How to normalize data between 0 and 1?
up vote
2
down vote
favorite
I have seen the min-max normalization formula in several answers (e.g. [1], [2], [3]), where data is normalized into the interval $left[0,1 right]$.
However, is there a method to normalize data into the interval $left(0,1 right)$, i.e. excluding 0 and 1?
EDIT:
My data is a sample from a uniform distribution within the range $left[a,b right]$. I would like to normalize it into the interval $left(0,1 right)$ while remaining uniformly distributed.
dataset normalization
asked Dec 4 at 15:30
skoestlmeier
12316
add a comment |
up vote
2
down vote
favorite
I have seen the min-max normalization formula in several answers (e.g. [1], [2], [3]), where data is normalized into the interval $left[0,1 right]$.
However, is there a method to normalize data into the interval $left(0,1 right)$, i.e. excluding 0 and 1?
EDIT:
My data is a sample from a uniform distribution within the range $left[a,b right]$. I would like to normalize it into the interval $left(0,1 right)$ while remaining uniformly distributed.
dataset normalization
asked Dec 4 at 15:30
skoestlmeier
12316
2
$$frac{1}{1 + exp(-x)} in (0,1)$$ for any $xin mathbb{R}$. Do you have some other requirements that would exclude this?
– Sycorax
Dec 4 at 15:47
Thanks @Sycorax, to clarify, i just edited my question to point out that my data sample should be uniformly distributed.
– skoestlmeier
Dec 4 at 16:01
add a comment |
up vote
2
down vote
favorite
up vote
2
down vote
favorite
I have seen the min-max normalization formula in several answers (e.g. [1], [2], [3]), where data is normalized into the interval $left[0,1 right]$.
However, is there a method to normalize data into the interval $left(0,1 right)$, i.e. excluding 0 and 1?
EDIT:
My data is a sample from a uniform distribution within the range $left[a,b right]$. I would like to normalize it into the interval $left(0,1 right)$ while remaining uniformly distributed.
dataset normalization
asked Dec 4 at 15:30
skoestlmeier
12316
I have seen the min-max normalization formula in several answers (e.g. [1], [2], [3]), where data is normalized into the interval $left[0,1 right]$.
However, is there a method to normalize data into the interval $left(0,1 right)$, i.e. excluding 0 and 1?
EDIT:
My data is a sample from a uniform distribution within the range $left[a,b right]$. I would like to normalize it into the interval $left(0,1 right)$ while remaining uniformly distributed.
dataset normalization
dataset normalization
asked Dec 4 at 15:30
skoestlmeier
12316
asked Dec 4 at 15:30
skoestlmeier
12316
edited Dec 4 at 16:00
asked Dec 4 at 15:30
skoestlmeier
12316
asked Dec 4 at 15:30
skoestlmeier
12316
asked Dec 4 at 15:30
skoestlmeier
12316
12316
2
$$frac{1}{1 + exp(-x)} in (0,1)$$ for any $xin mathbb{R}$. Do you have some other requirements that would exclude this?
– Sycorax
Dec 4 at 15:47
Thanks @Sycorax, to clarify, i just edited my question to point out that my data sample should be uniformly distributed.
– skoestlmeier
Dec 4 at 16:01
add a comment |
2
$$frac{1}{1 + exp(-x)} in (0,1)$$ for any $xin mathbb{R}$. Do you have some other requirements that would exclude this?
– Sycorax
Dec 4 at 15:47
Thanks @Sycorax, to clarify, i just edited my question to point out that my data sample should be uniformly distributed.
– skoestlmeier
Dec 4 at 16:01
2
2
$$frac{1}{1 + exp(-x)} in (0,1)$$ for any $xin mathbb{R}$. Do you have some other requirements that would exclude this?
– Sycorax
Dec 4 at 15:47
$$frac{1}{1 + exp(-x)} in (0,1)$$ for any $xin mathbb{R}$. Do you have some other requirements that would exclude this?
– Sycorax
Dec 4 at 15:47
Thanks @Sycorax, to clarify, i just edited my question to point out that my data sample should be uniformly distributed.
