How To Scale Each Column Of A Matrix
This is how I scale a single vector: vector = np.array([-4, -3, -2, -1, 0]) # pass the vector, current range of values, the desired range, and it returns the scaled vector scaledV
Solution 1:
If you want to do it by hand and understand what's going on:
First substract columnwise mins to make each columns have min 0.
Then divide by columnwise amplitude (max - min) to make each column have max 1.
Now each column is between 0 and 1. If you want it to be between -1 and 1, multiply by 2, and substract 1:
In [3]: mins = np.min(matrix, axis=0)
In [4]: maxs = np.max(matrix, axis=0)
In [5]: (matrix - mins[None, :]) / (maxs[None, :] - mins[None, :])
Out[5]:
array([[ 0. , 0. , 0. , 0.17857143, 0. ],
[ 0.25 , 0.25 , 0.02 , 0. , 0. ],
[ 0.5 , 0.5 , 0.16 , 0.16666667, 0. ],
[ 0.75 , 0.75 , 0.22 , 0.32142857, 0. ],
[ 1. , 1. , 1. , 1. , 1. ]])
In [6]: 2 * _ - 1
Out[6]:
array([[-1. , -1. , -1. , -0.64285714, -1. ],
[-0.5 , -0.5 , -0.96 , -1. , -1. ],
[ 0. , 0. , -0.68 , -0.66666667, -1. ],
[ 0.5 , 0.5 , -0.56 , -0.35714286, -1. ],
[ 1. , 1. , 1. , 1. , 1. ]])
I use [None, :]
for numpy to understand that I'm talking about "row vectors", not column ones.
Otherwise, use the wonderful sklearn
package, whose preprocessing
module has lots of useful transformers:
In [13]: from sklearn.preprocessing import MinMaxScaler
In [14]: scaler = MinMaxScaler(feature_range=(-1, 1))
In [15]: scaler.fit(matrix)
Out[15]: MinMaxScaler(copy=True, feature_range=(-1, 1))
In [16]: scaler.transform(matrix)
Out[16]:
array([[-1. , -1. , -1. , -0.64285714, -1. ],
[-0.5 , -0.5 , -0.96 , -1. , -1. ],
[ 0. , 0. , -0.68 , -0.66666667, -1. ],
[ 0.5 , 0.5 , -0.56 , -0.35714286, -1. ],
[ 1. , 1. , 1. , 1. , 1. ]])
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