DataScience: -log depth discussions with the nonlinear transformation processing of data analysis in machine learning logarithmic transformation, sigmoid / softmax conversion
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Nonlinear transformation of data processing in-depth discussion and analysis of machine learning
log logarithmic transformation
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Nonlinear transformation of data processing in-depth discussion and analysis of machine learning
log logarithmic transformation
If a (a> 0, and a ≠ 1) of the b-th power equal to N, i.e., ab = N, then the number of b referred to a as a substrate of N logarithmic , denoted logaN = b (where a known logarithmic base number , N called the real number ), which is a logarithmic transformation.
sigmoid / softmax conversion
Sigmoid function
Sigmoid function is a common S-shaped function in biology, also known as S-shaped growth curve. [1] In the information science, and by the nature of their single inverse function monocytogenes like, the Sigmoid function is often used as the neural network of the activation function , to map a variable between 0 and 1.
- Advantages: smooth, easy derivation.
- Disadvantages: calculated amount activation function, when evaluated error backpropagation gradient, derivation involving division; reverse propagation, where it is easy to disappear gradient occurs, the training could not complete the deep network.
Softmax function
In mathematics, especially in probability theory and related fields, normalized exponential function, also known as Softmax function is a logical function An extended. It will be a real number with an arbitrary K-dimensional vectors z "compressed" to another K-dimensional real vector σ (z) such that the range of each element in between (0,1), and all of the elements and 1. The multi-function than classification problems.
import math
z = [1.0, 2.0, 3.0, 4.0, 1.0, 2.0, 3.0]
z_exp = [math.exp(i) for i in z]
print(z_exp) # Result: [2.72, 7.39, 20.09, 54.6, 2.72, 7.39, 20.09]
sum_z_exp = sum(z_exp)
print(sum_z_exp) # Result: 114.98
# Result: [0.024, 0.064, 0.175, 0.475, 0.024, 0.064, 0.175]
softmax = [round(i / sum_z_exp, 3) for i in z_exp]
print(softmax)
