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→递推收敛学习算法（Convergent recursive learning algorithm）
==== 递推收敛学习算法（Convergent recursive learning algorithm） ====
==== 递推收敛学习算法（Convergent recursive learning algorithm） ====
这是一种为[https://en.wikipedia.org/wiki/Cerebellar_model_articulation_controller 小脑模型关节控制器]（CMAC）神经网络特别设计的学习方法。2004，递推最小二乘法被引入在线训练CMAC神经网络。<ref name="Qin1">Ting Qin, et al. "A learning algorithm of CMAC based on RLS." Neural Processing Letters 19.1 (2004): 49–61.</ref>这种算法可以使用任何新的输入数据，一步收敛并一步内更新所有权重。最开始，这种算法有[https://en.wikipedia.org/wiki/Computational_complexity_theory 计算复杂度]''O''(''N''<sup>3</sup>). 基于[https://en.wikipedia.org/wiki/QR_decomposition QR分解]，这种算法简化到''O''(''N'').<ref name="Qin2">Ting Qin, et al. "Continuous CMAC-QRLS and its systolic array." Neural Processing Letters 22.1 (2005): 1–16.</ref>
这是一种为[https://en.wikipedia.org/wiki/Cerebellar_model_articulation_controller 小脑模型关节控制器]（CMAC）神经网络特别设计的学习方法。2004，递推最小二乘法被引入在线训练CMAC神经网络。<ref name="Qin1">Ting Qin, et al. "A learning algorithm of CMAC based on RLS." Neural Processing Letters 19.1 (2004): 49–61.</ref>这种算法可以使用任何新的输入数据，一步收敛并一步内更新所有权重。最开始，这种算法有[https://en.wikipedia.org/wiki/Computational_complexity_theory 计算复杂度]''O''(''N''<sup>3</sup>). 基于[https://en.wikipedia.org/wiki/QR_decomposition QR分解]，这种算法简化到''O''(''N'').<ref name="Qin2">Ting Qin, et al. "Continuous CMAC-QRLS and its systolic array." Neural Processing Letters 22.1 (2005): 1–16.</ref>
=== 简单实现 ===
<syntaxhighlight lang="python">
# From Programming Collective Intelligence https://resources.oreilly.com/examples/9780596529321/blob/master/PCI_Code%20Folder/chapter4/nn.py
from math import tanh
from pysqlite2 import dbapi2 as sqlite
def dtanh(y):
return 1.0-y*y
class searchnet:
def __init__(self,dbname):
self.con=sqlite.connect(dbname)
def __del__(self):
self.con.close()
def maketables(self):
self.con.execute('create table hiddennode(create_key)')
self.con.execute('create table wordhidden(fromid,toid,strength)')
self.con.execute('create table hiddenurl(fromid,toid,strength)')
self.con.commit()
def getstrength(self,fromid,toid,layer):
if layer==0: table='wordhidden'
else: table='hiddenurl'
res=self.con.execute('select strength from %s where fromid=%d and toid=%d' % (table,fromid,toid)).fetchone()
if res==None:
if layer==0: return -0.2
if layer==1: return 0
return res[0]
def setstrength(self,fromid,toid,layer,strength):
if layer==0: table='wordhidden'
else: table='hiddenurl'
res=self.con.execute('select rowid from %s where fromid=%d and toid=%d' % (table,fromid,toid)).fetchone()
if res==None:
self.con.execute('insert into %s (fromid,toid,strength) values (%d,%d,%f)' % (table,fromid,toid,strength))
else:
rowid=res[0]
self.con.execute('update %s set strength=%f where rowid=%d' % (table,strength,rowid))
def generatehiddennode(self,wordids,urls):
if len(wordids)>3: return None
# Check if we already created a node for this set of words
sorted_words=[str(id) for id in wordids]
sorted_words.sort()
createkey='_'.join(sorted_words)
res=self.con.execute(
"select rowid from hiddennode where create_key='%s'" % createkey).fetchone()
# If not, create it
if res==None:
cur=self.con.execute(
