# 径向基（RBF）神经网络python实现

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  1 from numpy import array, append, vstack, transpose, reshape, \
2                   dot, true_divide, mean, exp, sqrt, log, \
4 from numpy.linalg import norm, lstsq
5 from multiprocessing import Process, Array
6 from random import sample
7 from time import time
8 from sys import stdout
9 from ctypes import c_double
10 from h5py import File
11
12
13 def metrics(a, b):
14     return norm(a - b)
15
16
17 def gaussian (x, mu, sigma):
18     return exp(- metrics(mu, x)**2 / (2 * sigma**2))
19
20
21 def multiQuadric (x, mu, sigma):
22     return pow(metrics(mu,x)**2 + sigma**2, 0.5)
23
24
25 def invMultiQuadric (x, mu, sigma):
26     return pow(metrics(mu,x)**2 + sigma**2, -0.5)
27
28
29 def plateSpine (x,mu):
30     r = metrics(mu,x)
31     return (r**2) * log(r)
32
33
34 class Rbf:
35     def __init__(self, prefix = 'rbf', workers = 4, extra_neurons = 0, from_files = None):
36         self.prefix = prefix
37         self.workers = workers
38         self.extra_neurons = extra_neurons
39
40         # Import partial model
41         if from_files is not None:
42             w_handle = self.w_handle = File(from_files['w'], 'r')
43             mu_handle = self.mu_handle = File(from_files['mu'], 'r')
44             sigma_handle = self.sigma_handle = File(from_files['sigma'], 'r')
45
46             self.w = w_handle['w']
47             self.mu = mu_handle['mu']
48             self.sigmas = sigma_handle['sigmas']
49
50             self.neurons = self.sigmas.shape[0]
51
52     def _calculate_error(self, y):
53         self.error = mean(abs(self.os - y))
54         self.relative_error = true_divide(self.error, mean(y))
55
56     def _generate_mu(self, x):
57         n = self.n
58         extra_neurons = self.extra_neurons
59
60         # TODO: Make reusable
62
63         mu_indices = sample(range(n), extra_neurons)
64         mu_new = x[mu_indices, :]
65         mu = vstack((mu_clusters, mu_new))
66
67         return mu
68
69     def _calculate_sigmas(self):
70         neurons = self.neurons
71         mu = self.mu
72
73         sigmas = zeros((neurons, ))
74         for i in xrange(neurons):
75             dists = [0 for _ in xrange(neurons)]
76             for j in xrange(neurons):
77                 if i != j:
78                     dists[j] = metrics(mu[i], mu[j])
79             sigmas[i] = mean(dists)* 2
80                       # max(dists) / sqrt(neurons * 2))
81         return sigmas
82
83     def _calculate_phi(self, x):
84         C = self.workers
85         neurons = self.neurons
86         mu = self.mu
87         sigmas = self.sigmas
88         phi = self.phi = None
89         n = self.n
90
91
92         def heavy_lifting(c, phi):
93             s = jobs[c][1] - jobs[c][0]
94             for k, i in enumerate(xrange(jobs[c][0], jobs[c][1])):
95                 for j in xrange(neurons):
96                     # phi[i, j] = metrics(x[i,:], mu[j])**3)
97                     # phi[i, j] = plateSpine(x[i,:], mu[j]))
98                     # phi[i, j] = invMultiQuadric(x[i,:], mu[j], sigmas[j]))
99                     phi[i, j] = multiQuadric(x[i,:], mu[j], sigmas[j])
100                     # phi[i, j] = gaussian(x[i,:], mu[j], sigmas[j]))
101                 if k % 1000 == 0:
102                     percent = true_divide(k, s)*100
103                     print(c, ': {:2.2f}%'.format(percent))
104             print(c, ': Done')
105
106         # distributing the work between 4 workers
107         shared_array = Array(c_double, n * neurons)
108         phi = frombuffer(shared_array.get_obj())
109         phi = phi.reshape((n, neurons))
110
111         jobs = []
112         workers = []
113
114         p = n / C
115         m = n % C
116         for c in range(C):
117             jobs.append((c*p, (c+1)*p + (m if c == C-1 else 0)))
