"vector augmented to 1" 是什么意思？
what does that mean "vector augmented to 1"?
我是机器学习和统计学的新手（好吧，我在大学里一直在学习数学，但那是大约 10-12 年前的事了）
能否请您解释一下本书第 4 页（第 5 页）中以下句子的含义 ( https://www.researchgate.net/publication/227612766_An_Empirical_Comparison_of_Machine_Learning_Models_for_Time_Series_Forecasting ):
The multilayer perceptron (often simply called neural network) is perhaps the most
popular network architecture in use today both for classification and regression (Bishop
[5]). The MLP is given as follows:
N
H
y ˆ = v0 +
j=1
X
vj g(wj T x′ )
(1)
where x′ is the input vector x, augmented with 1, i.e. x′ = (1, xT )T , wj is the weight
vector for j th hidden node, v0 , v1 , . . . , vN H are the weights for the output node, and y ˆ is
the network output. The function g represents the hidden node output, and it is given
in terms of a squashing function, for example (and that is what we used) the logistic
function: g(u) = 1/(1 + exp(−u)). A related model in the econometrics literature is
例如，我们有一个向量 x = [0.2, 0.3, 0.4, 0.5]
我如何对其进行转换以获得增加到 1 的 x′ 向量
x′ = (1, x)
这是矩阵和方程组同构的一部分。您现在拥有的是相当于右侧表达式的行，例如
w1 = 0.2*x1 + 0.3*x2 + 0.4*x3 + 0.5*x4
w2 = ...
w3 = ...
w4 = ...
当我们要求解系统时，我们需要扩充矩阵。这需要添加每个 w[n] 变量的系数。他们都是平凡的：
1*w1 = 0.2*x1 + 0.3*x2 + 0.4*x3 + 0.5*x4
1*w2 = ...
1*w3 = ...
1*w4 = ...
... 这就是我们得到增广矩阵的地方。当我们按位置假设变量时——w 按行，x 按列——剩下的只是系数，在一个漂亮的矩阵中。
我是机器学习和统计学的新手（好吧，我在大学里一直在学习数学，但那是大约 10-12 年前的事了） 能否请您解释一下本书第 4 页（第 5 页）中以下句子的含义 ( https://www.researchgate.net/publication/227612766_An_Empirical_Comparison_of_Machine_Learning_Models_for_Time_Series_Forecasting ):
The multilayer perceptron (often simply called neural network) is perhaps the most popular network architecture in use today both for classification and regression (Bishop [5]). The MLP is given as follows: N H y ˆ = v0 + j=1 X vj g(wj T x′ ) (1) where x′ is the input vector x, augmented with 1, i.e. x′ = (1, xT )T , wj is the weight vector for j th hidden node, v0 , v1 , . . . , vN H are the weights for the output node, and y ˆ is the network output. The function g represents the hidden node output, and it is given in terms of a squashing function, for example (and that is what we used) the logistic function: g(u) = 1/(1 + exp(−u)). A related model in the econometrics literature is
例如，我们有一个向量 x = [0.2, 0.3, 0.4, 0.5] 我如何对其进行转换以获得增加到 1 的 x′ 向量 x′ = (1, x)
这是矩阵和方程组同构的一部分。您现在拥有的是相当于右侧表达式的行，例如
w1 = 0.2*x1 + 0.3*x2 + 0.4*x3 + 0.5*x4
w2 = ...
w3 = ...
w4 = ...
当我们要求解系统时，我们需要扩充矩阵。这需要添加每个 w[n] 变量的系数。他们都是平凡的：
1*w1 = 0.2*x1 + 0.3*x2 + 0.4*x3 + 0.5*x4
1*w2 = ...
1*w3 = ...
1*w4 = ...
... 这就是我们得到增广矩阵的地方。当我们按位置假设变量时——w 按行，x 按列——剩下的只是系数，在一个漂亮的矩阵中。