– skoestlmeier
Dec 4 at 16:01
Thanks @Sycorax, to clarify, i just edited my question to point out that my data sample should be uniformly distributed.
– skoestlmeier
Dec 4 at 16:01
add a comment |
3 Answers
3
active
oldest
votes
up vote
3
down vote
accepted
Using the property that the CDF is uniformly distributed on $[0,1]$, you can compute the empirical CDF for $x$. This is essentially the same as ranking the data and then rescaling by the number of elements $n$. To enforce the requirement that the scaled data exclude 0 and 1, you can deviate from the standard ECDF procedure and construct the scale so that the outputs are $frac{1}{n+1}, frac{2}{n+1},cdots, frac{n}{n+1}$, which is likewise uniform.
answered Dec 4 at 16:07
Sycorax
38.2k997186
There's a whole class of symmetric versions of your scaling procedure: $u_alpha(i) = frac{i-alpha}{n+1-2alpha}$ (with $0leqalphaleq 1$, of which the above has $alpha=0$. (There's also asymmetric ones which have uses in some applications)
– Glen_b♦
Dec 6 at 5:12
Does this have any particular name?
– Sycorax
Dec 6 at 13:42
Several, I think but I can't recall any right now. It comes up in probability plotting. Blom 1958 "Statistical Estimates and Transformed Beta Variables" is the standard reference for this thing (and variations).
– Glen_b♦
Dec 7 at 8:49
add a comment |
up vote
4
down vote
A uniform distribution on $(a, b)$ is the same as a uniform distribution on $[a, b]$, since for any $X$ distributed uniformly on $[a, b]$, $P(X = a) = P(X = b) = 0$. So, just use the formulae for translating to $[0, 1]$. On the other hand, if your sample has a value equal to $a$ or $b$, then you can safely conclude that you don't actually have a continuous uniform distribution.
answered Dec 4 at 16:11
Kodiologist
16.5k22953
I don't agree with your latter statement. Following the same logic, you could exclude any data from ever being sampled from a uniform distribution.
– dedObed
Dec 4 at 19:47
@dedObed The argument works for any countable set of points, because any such set has Lebesgue measure zero, but not for uncountable sets.
– Kodiologist
Dec 4 at 20:27
I agree that a uniform distribution on (a, b) is the same as a uniform on [a, b]. The claim I challenge is "if your sample has a value equal to a or b [...] you don't actually have a continuous uniform distribution."
– dedObed
Dec 4 at 20:34
@dedObed I know. I'm saying that the argument works because ${a, b}$, the set of just the two values $a$ and $b$, is countable. It wouldn't if you used a non-null set, which is what would be required to "follow the same logic" to "exclude any data from ever being sampled from a uniform distribution".
– Kodiologist
Dec 4 at 20:36
1
@dedObed I guess the chief thing to keep in mind is that continuous distributions are the sort of ethereal mathematical entities you can't get in real life. Computers fake a continuous uniform distribution with a discrete distribution that covers a large number of floating-point values. It's close enough for many applied purposes, but, e.g., a random float will always be rational, whereas a random sample from a continuous uniform distribution will be almost surely irrational.
– Kodiologist
Dec 4 at 21:58
|
show 1 more comment
up vote
1
down vote
The formula $x' = frac{x - min{x}}{max{x} - min{x}}$ will normalize the values in $[0,1]$.
I am not sure of why you want to exclude $0$ and $1$, anyway one way would be to choose a new minimum and maximum values for the transformed variable, e.g. $[0+epsilon,1-epsilon]$. You can then transform the variable using
$$x' = epsilon + (1-2epsilon) cdot left(frac{x - min{x}}{max{x} - min{x}} right)$$
Another way could be, as suggested by Sycorax in his comment, to use a logistic transform
$$ x' = frac{1}{1 + exp(-x)} $$
This ensures that $forall x in mathbb{R} implies x' in (0,1)$.
