row of the matrix is the name of a predictor variable. The
names must match the names in `Tbl` . Pad the
names with extra blanks so each row of the character matrix has the
same length. |

String array or cell array of character vectors | Each element in the array is the name of a predictor variable.
The names must match the names in `Tbl` . |

`'all'` | All predictors are categorical. |

By default, if the predictor data is in a table
(`Tbl`

), `fscchi2`

assumes that a variable is
categorical if it is a logical vector, unordered categorical vector, character array, string
array, or cell array of character vectors. If the predictor data is a matrix
(`X`

), `fscchi2`

assumes that all predictors are
continuous. To identify any other predictors as categorical predictors, specify them by using
the `'CategoricalPredictors'`

name-value argument.

**Example: **`'CategoricalPredictors','all'`

**Data Types: **`single`

| `double`

| `logical`

| `char`

| `string`

| `cell`

`ClassNames`

— Names of classes to use for ranking

categorical array | character array | string array | logical vector | numeric vector | cell array of character vectors

Names of the classes to use for ranking, specified as the comma-separated pair consisting of `'ClassNames'`

and a categorical, character, or string array, a logical or numeric vector, or a cell array of character vectors. `ClassNames`

must have the same data type as `Y`

or the response variable in `Tbl`

.

If `ClassNames`

is a character array, then each element must correspond to
one row of the array.

Use `'ClassNames'`

to:

Specify the order of the

`Prior`

dimensions that corresponds to the class order.Select a subset of classes for ranking. For example, suppose that the set of all distinct class names in

`Y`

is`{'a','b','c'}`

. To rank predictors using observations from classes`'a'`

and`'c'`

only, specify`'ClassNames',{'a','c'}`

.

The default value for `'ClassNames'`

is the set of all distinct class names in `Y`

or the response variable in `Tbl`

. The default `'ClassNames'`

value has mathematical ordering if the response variable is ordinal. Otherwise, the default value has alphabetical ordering.

**Example: **`'ClassNames',{'b','g'}`

**Data Types: **`categorical`

| `char`

| `string`

| `logical`

| `single`

| `double`

| `cell`

`NumBins`

— Number of bins for binning continuous predictors

10 (default) | positive integer scalar

Number of bins for binning continuous predictors, specified as the comma-separated pair consisting of `'NumBins'`

and a positive integer scalar.

**Example: **`'NumBins',50`

**Data Types: **`single`

| `double`

`Prior`

— Prior probabilities

`'empirical'`

(default) | `'uniform'`

| vector of scalar values | structure

Prior probabilities for each class, specified as one of the following:

Character vector or string scalar.

Vector (one scalar value for each class). To specify the class order for the corresponding elements of

`'Prior'`

, set the`'ClassNames'`

name-value argument.Structure

`S`

with two fields.`S.ClassNames`

contains the class names as a variable of the same type as the response variable in`Y`

or`Tbl`

.`S.ClassProbs`

contains a vector of corresponding probabilities.

`fscchi2`

normalizes the weights in each class
(`'Weights'`

) to add up to the value of the prior probability of
the respective class.

**Example: **`'Prior','uniform'`

**Data Types: **`char`

| `string`

| `single`

| `double`

| `struct`

`UseMissing`

— Indicator for whether to use or discard missing values in predictors

`false`

(default) | `true`

Indicator for whether to use or discard missing values in predictors, specified as the
comma-separated pair consisting of `'UseMissing'`

and either
`true`

to use or `false`

to discard missing values
in predictors for ranking.

`fscchi2`

considers `NaN`

,
`''`

(empty character vector), `""`

(empty
string), `<missing>`

, and `<undefined>`

values to be missing values.

If you specify `'UseMissing',true`

, then
`fscchi2`

uses missing values for ranking. For a categorical
variable, `fscchi2`

treats missing values as an extra category.
For a continuous variable, `fscchi2`

places
`NaN`

values in a separate bin for binning.

If you specify `'UseMissing',false`

, then
`fscchi2`

does not use missing values for ranking. Because
`fscchi2`

computes importance scores individually for each
predictor, the function does not discard an entire row when values in the row are
partially missing. For each variable, `fscchi2`

uses all values
that are not missing.

**Example: **`'UseMissing',true`

**Data Types: **`logical`

`Weights`

— Observation weights

`ones(size(X,1),1)`

(default) | vector of scalar values | name of variable in `Tbl`

Observation weights, specified as the comma-separated pair consisting of
`'Weights'`

and a vector of scalar values or the name of a variable
in `Tbl`

. The function weights the observations in each row of
`X`

or `Tbl`

with the corresponding value in
`Weights`

. The size of `Weights`

must equal the
number of rows in `X`

or `Tbl`

.

If you specify the input data as a table `Tbl`

, then
`Weights`

can be the name of a variable in `Tbl`

that contains a numeric vector. In this case, you must specify
`Weights`

as a character vector or string scalar. For example, if
the weight vector is the column `W`

of `Tbl`

(`Tbl.W`

), then specify `'Weights,'W'`

.

`fscchi2`

normalizes the weights in each class to add up to the value of the prior probability of the respective class.

**Data Types: **`single`

| `double`

| `char`

| `string`

## Output Arguments

`idx`

— Indices of predictors ordered by predictor importance

numeric vector

Indices of predictors in `X`

or `Tbl`

ordered by
predictor importance, returned as a 1-by-*r* numeric vector, where
*r* is the number of ranked predictors.

If `fscchi2`

uses a subset of variables in `Tbl`

as
predictors, then the function indexes the predictors using only the subset. For example,
suppose `Tbl`

includes 10 columns and you specify the last five
columns of `Tbl`

as the predictor variables by using
`formula`

. If `idx(3)`

is `5`

,
then the third most important predictor is the 10th column in `Tbl`

,
which is the fifth predictor in the subset.

`scores`

— Predictor scores

numeric vector

Predictor scores, returned as a 1-by-*r* numeric vector, where
*r* is the number of ranked predictors.

A large score value indicates that the corresponding predictor is important.

For example, suppose `Tbl`

includes 10 columns and you specify the last
five columns of `Tbl`

as the predictor variables by using
`formula`

. Then, `score(3)`

contains the score
value of the 8th column in `Tbl`

, which is the third predictor in the
subset.

## Algorithms

### Univariate Feature Ranking Using Chi-Square Tests

`fscchi2`

examines whether each predictor variable is independent of a response variable by using individual chi-square tests. A small*p*-value of the test statistic indicates that the corresponding predictor variable is dependent on the response variable, and, therefore is an important feature.The output

`scores`

is –log(*p*). Therefore, a large score value indicates that the corresponding predictor is important. If a*p*-value is smaller than`eps(0)`

, then the output is`Inf`

.`fscchi2`

examines a continuous variable after binning, or discretizing, the variable. You can specify the number of bins using the`'NumBins'`

name-value pair argument.

**Introduced in R2020a**

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