Python 垃圾邮件。垃圾邮件lassoWeighted错误输出？

大家晚上好。我无法理解Spams.lassowighted函数的输出。如果您在他们的页面上运行示例 :

---

您将得到一个矩阵a 64x1作为输出，该矩阵只包含一个非零元素。这对于每种情况都是一样的，它每次只给每个信号一个非零元素。我不明白为什么解在| | x−Dα| | 2+λ| | diag（w）α| | 1。将是只有一个非零元素的a

输出矩阵

alpha

必须有10000列，因为X是64x10000，而字典是64x256（因为Da=X）。所以

alpha

应该是256x10000。查看Inria Spams文档，其输出为：

参数

lambda1

确定非零的数量，因为它与l1正则化器相乘。它们的实现还具有参数

L

，这是每个稀疏向量的最大非零数

因此，如果我运行以下命令：

import spams
import numpy as np
import time

np.random.seed(0)
print "test lasso weighted"
X = np.asfortranarray(np.random.normal(size=(64,10000)))
X = np.asfortranarray(X / np.tile(np.sqrt((X*X).sum(axis=0)),(X.shape[0],1)),dtype=float)
D = np.asfortranarray(np.random.normal(size=(64,256)))
D = np.asfortranarray(D / np.tile(np.sqrt((D*D).sum(axis=0)),(D.shape[0],1)),dtype=float)
param = { 'L' : 20,
    'lambda1' : 0.15, 'numThreads' : 8, 'mode' : spams.PENALTY}
W = np.asfortranarray(np.random.random(size = (D.shape[1],X.shape[1])),dtype=float)
tic = time.time()
alpha = spams.lassoWeighted(X,D,W,**param)
tac = time.time()
t = tac - tic
non_zero = []
for col in alpha.T:
    non_zero.append(col.nnz)
print 'Shape Output Matrix:', alpha.shape
print 'Min non-zeros of %d columns: %d'%(alpha.shape[1], np.min(non_zero)) 
print 'Max non-zeros of %d columns: %d'%(alpha.shape[1], np.max(non_zero)) 
print "%f signals processed per second\n" %(float(X.shape[1]) / t)

我得到：

test lasso weighted
Shape Output Matrix: (256, 10000)
Min non-zeros of 10000 columns: 20
Max non-zeros of 10000 columns: 20
7691.130169 signals processed per second

所以10000个稀疏近似，实际上是256x1向量，每个都有20个非零

如果我们将

params

更改为（最多5个非零）：

输出：

test lasso weighted
Shape Output Matrix: (256, 10000)
Min non-zeros of 10000 columns: 5
Max non-zeros of 10000 columns: 5
26600.540090 signals processed per second

test lasso weighted
Shape Output Matrix: (256, 10000)
Min non-zeros of 10000 columns: 40
Max non-zeros of 10000 columns: 61
1697.975321 signals processed per second

如果您想要更密集的稀疏近似值（alpha列），您可以将

L

变大或将其全部删除：

param = { 'lambda1' : 0.15, 'numThreads' : 8, 'mode' : spams.PENALTY}

输出：

test lasso weighted
Shape Output Matrix: (256, 10000)
Min non-zeros of 10000 columns: 5
Max non-zeros of 10000 columns: 5
26600.540090 signals processed per second

test lasso weighted
Shape Output Matrix: (256, 10000)
Min non-zeros of 10000 columns: 40
Max non-zeros of 10000 columns: 61
1697.975321 signals processed per second

test lasso weighted
Shape Output Matrix: (256, 10000)
Min non-zeros of 10000 columns: 40
Max non-zeros of 10000 columns: 61
1697.975321 signals processed per second