However, depending on the original distribution of $x$, $x'$ might span only a limited range of the interval $(0,1)$, so you might want to try e.g. to standardize $x$ before applying the logistic transform.
answered Dec 4 at 16:01
matteo
1,371513
add a comment |
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
3
down vote
accepted
Using the property that the CDF is uniformly distributed on $[0,1]$, you can compute the empirical CDF for $x$. This is essentially the same as ranking the data and then rescaling by the number of elements $n$. To enforce the requirement that the scaled data exclude 0 and 1, you can deviate from the standard ECDF procedure and construct the scale so that the outputs are $frac{1}{n+1}, frac{2}{n+1},cdots, frac{n}{n+1}$, which is likewise uniform.
answered Dec 4 at 16:07
Sycorax
38.2k997186
There's a whole class of symmetric versions of your scaling procedure: $u_alpha(i) = frac{i-alpha}{n+1-2alpha}$ (with $0leqalphaleq 1$, of which the above has $alpha=0$. (There's also asymmetric ones which have uses in some applications)
– Glen_b♦
Dec 6 at 5:12
Does this have any particular name?
– Sycorax
Dec 6 at 13:42
Several, I think but I can't recall any right now. It comes up in probability plotting. Blom 1958 "Statistical Estimates and Transformed Beta Variables" is the standard reference for this thing (and variations).
– Glen_b♦
Dec 7 at 8:49
add a comment |
up vote
3
down vote
accepted
Using the property that the CDF is uniformly distributed on $[0,1]$, you can compute the empirical CDF for $x$. This is essentially the same as ranking the data and then rescaling by the number of elements $n$. To enforce the requirement that the scaled data exclude 0 and 1, you can deviate from the standard ECDF procedure and construct the scale so that the outputs are $frac{1}{n+1}, frac{2}{n+1},cdots, frac{n}{n+1}$, which is likewise uniform.
answered Dec 4 at 16:07
Sycorax
38.2k997186
There's a whole class of symmetric versions of your scaling procedure: $u_alpha(i) = frac{i-alpha}{n+1-2alpha}$ (with $0leqalphaleq 1$, of which the above has $alpha=0$. (There's also asymmetric ones which have uses in some applications)
– Glen_b♦
Dec 6 at 5:12
Does this have any particular name?
– Sycorax
Dec 6 at 13:42
Several, I think but I can't recall any right now. It comes up in probability plotting. Blom 1958 "Statistical Estimates and Transformed Beta Variables" is the standard reference for this thing (and variations).
– Glen_b♦
Dec 7 at 8:49
add a comment |
up vote
3
down vote
accepted
up vote
3
down vote
accepted
Using the property that the CDF is uniformly distributed on $[0,1]$, you can compute the empirical CDF for $x$. This is essentially the same as ranking the data and then rescaling by the number of elements $n$. To enforce the requirement that the scaled data exclude 0 and 1, you can deviate from the standard ECDF procedure and construct the scale so that the outputs are $frac{1}{n+1}, frac{2}{n+1},cdots, frac{n}{n+1}$, which is likewise uniform.
answered Dec 4 at 16:07
Sycorax
38.2k997186
Using the property that the CDF is uniformly distributed on $[0,1]$, you can compute the empirical CDF for $x$. This is essentially the same as ranking the data and then rescaling by the number of elements $n$. To enforce the requirement that the scaled data exclude 0 and 1, you can deviate from the standard ECDF procedure and construct the scale so that the outputs are $frac{1}{n+1}, frac{2}{n+1},cdots, frac{n}{n+1}$, which is likewise uniform.
answered Dec 4 at 16:07
Sycorax
38.2k997186
edited Dec 5 at 15:08
answered Dec 4 at 16:07
Sycorax
38.2k997186
answered Dec 4 at 16:07
Sycorax
38.2k997186
answered Dec 4 at 16:07
Sycorax
38.2k997186
38.2k997186
There's a whole class of symmetric versions of your scaling procedure: $u_alpha(i) = frac{i-alpha}{n+1-2alpha}$ (with $0leqalphaleq 1$, of which the above has $alpha=0$. (There's also asymmetric ones which have uses in some applications)
– Glen_b♦
Dec 6 at 5:12
Does this have any particular name?
