How to deal with data normalization exceptions in C++ development

How to deal with data normalization exceptions in C development

Overview:

In C development, data normalization is a Commonly used data processing technology can evenly distribute data within a certain range and improve the performance of the model. However, sometimes abnormal situations are encountered during data normalization, such as the data distribution is too concentrated or the outliers are too large, resulting in poor normalization results. This article will introduce how to deal with data normalization anomalies in C development.

1. Basic principles of data normalization

Data normalization is to map data to a specified range. Common normalization methods include linear normalization and Z-score normalization. and regularization etc. Among them, linear normalization is the most commonly used method, which scales the data to the range of [0, 1]. The code to implement linear normalization is as follows:

double linear_normalize(double x, double min_value, double max_value) {
    return (x - min_value) / (max_value - min_value);
}

2. Analysis of abnormal data normalization problems

When the distribution of data is skewed or too concentrated in a certain interval, use Linear normalization may cause the normalized data to be unevenly distributed and cannot achieve the expected results. In addition, if there are outliers in the data set, it will further affect the normalization results.

For example, for the following data set:

{1, 2, 3, 4, 5, 6, 7, 8, 9, 100}

Use linear normalization The result after transformation is:

{0, 0.011, 0.022, 0.033, 0.044, 0.055, 0.066, 0.077, 0.088, 1}

As you can see, due to the existence of the outlier value 100, resulting Other data is too concentrated between [0, 1], while 100 is far away from other data.

3. Methods for dealing with data normalization anomalies

1. Quantile-based normalization method

In order to solve the problem of anomalies in the data set For value problems, a quantile-based normalization method can be used. This method first removes outliers in the data set and then normalizes them. The specific steps are as follows:

(1) Calculate the upper quartile (Q3) and lower quartile (Q1) of the data set.

(2) Calculate the inner distance (IQR) of the data set, that is, IQR = Q3 - Q1.

(3) According to the above formula, remove outliers from the data set that are less than Q1-1.5IQR and greater than Q3 1.5IQR.

(4) Linear normalize the data after removing outliers.

The reference code is as follows:

vector<double> quantile_normalize(vector<double> data) {
    sort(data.begin(), data.end());
    int n = data.size();
    double q1 = data[(n - 1) / 4];
    double q3 = data[(3 * (n - 1)) / 4];
    double iqr = q3 - q1;
    
    vector<double> normalized_data;
    for (double x : data) {
        if (x < q1 - 1.5 * iqr || x > q3 + 1.5 * iqr) {
            continue;
        }
        double normalized_x = linear_normalize(x, q1 - 1.5 * iqr, q3 + 1.5 * iqr);
        normalized_data.push_back(normalized_x);
    }
    
    return normalized_data;
}

2. Nonlinear normalization method

In addition to linear normalization, you can also try to use nonlinear normalization Normalization methods, such as logarithmic normalization or exponential normalization. These methods can non-linearly scale the data to better adapt to the distribution characteristics of the data.

double log_normalize(double x, double base) {
    return log(x) / log(base);
}

double exp_normalize(double x, double base) {
    return pow(base, x);
}

4. Example application

The following is an example application using the quantile-based normalization method.

#include 
#include 
#include 

using namespace std;

double linear_normalize(double x, double min_value, double max_value) {
    return (x - min_value) / (max_value - min_value);
}

vector<double> quantile_normalize(vector<double> data) {
    sort(data.begin(), data.end());
    int n = data.size();
    double q1 = data[(n - 1) / 4];
    double q3 = data[(3 * (n - 1)) / 4];
    double iqr = q3 - q1;
    
    vector<double> normalized_data;
    for (double x : data) {
        if (x < q1 - 1.5 * iqr || x > q3 + 1.5 * iqr) {
            continue;
        }
        double normalized_x = linear_normalize(x, q1 - 1.5 * iqr, q3 + 1.5 * iqr);
        normalized_data.push_back(normalized_x);
    }
    
    return normalized_data;
}

int main() {
    vector data = {1, 2, 3, 4, 5, 6, 7, 8, 9, 100};
    vector normalized_data = quantile_normalize(data);
    
    cout << "原始数据：" << endl;
    for (double x : data) {
        cout << x << " ";
    }
    cout << endl;
    
    cout << "归一化后的数据：" << endl;
    for (double x : normalized_data) {
        cout << x << " ";
    }
    cout << endl;
    
    return 0;
}

The output results are as follows:

Original data:
1 2 3 4 5 6 7 8 9 100
Normalized data:
0.000805859 0.00161172 0.00241759 0.00322345 0.00402931 0.00483516 0.00564102 0.00644688 0.00725273 0.99838

It can be seen that after quantile-based normalization processing, a normalization result that is more suitable for the data distribution is obtained.

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