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Replacing "creation" eith "extraction". More accurate term from literature.
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edit approved Dec 24, 2012 at 4:22
soufanom
edit approved Dec 24, 2012 at 4:22
soufanom
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Feature Space

Feature space refers to the $n$-dimensions where your variables live (not including a target variable, if it is present). The term is used often in ML literature because a task in ML is feature creationextraction, hence we view all variables as features. For example, consider the data set with:

Target

  1. $Y \equiv$ Thickness of car tires after some testing period

Variables

  1. $X_1 \equiv$ distance travelled in test
  2. $X_2 \equiv$ time duration of test
  3. $X_3 \equiv$ amount of chemical $C$ in tires

The feature space is $\mathbf{R}^3$, or more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature creationextraction part):

  • $X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.

This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$.

Mappings

Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:

$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$

Feature Space

Feature space refers to the $n$-dimensions where your variables live (not including a target variable, if it is present). The term is used often in ML literature because a task in ML is feature creation, hence we view all variables as features. For example, consider the data set with:

Target

  1. $Y \equiv$ Thickness of car tires after some testing period

Variables

  1. $X_1 \equiv$ distance travelled in test
  2. $X_2 \equiv$ time duration of test
  3. $X_3 \equiv$ amount of chemical $C$ in tires

The feature space is $\mathbf{R}^3$, or more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature creation part):

  • $X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.

This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$.

Mappings

Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:

$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$

Feature Space

Feature space refers to the $n$-dimensions where your variables live (not including a target variable, if it is present). The term is used often in ML literature because a task in ML is feature extraction, hence we view all variables as features. For example, consider the data set with:

Target

  1. $Y \equiv$ Thickness of car tires after some testing period

Variables

  1. $X_1 \equiv$ distance travelled in test
  2. $X_2 \equiv$ time duration of test
  3. $X_3 \equiv$ amount of chemical $C$ in tires

The feature space is $\mathbf{R}^3$, or more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature extraction part):

  • $X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.

This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$.

Mappings

Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:

$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$

added 51 characters in body
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Cam.Davidson.Pilon
Cam.Davidson.Pilon
  • 12.3k
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Feature Space

Feature space refers to the $n$-dimensions where your data livesvariables live (not including a target variable, if it is present). The term is used more often in ML literature because a task in ML is feature creation, hence we view all variables as features. For example, consider the data set with:

Target

  1. $Y \equiv$ Thickness of car tires after some testing period

Variables

  1. $X_1 \equiv$ distance travelled in test
  2. $X_2 \equiv$ time duration of test
  3. $X_3 \equiv$ amount of chemical $C$ in tires

The feature space is $\mathbf{R}^3$, or more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature creation part):

  • $X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.

This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$.

Mappings

Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:

$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$

Feature Space

Feature space refers to the $n$-dimensions where your data lives. The term is used more often in ML literature because a task in ML is feature creation, hence we view all variables as features. For example, consider the data set with:

Target

  1. $Y \equiv$ Thickness of car tires after some testing period

Variables

  1. $X_1 \equiv$ distance travelled in test
  2. $X_2 \equiv$ time duration of test
  3. $X_3 \equiv$ amount of chemical $C$ in tires

The feature space is $\mathbf{R}^3$, or more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature creation part):

  • $X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.

This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$.

Mappings

Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:

$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$

Feature Space

Feature space refers to the $n$-dimensions where your variables live (not including a target variable, if it is present). The term is used often in ML literature because a task in ML is feature creation, hence we view all variables as features. For example, consider the data set with:

Target

  1. $Y \equiv$ Thickness of car tires after some testing period

Variables

  1. $X_1 \equiv$ distance travelled in test
  2. $X_2 \equiv$ time duration of test
  3. $X_3 \equiv$ amount of chemical $C$ in tires

The feature space is $\mathbf{R}^3$, or more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature creation part):

  • $X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.

This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$.

Mappings

Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:

$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$

Source Link
Cam.Davidson.Pilon
Cam.Davidson.Pilon
  • 12.3k
  • 6
  • 54
  • 77

Feature Space

Feature space refers to the $n$-dimensions where your data lives. The term is used more often in ML literature because a task in ML is feature creation, hence we view all variables as features. For example, consider the data set with:

Target

  1. $Y \equiv$ Thickness of car tires after some testing period

Variables

  1. $X_1 \equiv$ distance travelled in test
  2. $X_2 \equiv$ time duration of test
  3. $X_3 \equiv$ amount of chemical $C$ in tires

The feature space is $\mathbf{R}^3$, or more accurately, the positive quadrant in $\mathbf{R}^3$ as all the $X$ variables can only be positive quantities. Domain knowledge about tires might suggest that the speed the vehicle was moving at is important, hence we generate another variable, $X_4$ (this is the feature creation part):

  • $X_4 =\frac{X_1}{X_2} \equiv$ the speed of the vehicle during testing.

This extends our old feature space into a new one, the positive part of $\mathbf{R}^4$.

Mappings

Furthermore, a mapping in our example is a function, $\phi$, from $\mathbf{R}^3$ to $\mathbf{R}^4$:

$$\phi(x_1,x_2,x_3) = (x_1, x_2, x_3, \frac{x_1}{x_2} )$$