– Sycorax
Dec 6 at 13:42
Several, I think but I can't recall any right now. It comes up in probability plotting. Blom 1958 "Statistical Estimates and Transformed Beta Variables" is the standard reference for this thing (and variations).
– Glen_b♦
Dec 7 at 8:49
add a comment |
There's a whole class of symmetric versions of your scaling procedure: $u_alpha(i) = frac{i-alpha}{n+1-2alpha}$ (with $0leqalphaleq 1$, of which the above has $alpha=0$. (There's also asymmetric ones which have uses in some applications)
– Glen_b♦
Dec 6 at 5:12
Does this have any particular name?
– Sycorax
Dec 6 at 13:42
Several, I think but I can't recall any right now. It comes up in probability plotting. Blom 1958 "Statistical Estimates and Transformed Beta Variables" is the standard reference for this thing (and variations).
– Glen_b♦
Dec 7 at 8:49
There's a whole class of symmetric versions of your scaling procedure: $u_alpha(i) = frac{i-alpha}{n+1-2alpha}$ (with $0leqalphaleq 1$, of which the above has $alpha=0$. (There's also asymmetric ones which have uses in some applications)
– Glen_b♦
Dec 6 at 5:12
There's a whole class of symmetric versions of your scaling procedure: $u_alpha(i) = frac{i-alpha}{n+1-2alpha}$ (with $0leqalphaleq 1$, of which the above has $alpha=0$. (There's also asymmetric ones which have uses in some applications)
– Glen_b♦
Dec 6 at 5:12
Does this have any particular name?
– Sycorax
Dec 6 at 13:42
Does this have any particular name?
– Sycorax
Dec 6 at 13:42
Several, I think but I can't recall any right now. It comes up in probability plotting. Blom 1958 "Statistical Estimates and Transformed Beta Variables" is the standard reference for this thing (and variations).
– Glen_b♦
Dec 7 at 8:49
Several, I think but I can't recall any right now. It comes up in probability plotting. Blom 1958 "Statistical Estimates and Transformed Beta Variables" is the standard reference for this thing (and variations).
– Glen_b♦
Dec 7 at 8:49
add a comment |
up vote
4
down vote
A uniform distribution on $(a, b)$ is the same as a uniform distribution on $[a, b]$, since for any $X$ distributed uniformly on $[a, b]$, $P(X = a) = P(X = b) = 0$. So, just use the formulae for translating to $[0, 1]$. On the other hand, if your sample has a value equal to $a$ or $b$, then you can safely conclude that you don't actually have a continuous uniform distribution.
answered Dec 4 at 16:11
Kodiologist
16.5k22953
I don't agree with your latter statement. Following the same logic, you could exclude any data from ever being sampled from a uniform distribution.
– dedObed
Dec 4 at 19:47
@dedObed The argument works for any countable set of points, because any such set has Lebesgue measure zero, but not for uncountable sets.
– Kodiologist
Dec 4 at 20:27
I agree that a uniform distribution on (a, b) is the same as a uniform on [a, b]. The claim I challenge is "if your sample has a value equal to a or b [...] you don't actually have a continuous uniform distribution."
– dedObed
Dec 4 at 20:34
@dedObed I know. I'm saying that the argument works because ${a, b}$, the set of just the two values $a$ and $b$, is countable. It wouldn't if you used a non-null set, which is what would be required to "follow the same logic" to "exclude any data from ever being sampled from a uniform distribution".
– Kodiologist
Dec 4 at 20:36
1
@dedObed I guess the chief thing to keep in mind is that continuous distributions are the sort of ethereal mathematical entities you can't get in real life. Computers fake a continuous uniform distribution with a discrete distribution that covers a large number of floating-point values. It's close enough for many applied purposes, but, e.g., a random float will always be rational, whereas a random sample from a continuous uniform distribution will be almost surely irrational.
