散布熵Dispersion Entropy的matlab代码

以下是一份简单的 Matlab 代码，用于计算散布熵（Dispersion Entropy）：

function DE = dispersion_entropy(X, m, r)

% X: 输入信号，是一个行向量
% m: 子序列长度
% r: 相邻点之间的最大距离

N = length(X);
DE = 0;

for i = 1:(N - m + 1)
    subseq = X(i:(i + m - 1));
    num_pairs = (m * (m - 1)) / 2;
    count = 0;
    for j = 1:(m - 1)
        for k = (j + 1):m
            if abs(subseq(j) - subseq(k)) > r
                count = count + 1;
            end
        end
    end
    p = count / num_pairs;
    if p > 0
        DE = DE - p * log(p);
    end
end

DE = DE / (N - m + 1);

end

代码中的 `X` 是输入信号，是一个行向量。`m` 是子序列长度，`r` 是相邻点之间的最大距离。函数首先计算输入信号中每个长度为 `m` 的子序列的散布熵，并将所有子序列的散布熵平均作为最终的散布熵。

相关问题

python dispersion entropy

在Python中，"dispersion entropy"通常是指数据分散度和熵的概念结合在一起的统计测量指标，它用于衡量数据点分布的均匀程度。Dispersion entropy可以用来评估一组观测值在某一特征上的离散度，并考虑了数值之间的相对频率。在信息论中，熵是用来描述随机变量不确定性的量。

具体计算 Dispersion Entropy 的时候，可能会涉及对数函数，因为熵经常与概率有关，而对数能够减少大的数值对结果的影响。一个常见的公式是将每个数据点视为概率分布的一部分，然后取分布的熵作为结果。例如，对于数据集 {x1, x2, ..., xn}，其熵 H 可能会基于如下的公式计算：

H = -Σ(p_i * log(p_i))

其中，p_i 是第 i 个数值 xi 出现的概率，log 是自然对数（通常是 base e）。

如果你想要在Python中实现这个概念，你可以使用numpy库进行数学运算，scipy库可能也提供相关的熵计算函数。下面是一个简化的示例：

import numpy as np

def dispersion_entropy(data):
    # 数据转换为频率分布
    freq = np.histogram(data, bins='auto')[0] / len(data)
    
    # 计算熵
    try:
        return -np.sum(freq * np.log2(freq))
    except ZeroDivisionError:
        return 0  # 针对所有数据都相同的极端情况处理

data = [你的数据列表]
entropy_value = dispersion_entropy(data)

This function calculates fluctuation-based dispersion entropy (FDispEn) of a univariate

The "fluctuation-based dispersion entropy" or FDispEn is a measure of the complexity and disorder in a univariate time series or signal. It's often used in the field of physics, information theory, and data analysis to quantify how much the values in the series deviate from their mean, which can provide insights into the irregularity or unpredictability of the system that generated the data.

The calculation of FDispEn typically involves several steps:

1. **Mean Calculation**: Compute the average value of the data.
2. **Fluctuation Calculation**: Subtract the mean from each data point to get the fluctuations (deviations).
3. **Square the Fluctuations**: Square the resulting deviations to emphasize the impact of larger discrepancies.
4. **Normalization**: Divide each squared deviation by the total sum of squares to normalize the result between 0 and 1.
5. **Entropy Calculation**: Use the Shannon entropy formula, where entropy is proportional to the negative sum of the square fluctuations times their probabilities. In this case, the probability is the frequency or relative occurrence of each deviation.

Here's a simplified version of a MATLAB code snippet to calculate FDispEn for a given vector `x`:

function fdispEn = compute_FDispEn(x)
    % Step 1: Calculate mean
    mean_val = mean(x);
    
    % Step 2: Calculate fluctuations
    fluctuations = x - mean_val;
    
    % Step 3: Square the fluctuations
    squared_fluctuations = fluctuations.^2;
    
    % Step 4: Normalize (calculate probabilities)
    norm_squares = squared_fluctuations / sum(squared_fluctuations);
    
    % Step 5: Compute entropy (using base 2 for simplicity)
    prob_sum = sum(norm_squares);
    if prob_sum == 0
        warning('All data points are identical, FDispEn is undefined');
    else
        fdispEn = -sum(norm_squares .* log2(norm_squares)) / log2(prob_sum); % Note: log2 is not included in base 'e' MATLAB logs by default
    end
end