<p>问题是因为以下代码</p>
<pre><code>(N - m + 1.0)**(-1)
</code></pre>
<P>考虑当{{CD1>}和^ ^ <CD2>}时发生的情况,当A组由GROMPBY产生时,其大小将为1。由于<code>m==2</code>这最终成为</p>
<pre><code>(1-2+1)**-1 == 0
</code></pre>
<p>我们{<cd4>}是未定义的,错误也是未定义的</p>
<p>现在如果我们从理论上看,你如何定义只有一个值的时间序列的近似熵;高度不可预测,因此应尽可能高。对于这种情况,让我们将其设置为<code>np.nan</code>,表示它未定义(熵总是大于等于0)</p>
<h2>代码</h2>
<pre><code>import pandas as pd
import numpy as np
def ApEn(U, m = 2, r = 0.2):
'''
Approximate Entropy
Quantify the amount of regularity over time-series data.
Input parameters:
U = Time series
m = Length of compared run of data (subseries length)
r = Filtering level (tolerance). A positive number
'''
def _maxdist(x_i, x_j):
return max([abs(ua - va) for ua, va in zip(x_i, x_j)])
def _phi(m):
x = [U.tolist()[i:i + m] for i in range(N - m + 1)]
C = [len([1 for x_j in x if _maxdist(x_i, x_j) <= r]) / (N - m + 1.0) for x_i in x]
if (N - m + 1) == 0:
return np.nan
return (N - m + 1)**(-1) * sum(np.log(C))
N = len(U)
return abs(_phi(m + 1) - _phi(m))
def Entropy(df):
'''
Calculate entropy for individual direction
'''
df = df[['Time','Direction','X','Y']]
diff_dir = df.iloc[0:,1].ne(df.iloc[0:,1].shift()).cumsum()
# Calculate ApEn grouped by direction.
df['ApEn_X'] = df.groupby(diff_dir)['X'].transform(ApEn)
df['ApEn_Y'] = df.groupby(diff_dir)['Y'].transform(ApEn)
return df
np.random.seed(0)
df = pd.DataFrame(np.random.randint(0,50, size = (10, 2)), columns=list('XY'))
df['Time'] = range(1, len(df) + 1)
direction = ['Left','Left','Left','Left','Left','Right','Right','Right','Left','Left']
df['Direction'] = direction
# Calculate defensive regularity
print (Entropy(df))
</code></pre>
<p>输出:</p>
<pre><code> Time Direction X Y ApEn_X ApEn_Y
0 1 Left 6 16 0.287682 0.287682
1 2 Left 22 6 0.287682 0.287682
2 3 Left 16 5 0.287682 0.287682
3 4 Left 5 48 0.287682 0.287682
4 5 Left 11 21 0.287682 0.287682
5 6 Right 44 25 0.693147 0.693147
6 7 Right 14 12 0.693147 0.693147
7 8 Right 43 40 0.693147 0.693147
8 9 Left 46 44 NaN NaN
9 10 Left 49 2 NaN NaN
</code></pre>
<p>较大样本(导致0**-1问题)</p>
<pre><code>np.random.seed(0)
df = pd.DataFrame(np.random.randint(0,50, size = (100, 2)), columns=list('XY'))
df['Time'] = range(1, len(df) + 1)
direction = ['Left','Right','Up','Down']
df['Direction'] = np.random.choice((direction), len(df))
print (Entropy(df))
</code></pre>
<p>输出:</p>
<pre><code> Time Direction X Y ApEn_X ApEn_Y
0 1 Left 44 47 NaN NaN
1 2 Left 0 3 NaN NaN
2 3 Down 3 39 NaN NaN
3 4 Right 9 19 NaN NaN
4 5 Up 21 36 NaN NaN
.. ... ... .. .. ... ...
95 96 Up 19 33 NaN NaN
96 97 Left 40 32 NaN NaN
97 98 Up 36 6 NaN NaN
98 99 Left 21 31 NaN NaN
99 100 Right 13 7 NaN NaN
</code></pre>