– Kodiologist
Dec 4 at 21:58
|
show 1 more comment
up vote
4
down vote
A uniform distribution on $(a, b)$ is the same as a uniform distribution on $[a, b]$, since for any $X$ distributed uniformly on $[a, b]$, $P(X = a) = P(X = b) = 0$. So, just use the formulae for translating to $[0, 1]$. On the other hand, if your sample has a value equal to $a$ or $b$, then you can safely conclude that you don't actually have a continuous uniform distribution.
answered Dec 4 at 16:11
Kodiologist
16.5k22953
I don't agree with your latter statement. Following the same logic, you could exclude any data from ever being sampled from a uniform distribution.
– dedObed
Dec 4 at 19:47
@dedObed The argument works for any countable set of points, because any such set has Lebesgue measure zero, but not for uncountable sets.
– Kodiologist
Dec 4 at 20:27
I agree that a uniform distribution on (a, b) is the same as a uniform on [a, b]. The claim I challenge is "if your sample has a value equal to a or b [...] you don't actually have a continuous uniform distribution."
– dedObed
Dec 4 at 20:34
@dedObed I know. I'm saying that the argument works because ${a, b}$, the set of just the two values $a$ and $b$, is countable. It wouldn't if you used a non-null set, which is what would be required to "follow the same logic" to "exclude any data from ever being sampled from a uniform distribution".
– Kodiologist
Dec 4 at 20:36
1
@dedObed I guess the chief thing to keep in mind is that continuous distributions are the sort of ethereal mathematical entities you can't get in real life. Computers fake a continuous uniform distribution with a discrete distribution that covers a large number of floating-point values. It's close enough for many applied purposes, but, e.g., a random float will always be rational, whereas a random sample from a continuous uniform distribution will be almost surely irrational.
– Kodiologist
Dec 4 at 21:58
|
show 1 more comment
up vote
4
down vote
up vote
4
down vote
A uniform distribution on $(a, b)$ is the same as a uniform distribution on $[a, b]$, since for any $X$ distributed uniformly on $[a, b]$, $P(X = a) = P(X = b) = 0$. So, just use the formulae for translating to $[0, 1]$. On the other hand, if your sample has a value equal to $a$ or $b$, then you can safely conclude that you don't actually have a continuous uniform distribution.
answered Dec 4 at 16:11
Kodiologist
16.5k22953
A uniform distribution on $(a, b)$ is the same as a uniform distribution on $[a, b]$, since for any $X$ distributed uniformly on $[a, b]$, $P(X = a) = P(X = b) = 0$. So, just use the formulae for translating to $[0, 1]$. On the other hand, if your sample has a value equal to $a$ or $b$, then you can safely conclude that you don't actually have a continuous uniform distribution.
answered Dec 4 at 16:11
Kodiologist
16.5k22953
edited Dec 4 at 19:35
answered Dec 4 at 16:11
Kodiologist
16.5k22953
answered Dec 4 at 16:11
Kodiologist
16.5k22953
answered Dec 4 at 16:11
Kodiologist
16.5k22953
16.5k22953
I don't agree with your latter statement. Following the same logic, you could exclude any data from ever being sampled from a uniform distribution.
– dedObed
Dec 4 at 19:47
@dedObed The argument works for any countable set of points, because any such set has Lebesgue measure zero, but not for uncountable sets.
– Kodiologist
Dec 4 at 20:27
I agree that a uniform distribution on (a, b) is the same as a uniform on [a, b]. The claim I challenge is "if your sample has a value equal to a or b [...] you don't actually have a continuous uniform distribution."
– dedObed
Dec 4 at 20:34
@dedObed I know. I'm saying that the argument works because ${a, b}$, the set of just the two values $a$ and $b$, is countable. It wouldn't if you used a non-null set, which is what would be required to "follow the same logic" to "exclude any data from ever being sampled from a uniform distribution".
– Kodiologist
Dec 4 at 20:36
1
@dedObed I guess the chief thing to keep in mind is that continuous distributions are the sort of ethereal mathematical entities you can't get in real life. Computers fake a continuous uniform distribution with a discrete distribution that covers a large number of floating-point values. It's close enough for many applied purposes, but, e.g., a random float will always be rational, whereas a random sample from a continuous uniform distribution will be almost surely irrational.
