Decimal Point Normalization in Python

Question

I am trying to apply normalization to my data and I have tried the Conventional scaling techniques using sklearn packages readily available for this kind of requirement. However, I am looking to implement something called Decimal scaling.

I read about it in this research paper and looks like a technique which can improve results of a neural network regression. As per my understanding, this is what I believe needs to be done -

• Suppose the range of attribute X is −4856 to 28. The maximum absolute value of X is 4856.
• To normalize by decimal scaling I will need to divide each value by 10000 (c = 4). In this case, −4856 becomes −0.4856 while 28 becomes 0.0028.
• So for all values: new value = old value/ 10^c

How can I reproduce this as a function in Python so as to normalize all the features(column by column) in my data set?

Input:
A      B    C
30    90    75
56   168    140
28    84        70
369  1107   922.5
485  1455   1212.5
4856 14568  12140
40    120   100
56    168   140
45    135   112.5
78    234   195
899  2697   2247.5

Output:
A       B       C
0.003   0.0009  0.0075
0.0056  0.00168 0.014
0.0028  0.00084 0.007
0.0369  0.01107 0.09225
0.0485  0.01455 0.12125
0.4856  0.14568 1.214
0.004   0.0012  0.01
0.0056  0.00168 0.014
0.0045  0.00135 0.01125
0.0078  0.00234 0.0195
0.0899  0.02697 0.22475

Answer 1

Thank you guys for asking questions which led me to think about my problem more clearly and break it into steps. I have arrived to a solution. Here's how my solution looks like:

def Dec_scale(df):
    for x in df:
        p = df[x].max()
        q = len(str(abs(p)))
        df[x] = df[x]/10**q 

I hope this solution looks agreeable!

Answer 2

def decimal_scaling (df):
df_abs = abs(df)
max_valus= df_abs.max()
log_num=[]
for i in range(max_valus.shape[0]):
    log_num.append(int(math.log10(max_valus[i]))+1)
log_num = np.array(log_num)
log_num = [pow(10, number) for number in log_num]
X_full =df/log_num
return X_full