"insert into hiddennode (create_key) values ('%s')" % createkey)
hiddenid=cur.lastrowid
# Put in some default weights
for wordid in wordids:
self.setstrength(wordid,hiddenid,0,1.0/len(wordids))
for urlid in urls:
self.setstrength(hiddenid,urlid,1,0.1)
self.con.commit()
def getallhiddenids(self,wordids,urlids):
l1={}
for wordid in wordids:
cur=self.con.execute(
'select toid from wordhidden where fromid=%d' % wordid)
for row in cur: l1[row[0]]=1
for urlid in urlids:
cur=self.con.execute(
'select fromid from hiddenurl where toid=%d' % urlid)
for row in cur: l1[row[0]]=1
return l1.keys()
def setupnetwork(self,wordids,urlids):
# value lists
self.wordids=wordids
self.hiddenids=self.getallhiddenids(wordids,urlids)
self.urlids=urlids
# node outputs
self.ai = [1.0]*len(self.wordids)
self.ah = [1.0]*len(self.hiddenids)
self.ao = [1.0]*len(self.urlids)
# create weights matrix
self.wi = [[self.getstrength(wordid,hiddenid,0)
for hiddenid in self.hiddenids]
for wordid in self.wordids]
self.wo = [[self.getstrength(hiddenid,urlid,1)
for urlid in self.urlids]
for hiddenid in self.hiddenids]
def feedforward(self):
# the only inputs are the query words
for i in range(len(self.wordids)):
self.ai[i] = 1.0
# hidden activations
for j in range(len(self.hiddenids)):
sum = 0.0
for i in range(len(self.wordids)):
sum = sum + self.ai[i] * self.wi[i][j]
self.ah[j] = tanh(sum)
# output activations
for k in range(len(self.urlids)):
sum = 0.0
for j in range(len(self.hiddenids)):
sum = sum + self.ah[j] * self.wo[j][k]
self.ao[k] = tanh(sum)
return self.ao[:]
def getresult(self,wordids,urlids):
self.setupnetwork(wordids,urlids)
return self.feedforward()
def backPropagate(self, targets, N=0.5):
# calculate errors for output
output_deltas = [0.0] * len(self.urlids)
for k in range(len(self.urlids)):
error = targets[k]-self.ao[k]
output_deltas[k] = dtanh(self.ao[k]) * error
# calculate errors for hidden layer
hidden_deltas = [0.0] * len(self.hiddenids)
for j in range(len(self.hiddenids)):
error = 0.0
for k in range(len(self.urlids)):
error = error + output_deltas[k]*self.wo[j][k]
hidden_deltas[j] = dtanh(self.ah[j]) * error
# update output weights
for j in range(len(self.hiddenids)):
for k in range(len(self.urlids)):
change = output_deltas[k]*self.ah[j]
self.wo[j][k] = self.wo[j][k] + N*change
# update input weights
for i in range(len(self.wordids)):
for j in range(len(self.hiddenids)):
change = hidden_deltas[j]*self.ai[i]
self.wi[i][j] = self.wi[i][j] + N*change
def trainquery(self,wordids,urlids,selectedurl):
# generate a hidden node if necessary
self.generatehiddennode(wordids,urlids)
self.setupnetwork(wordids,urlids)
self.feedforward()
targets=[0.0]*len(urlids)
targets[urlids.index(selectedurl)]=1.0
error = self.backPropagate(targets)
self.updatedatabase()
def updatedatabase(self):
# set them to database values
for i in range(len(self.wordids)):
for j in range(len(self.hiddenids)):
self.setstrength(self.wordids[i],self. hiddenids[j],0,self.wi[i][j])
for j in range(len(self.hiddenids)):
for k in range(len(self.urlids)):
self.setstrength(self.hiddenids[j],self.urlids[k],1,self.wo[j][k])
self.con.commit()
</syntaxhighlight>
== 变体 ==
== 变体 ==