– Kodiologist
Dec 4 at 21:58
|
show 1 more comment
I don't agree with your latter statement. Following the same logic, you could exclude any data from ever being sampled from a uniform distribution.
– dedObed
Dec 4 at 19:47
@dedObed The argument works for any countable set of points, because any such set has Lebesgue measure zero, but not for uncountable sets.
– Kodiologist
Dec 4 at 20:27
I agree that a uniform distribution on (a, b) is the same as a uniform on [a, b]. The claim I challenge is "if your sample has a value equal to a or b [...] you don't actually have a continuous uniform distribution."
– dedObed
Dec 4 at 20:34
@dedObed I know. I'm saying that the argument works because ${a, b}$, the set of just the two values $a$ and $b$, is countable. It wouldn't if you used a non-null set, which is what would be required to "follow the same logic" to "exclude any data from ever being sampled from a uniform distribution".
– Kodiologist
Dec 4 at 20:36
1
@dedObed I guess the chief thing to keep in mind is that continuous distributions are the sort of ethereal mathematical entities you can't get in real life. Computers fake a continuous uniform distribution with a discrete distribution that covers a large number of floating-point values. It's close enough for many applied purposes, but, e.g., a random float will always be rational, whereas a random sample from a continuous uniform distribution will be almost surely irrational.
– Kodiologist
Dec 4 at 21:58
I don't agree with your latter statement. Following the same logic, you could exclude any data from ever being sampled from a uniform distribution.
– dedObed
Dec 4 at 19:47
I don't agree with your latter statement. Following the same logic, you could exclude any data from ever being sampled from a uniform distribution.
– dedObed
Dec 4 at 19:47
@dedObed The argument works for any countable set of points, because any such set has Lebesgue measure zero, but not for uncountable sets.
– Kodiologist
Dec 4 at 20:27
@dedObed The argument works for any countable set of points, because any such set has Lebesgue measure zero, but not for uncountable sets.
– Kodiologist
Dec 4 at 20:27
I agree that a uniform distribution on (a, b) is the same as a uniform on [a, b]. The claim I challenge is "if your sample has a value equal to a or b [...] you don't actually have a continuous uniform distribution."
– dedObed
Dec 4 at 20:34
I agree that a uniform distribution on (a, b) is the same as a uniform on [a, b]. The claim I challenge is "if your sample has a value equal to a or b [...] you don't actually have a continuous uniform distribution."
– dedObed
Dec 4 at 20:34
@dedObed I know. I'm saying that the argument works because ${a, b}$, the set of just the two values $a$ and $b$, is countable. It wouldn't if you used a non-null set, which is what would be required to "follow the same logic" to "exclude any data from ever being sampled from a uniform distribution".
– Kodiologist
Dec 4 at 20:36
@dedObed I know. I'm saying that the argument works because ${a, b}$, the set of just the two values $a$ and $b$, is countable. It wouldn't if you used a non-null set, which is what would be required to "follow the same logic" to "exclude any data from ever being sampled from a uniform distribution".
– Kodiologist
Dec 4 at 20:36
1
1
@dedObed I guess the chief thing to keep in mind is that continuous distributions are the sort of ethereal mathematical entities you can't get in real life. Computers fake a continuous uniform distribution with a discrete distribution that covers a large number of floating-point values. It's close enough for many applied purposes, but, e.g., a random float will always be rational, whereas a random sample from a continuous uniform distribution will be almost surely irrational.
– Kodiologist
Dec 4 at 21:58
@dedObed I guess the chief thing to keep in mind is that continuous distributions are the sort of ethereal mathematical entities you can't get in real life. Computers fake a continuous uniform distribution with a discrete distribution that covers a large number of floating-point values. It's close enough for many applied purposes, but, e.g., a random float will always be rational, whereas a random sample from a continuous uniform distribution will be almost surely irrational.
– Kodiologist
Dec 4 at 21:58
|
show 1 more comment
up vote
1
down vote
The formula $x' = frac{x - min{x}}{max{x} - min{x}}$ will normalize the values in $[0,1]$.
