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Answers for “标准化的公式是什么?”

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Meet the concept

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Standardization (or Z-score normalization) is a linear transformation that centers the data around zero and scales it to have a standard deviation of one. It subtracts the mean of the feature from each data point and divides by the standard deviation.

Conditions: Applied to a continuous numerical feature.; Requires knowing the mean and standard deviation of the feature.; The standard deviation must not be zero (to avoid division by zero).

Meet the concept

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Standardization transforms a feature value xx into z=x−μσz = \frac{x - \mu}{\sigma}, targeting a mean of 0 and a standard deviation of 1 for the transformed feature.

Conditions: Applied per numerical feature.; Uses the feature mean μ\mu and standard deviation σ\sigma.; Assumes σ>0\sigma > 0.

Find a method

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Import `MinMaxScaler` from `sklearn.preprocessing`, instantiate it, and call `fit_transform` on the selected DataFrame columns. This fits the scaler to the data (learning min/max) and transforms the values to the [0, 1] range.

Conditions: Input data is numerical.; Scikit-learn library is installed.

Find a method

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Import `StandardScaler` from `sklearn.preprocessing`, instantiate it, and call `fit_transform` on the selected DataFrame columns. This transforms the data to have mean 0 and standard deviation 1.

Conditions: Input data is numerical.; Scikit-learn library is installed.

Meet the concept

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Min-max normalization transforms a feature value XX into Xnorm=X−Xmin⁡Xmax⁡−Xmin⁡X_{\text{norm}} = \frac{X - X_{\min}}{X_{\max} - X_{\min}}, mapping the feature's observed range onto the interval [0,1][0, 1].

Conditions: Applied per numerical feature.; Requires a finite minimum Xmin⁡X_{\min} and maximum Xmax⁡X_{\max} for the feature.; Assumes Xmax⁡≠XminX_{\max} \neq X_{min} to avoid division by zero.

Understand why

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Standardization centers data at the mean (μ\mu), so values below the mean become negative. Min-max normalization shifts and scales data so the minimum becomes 0 and the maximum becomes 1, keeping all values non-negative within [0, 1].

Conditions: Standardization uses z=x−μσz = \frac{x - \mu}{\sigma}.; Min-max uses Xnorm=X−Xmin⁡Xmax⁡−Xmin⁡X_{\text{norm}} = \frac{X - X_{\min}}{X_{\max} - X_{\min}}.

Meet the concept

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The least squares cost function measures the average squared difference between the predicted values (based on the model parameters and features) and the actual target values. It is commonly used in linear regression to evaluate model performance.

Conditions: Used for regression problems where the goal is to predict a continuous value.; Assumes a linear relationship between the features and the target variable.

Understand why

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No, standardization does not change the general shape of its distribution; it only shifts the mean to zero and scales the standard deviation to one. It is a linear transformation, so a highly skewed distribution remains skewed after standardization.

Conditions: The dataset has a well-defined mean and standard deviation.; Standardization is applied as a linear transformation.

Meet the concept

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Min-max normalization is a linear transformation that scales the raw feature values to a fixed range, typically [0, 1]. It subtracts the minimum value of the feature from each data point and then divides by the range (maximum minus minimum).

Conditions: Applied to a continuous numerical feature.; Requires knowing the minimum and maximum values of the feature.; The maximum and minimum values must not be equal (to avoid division by zero).