118             worker = Process(target = heavy_lifting, args = (c, phi))
119             workers.append(worker)
120             worker.start()
121
122         for worker in workers:
123             worker.join()
124
125         return phi
126
127     def _do_algebra(self, y):
128         phi = self.phi
129
130         w = lstsq(phi, y)[0]
131         os = dot(w, transpose(phi))
132         return w, os
133         # Saving to HDF5
134         os_h5 = os_handle.create_dataset('os', data = os)
135
136     def train(self, x, y):
137         self.n = x.shape[0]
138
139         ## Initialize HDF5 caches
140         prefix = self.prefix
141         postfix = str(self.n) + '-' + str(self.extra_neurons) + '.hdf5'
142         name_template = prefix + '-{}-' + postfix
143         phi_handle = self.phi_handle = File(name_template.format('phi'), 'w')
144         os_handle = self.w_handle = File(name_template.format('os'), 'w')
145         w_handle = self.w_handle = File(name_template.format('w'), 'w')
146         mu_handle = self.mu_handle = File(name_template.format('mu'), 'w')
147         sigma_handle = self.sigma_handle = File(name_template.format('sigma'), 'w')
148
149         ## Mu generation
150         mu = self.mu = self._generate_mu(x)
151         self.neurons = mu.shape[0]
152         print('({} neurons)'.format(self.neurons))
153         # Save to HDF5
154         mu_h5 = mu_handle.create_dataset('mu', data = mu)
155
156         ## Sigma calculation
157         print('Calculating Sigma...')
158         sigmas = self.sigmas = self._calculate_sigmas()
159         # Save to HDF5
160         sigmas_h5 = sigma_handle.create_dataset('sigmas', data = sigmas)
161         print('Done')
162
163         ## Phi calculation
164         print('Calculating Phi...')
165         phi = self.phi = self._calculate_phi(x)
166         print('Done')
167         # Saving to HDF5
168         print('Serializing...')
169         phi_h5 = phi_handle.create_dataset('phi', data = phi)
170         del phi
171         self.phi = phi_h5
172         print('Done')
173
174         ## Algebra
175         print('Doing final algebra...')
176         w, os = self.w, _ = self._do_algebra(y)
177         # Saving to HDF5
178         w_h5 = w_handle.create_dataset('w', data = w)
179         os_h5 = os_handle.create_dataset('os', data = os)
180
181         ## Calculate error
182         self._calculate_error(y)
183         print('Done')
184
185     def predict(self, test_data):
186         mu = self.mu = self.mu.value
187         sigmas = self.sigmas = self.sigmas.value
188         w = self.w = self.w.value
189
190         print('Calculating phi for test data...')
191         phi = self._calculate_phi(test_data)
192         os = dot(w, transpose(phi))
193         savetxt('iok3834.txt', os, delimiter='\n')
194         return os
195
196     @property
197     def summary(self):
198         return '\n'.join( \
199             ['-----------------',
200             'Training set size: {}'.format(self.n),
201             'Hidden layer size: {}'.format(self.neurons),
202             '-----------------',
203             'Absolute error   : {:02.2f}'.format(self.error),
204             'Relative error   : {:02.2f}%'.format(self.relative_error * 100)])
205
206
207 def predict(test_data):
208     mu = File('rbf-mu-212243-2400.hdf5', 'r')['mu'].value
209     sigmas = File('rbf-sigma-212243-2400.hdf5', 'r')['sigmas'].value
210     w = File('rbf-w-212243-2400.hdf5', 'r')['w'].value
211
212     n = test_data.shape[0]
213     neur = mu.shape[0]
214
215     mu = transpose(mu)
216     mu.reshape((n, neur))
217
218     phi = zeros((n, neur))
219     for i in range(n):
220         for j in range(neur):
221             phi[i, j] = multiQuadric(test_data[i,:], mu[j], sigmas[j])
222
223     os = dot(w, transpose(phi))
224     savetxt('iok3834.txt', os, delimiter='\n')
225     return os

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