I am not sure of why you want to exclude $0$ and $1$, anyway one way would be to choose a new minimum and maximum values for the transformed variable, e.g. $[0+epsilon,1-epsilon]$. You can then transform the variable using
$$x' = epsilon + (1-2epsilon) cdot left(frac{x - min{x}}{max{x} - min{x}} right)$$
Another way could be, as suggested by Sycorax in his comment, to use a logistic transform
$$ x' = frac{1}{1 + exp(-x)} $$
This ensures that $forall x in mathbb{R} implies x' in (0,1)$.
However, depending on the original distribution of $x$, $x'$ might span only a limited range of the interval $(0,1)$, so you might want to try e.g. to standardize $x$ before applying the logistic transform.
answered Dec 4 at 16:01
matteo
1,371513
add a comment |
up vote
1
down vote
The formula $x' = frac{x - min{x}}{max{x} - min{x}}$ will normalize the values in $[0,1]$.
I am not sure of why you want to exclude $0$ and $1$, anyway one way would be to choose a new minimum and maximum values for the transformed variable, e.g. $[0+epsilon,1-epsilon]$. You can then transform the variable using
$$x' = epsilon + (1-2epsilon) cdot left(frac{x - min{x}}{max{x} - min{x}} right)$$
Another way could be, as suggested by Sycorax in his comment, to use a logistic transform
$$ x' = frac{1}{1 + exp(-x)} $$
This ensures that $forall x in mathbb{R} implies x' in (0,1)$.
However, depending on the original distribution of $x$, $x'$ might span only a limited range of the interval $(0,1)$, so you might want to try e.g. to standardize $x$ before applying the logistic transform.
answered Dec 4 at 16:01
matteo
1,371513
add a comment |
up vote
1
down vote
up vote
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down vote
The formula $x' = frac{x - min{x}}{max{x} - min{x}}$ will normalize the values in $[0,1]$.
I am not sure of why you want to exclude $0$ and $1$, anyway one way would be to choose a new minimum and maximum values for the transformed variable, e.g. $[0+epsilon,1-epsilon]$. You can then transform the variable using
$$x' = epsilon + (1-2epsilon) cdot left(frac{x - min{x}}{max{x} - min{x}} right)$$
Another way could be, as suggested by Sycorax in his comment, to use a logistic transform
$$ x' = frac{1}{1 + exp(-x)} $$
This ensures that $forall x in mathbb{R} implies x' in (0,1)$.
However, depending on the original distribution of $x$, $x'$ might span only a limited range of the interval $(0,1)$, so you might want to try e.g. to standardize $x$ before applying the logistic transform.
answered Dec 4 at 16:01
matteo
1,371513
The formula $x' = frac{x - min{x}}{max{x} - min{x}}$ will normalize the values in $[0,1]$.
I am not sure of why you want to exclude $0$ and $1$, anyway one way would be to choose a new minimum and maximum values for the transformed variable, e.g. $[0+epsilon,1-epsilon]$. You can then transform the variable using
$$x' = epsilon + (1-2epsilon) cdot left(frac{x - min{x}}{max{x} - min{x}} right)$$
Another way could be, as suggested by Sycorax in his comment, to use a logistic transform
$$ x' = frac{1}{1 + exp(-x)} $$
This ensures that $forall x in mathbb{R} implies x' in (0,1)$.
However, depending on the original distribution of $x$, $x'$ might span only a limited range of the interval $(0,1)$, so you might want to try e.g. to standardize $x$ before applying the logistic transform.
answered Dec 4 at 16:01
matteo
1,371513
answered Dec 4 at 16:01
matteo
1,371513
answered Dec 4 at 16:01
matteo
1,371513
answered Dec 4 at 16:01
matteo
1,371513
1,371513
add a comment |
add a comment |
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$$frac{1}{1 + exp(-x)} in (0,1)$$ for any $xin mathbb{R}$. Do you have some other requirements that would exclude this?
– Sycorax
Dec 4 at 15:47
Thanks @Sycorax, to clarify, i just edited my question to point out that my data sample should be uniformly distributed.
– skoestlmeier
Dec 4 at 16:01