GNN大有可为,从这篇开始学以致用

机器学习初学者

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2021-07-27 10:02

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 walkwith 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-pythondef 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 Word2Vecfrom 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.

往期精彩回顾




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