作者：十方
说到GNN,各位炼丹师会想到哪些算法呢?不管想到哪些算法,我们真正用到过哪些呢?确实我们可能都看过GNN相关论文,但是还是缺乏实战经验的.特别是对于推荐系统而言,我们又该如何应用这些模型呢?下面我们就从DeepWalk这篇论文开始,先讲原理,再讲实战,最后讲应用.
GNN相关背景知识
GNN的本质,是要学习网络中每个节点的表达的,这些潜在的表达对图中每个节点的“社交”关系进行了编码,把离散值的节点编码成稠密向量,后续可用于分类回归,或者作为下游任务的特征.Deepwalk充分利用了随机游走提取的“句子”,去学习句子中每个单词的表达.Deepwalk原文就提到了在数据稀疏的情况下可以把F1-scores提升10%,在一些实验中,能够用更少的训练数据获得了更好的效果.看下图的例子:
Deepwalk
问题定义:先把问题定义为给社交网络中的每个节点进行分类,图可以表达为G=<V,E>,V就是图上所有节点,E是所有边.有一部分有label的数据GL=(V,E,X,Y),X就是节点的特征,Y就是分类的label.在传统机器学习算法中,我们都是直接学习(X,Y),并没有充分利用节点间的依赖关系.Deepwalk可以捕捉图上的拓扑关系,通过无监督方法学习每个节点的特征,学到的图特征和标签的分布是相互独立的.
随机游走:选定一个根节点,“随机”走出一条路径,基于相邻的节点必然相似,我们就可以用这种策略去挖掘网络的社群信息.随机游走很方便并行,可以同时提取一张图上各个部分的信息.即使图有小的改动,这些路径也不需要重新计算.和word的出现频率类似,通过随机游走得到的节点访问频率都符合幂律分布,所以我们就可以用NLP相关方法对随机游走结果做相似处理,如下图所示:
所以在随机游走后,我们只需要通过下公式,学习节点向量即可:
该公式就是skip-gram,通过某个节点学习它左右的节点.我们都知道skip-gram用于文本时的语料库就是一个个句子,现在我们提取图的句子.如下所示:
算法很简单,把所有节点顺序打乱(加速收敛),然后遍历这些节点随机游走出序列,再通过skipgram算法去拟合每个节点的向量.如此反复.注:这里的随机是均匀分布去随机.当然有些图会有些“副产物”,比如用户浏览网页的顺序,可以直接输入到模型.
接下来我们看下deepwalks的核心代码:
# 代码来源
# https://github.com/phanein/deepwalk
# Random walk
with open(f, 'w') as fout:
for walk in graph.build_deepwalk_corpus_iter(G=G, # 图
num_paths=num_paths, # 路径数
path_length=path_length, # 路径长度
alpha=alpha, #
rand=rand): #
fout.write(u"{}\n".format(u" ".join(v for v in walk)))
class Graph(defaultdict):
"""
Efficient basic implementation of nx
这里我们看到,
该类继承defaultdict,
图其实可以简单的表示为dict,
key为节点,value为与之相连的节点
"""
def __init__(self):
super(Graph, self).__init__(list)
def nodes(self):
return self.keys()
def adjacency_iter(self):
return self.iteritems()
def subgraph(self, nodes={}):
# 提取子图
subgraph = Graph()
for n in nodes:
if n in self:
subgraph[n] = [x for x in self[n] if x in nodes]
return subgraph
def make_undirected(self):
#因为是无向图,所以v in self[u]并且 u in self[v]
t0 = time()
for v in list(self):
for other in self[v]:
if v != other:
self[other].append(v)
t1 = time()
logger.info('make_directed: added missing edges {}s'.format(t1-t0))
self.make_consistent()
return self
def make_consistent(self):
# 去重
t0 = time()
for k in iterkeys(self):
self[k] = list(sorted(set(self[k])))
t1 = time()
logger.info('make_consistent: made consistent in {}s'.format(t1-t0))
self.remove_self_loops()
return self
def remove_self_loops(self):
# 自已不会与自己有连接
removed = 0
t0 = time()
for x in self:
if x in self[x]:
self[x].remove(x)
removed += 1
t1 = time()
logger.info('remove_self_loops: removed {} loops in {}s'.format(removed, (t1-t0)))
return self
def check_self_loops(self):
for x in self:
for y in self[x]:
if x == y:
return True
return False
def has_edge(self, v1, v2):
# 两个节点是否有边
if v2 in self[v1] or v1 in self[v2]:
return True
return False
def degree(self, nodes=None):
# 节点的度数
if isinstance(nodes, Iterable):
return {v:len(self[v]) for v in nodes}
else:
return len(self[nodes])
def order(self):
"Returns the number of nodes in the graph"
return len(self)
def number_of_edges(self):
# 图中边的数量
"Returns the number of nodes in the graph"
return sum([self.degree(x) for x in self.keys()])/2
def number_of_nodes(self):
# 图中结点数量
"Returns the number of nodes in the graph"
return self.order()
# 核心代码
def random_walk(self, path_length, alpha=0, rand=random.Random(), start=None):
""" Returns a truncated random walk.
path_length: Length of the random walk.
alpha: probability of restarts.
start: the start node of the random walk.
"""
G = self
if start:
path = [start]
else:
# Sampling is uniform w.r.t V, and not w.r.t E
path = [rand.choice(list(G.keys()))]
while len(path) < path_length:
cur = path[-1]
if len(G[cur]) > 0:
if rand.random() >= alpha:
path.append(rand.choice(G[cur])) # 相邻节点随机选
else:
path.append(path[0]) # 有一定概率选择回到起点
else:
break
return [str(node) for node in path]
# TODO add build_walks in here
def build_deepwalk_corpus(G, num_paths, path_length, alpha=0,
rand=random.Random(0)):
walks = []
nodes = list(G.nodes())
# 这里和上面论文算法流程对应
for cnt in range(num_paths): # 外循环,相当于要迭代多少epoch
rand.shuffle(nodes) # 打乱nodes顺序,加速收敛
for node in nodes: # 每个node都会产生一条路径
walks.append(G.random_walk(path_length, rand=rand, alpha=alpha, start=node))
return walks
def build_deepwalk_corpus_iter(G, num_paths, path_length, alpha=0,
rand=random.Random(0)):
# 流式处理用
walks = []
nodes = list(G.nodes())
for cnt in range(num_paths):
rand.shuffle(nodes)
for node in nodes:
yield G.random_walk(path_length, rand=rand, alpha=alpha, start=node)
def clique(size):
return from_adjlist(permutations(range(1,size+1)))
# http://stackoverflow.com/questions/312443/how-do-you-split-a-list-into-evenly-sized-chunks-in-python
def grouper(n, iterable, padvalue=None):
"grouper(3, 'abcdefg', 'x') --> ('a','b','c'), ('d','e','f'), ('g','x','x')"
return zip_longest(*[iter(iterable)]*n, fillvalue=padvalue)
def parse_adjacencylist(f):
adjlist = []
for l in f:
if l and l[0] != "#":
introw = [int(x) for x in l.strip().split()]
row = [introw[0]]
row.extend(set(sorted(introw[1:])))
adjlist.extend([row])
return adjlist
def parse_adjacencylist_unchecked(f):
adjlist = []
for l in f:
if l and l[0] != "#":
adjlist.extend([[int(x) for x in l.strip().split()]])
return adjlist
def load_adjacencylist(file_, undirected=False, chunksize=10000, unchecked=True):
if unchecked:
parse_func = parse_adjacencylist_unchecked
convert_func = from_adjlist_unchecked
else:
parse_func = parse_adjacencylist
convert_func = from_adjlist
adjlist = []
t0 = time()
total = 0
with open(file_) as f:
for idx, adj_chunk in enumerate(map(parse_func, grouper(int(chunksize), f))):
adjlist.extend(adj_chunk)
total += len(adj_chunk)
t1 = time()
logger.info('Parsed {} edges with {} chunks in {}s'.format(total, idx, t1-t0))
t0 = time()
G = convert_func(adjlist)
t1 = time()
logger.info('Converted edges to graph in {}s'.format(t1-t0))
if undirected:
t0 = time()
G = G.make_undirected()
t1 = time()
logger.info('Made graph undirected in {}s'.format(t1-t0))
return G
def load_edgelist(file_, undirected=True):
G = Graph()
with open(file_) as f:
for l in f:
x, y = l.strip().split()[:2]
x = int(x)
y = int(y)
G[x].append(y)
if undirected:
G[y].append(x)
G.make_consistent()
return G
def load_matfile(file_, variable_name="network", undirected=True):
mat_varables = loadmat(file_)
mat_matrix = mat_varables[variable_name]
return from_numpy(mat_matrix, undirected)
def from_networkx(G_input, undirected=True):
G = Graph()
for idx, x in enumerate(G_input.nodes()):
for y in iterkeys(G_input[x]):
G[x].append(y)
if undirected:
G.make_undirected()
return G
def from_numpy(x, undirected=True):
G = Graph()
if issparse(x):
cx = x.tocoo()
for i,j,v in zip(cx.row, cx.col, cx.data):
G[i].append(j)
else:
raise Exception("Dense matrices not yet supported.")
if undirected:
G.make_undirected()
G.make_consistent()
return G
def from_adjlist(adjlist):
G = Graph()
for row in adjlist:
node = row[0]
neighbors = row[1:]
G[node] = list(sorted(set(neighbors)))
return G
def from_adjlist_unchecked(adjlist):
G = Graph()
for row in adjlist:
node = row[0]
neighbors = row[1:]
G[node] = neighbors
return G
至于skipgram,大家可以直接用gensim工具即可.
from gensim.models import Word2Vec
from gensim.models.word2vec import Vocab
logger = logging.getLogger("deepwalk")
class Skipgram(Word2Vec):
"""A subclass to allow more customization of the Word2Vec internals."""
def __init__(self, vocabulary_counts=None, **kwargs):
self.vocabulary_counts = None
kwargs["min_count"] = kwargs.get("min_count", 0)
kwargs["workers"] = kwargs.get("workers", cpu_count())
kwargs["size"] = kwargs.get("size", 128)
kwargs["sentences"] = kwargs.get("sentences", None)
kwargs["window"] = kwargs.get("window", 10)
kwargs["sg"] = 1
kwargs["hs"] = 1
if vocabulary_counts != None:
self.vocabulary_counts = vocabulary_counts
super(Skipgram, self).__init__(**kwargs)
应用
在推荐场景中,无论是推荐商品还是广告,用户和item其实都可以通过点击/转化/购买等行为构建二部图,在此二部图中进行随机游走,学习每个节点的向量,在特定场景,缺乏特征和标签的情况下,可以通过user2user或者item2iterm的方式,很好的泛化到其他的标签.GNN提取的向量也可以用于下游双塔召回模型或者排序模型.如果有社交网络,通过挖掘人与人直接的关系提取特征,供下游任务也是个不错的选择.当然大家也可以尝试在一些推荐比赛中用于丰富特征.
