說到GNN,各位煉丹師會想到哪些算法呢?不管想到哪些算法,我們真正用到過哪些呢?確實我們可能都看過GNN相關論文,但是還是缺乏實戰經驗的.特別是對于推薦系統而言,我們又該如何應用這些模型呢?下面我們就從DeepWalk這篇論文開始,先講原理,再講實戰,最后講應用.

GNN相關背景知識

GNN的本質,是要學習網絡中每個節點的表達的,這些潛在的表達對圖中每個節點的“社交”關系進行了編碼,把離散值的節點編碼成稠密向量,后續可用于分類回歸,或者作為下游任務的特征.Deepwalk充分利用了隨機游走提取的“句子”,去學習句子中每個單詞的表達.Deepwalk原文就提到了在數據稀疏的情況下可以把F1-scores提升10%,在一些實驗中,能夠用更少的訓練數據獲得了更好的效果.看下圖的例子:

Deepwalk

問題定義:

先把問題定義為給社交網絡中的每個節點進行分類,圖可以表達為G=<V,E>,V就是圖上所有節點,E是所有邊.有一部分有label的數據GL=(V,E,X,Y),X就是節點的特征,Y就是分類的label.在傳統機器學習算法中,我們都是直接學習(X,Y),并沒有充分利用節點間的依賴關系.Deepwalk可以捕捉圖上的拓撲關系,通過無監督方法學習每個節點的特征,學到的圖特征和標簽的分布是相互獨立的.

隨機游走:

選定一個根節點,“隨機”走出一條路徑,基于相鄰的節點必然相似,我們就可以用這種策略去挖掘網絡的社群信息.隨機游走很方便并行,可以同時提取一張圖上各個部分的信息.即使圖有小的改動,這些路徑也不需要重新計算.和word的出現頻率類似,通過隨機游走得到的節點訪問頻率都符合冪律分布,所以我們就可以用NLP相關方法對隨機游走結果做相似處理,如下圖所示:

所以在隨機游走后,我們只需要通過下公式,學習節點向量即可:

該公式就是skip-gram,通過某個節點學習它左右的節點.我們都知道skip-gram用于文本時的語料庫就是一個個句子,現在我們提取圖的句子.如下所示:

算法很簡單,把所有節點順序打亂(加速收斂),然后遍歷這些節點隨機游走出序列,再通過skipgram算法去擬合每個節點的向量.如此反復.注:這里的隨機是均勻分布去隨機.當然有些圖會有些“副產物”,比如用戶瀏覽網頁的順序,可以直接輸入到模型.

接下來我們看下deepwalks的核心代碼:

# 代碼來源 # phanein/deepwalk # Random walk with open(f, 'w') as fout:for walk in graph.build_deepwalk_corpus_iter(G=G, # 圖num_paths=num_paths, # 路徑數path_length=path_length, # 路徑長度alpha=alpha, #rand=rand): #fout.write(u"{}\n".format(u" ".join(v for v in walk)))class Graph(defaultdict):""" Efficient basic implementation of nx 這里我們看到, 該類繼承defaultdict, 圖其實可以簡單的表示為dict, key為節點,value為與之相連的節點 """ 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={}):# 提取子圖subgraph = Graph()for n in nodes:if n in self:subgraph[n] = [x for x in self[n] if x in nodes]return subgraphdef make_undirected(self):#因為是無向圖,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 selfdef 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 selfdef remove_self_loops(self):# 自已不會與自己有連接removed = 0t0 = time()for x in self:if x in self[x]: self[x].remove(x)removed += 1t1 = time()logger.info('remove_self_loops: removed {} loops in {}s'.format(removed, (t1-t0)))return selfdef check_self_loops(self):for x in self:for y in self[x]:if x == y:return Truereturn Falsedef has_edge(self, v1, v2):# 兩個節點是否有邊if v2 in self[v1] or v1 in self[v2]:return Truereturn Falsedef degree(self, nodes=None):# 節點的度數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):# 圖中邊的數量"Returns the number of nodes in the graph"return sum([self.degree(x) for x in self.keys()])/2def number_of_nodes(self):# 圖中結點數量"Returns the number of nodes in the graph"return self.order()# 核心代碼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 = selfif start:path = [start]else:# Sampling is uniform w.r.t V, and not w.r.t Epath = [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])) # 相鄰節點隨機選else:path.append(path[0]) # 有一定概率選擇回到起點else:breakreturn [str(node) for node in path]# TODO add build_walks in heredef build_deepwalk_corpus(G, num_paths, path_length, alpha=0,rand=random.Random(0)):walks = []nodes = list(G.nodes())# 這里和上面論文算法流程對應for cnt in range(num_paths): # 外循環,相當于要迭代多少epochrand.shuffle(nodes) # 打亂nodes順序,加速收斂for node in nodes: # 每個node都會產生一條路徑walks.append(G.random_walk(path_length, rand=rand, alpha=alpha, start=node))return walksdef build_deepwalk_corpus_iter(G, num_paths, path_length, alpha=0,rand=random.Random(0)):# 流式處理用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))) # How do you split a list into evenly sized chunks? 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 adjlistdef 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 adjlistdef load_adjacencylist(file_, undirected=False, chunksize=10000, unchecked=True):if unchecked:parse_func = parse_adjacencylist_uncheckedconvert_func = from_adjlist_uncheckedelse:parse_func = parse_adjacencylistconvert_func = from_adjlistadjlist = []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 Gdef 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 Gdef 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 Gdef from_adjlist(adjlist):G = Graph()for row in adjlist:node = row[0]neighbors = row[1:]G[node] = list(sorted(set(neighbors)))return Gdef from_adjlist_unchecked(adjlist):G = Graph()for row in adjlist:node = row[0]neighbors = row[1:]G[node] = neighborsreturn 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 Vocablogger = 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 = Nonekwargs["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"] = 1kwargs["hs"] = 1if vocabulary_counts != None:self.vocabulary_counts = vocabulary_countssuper(Skipgram, self).__init__(**kwargs)

應用

在推薦場景中,無論是推薦商品還是廣告,用戶和item其實都可以通過點擊/轉化/購買等行為構建二部圖,在此二部圖中進行隨機游走,學習每個節點的向量,在特定場景,缺乏特征和標簽的情況下,可以通過user2user或者item2iterm的方式,很好的泛化到其他的標簽.GNN提取的向量也可以用于下游雙塔召回模型或者排序模型.如果有社交網絡,通過挖掘人與人直接的關系提取特征,供下游任務也是個不錯的選擇.當然大家也可以嘗試在一些推薦比賽中用于豐富特征.

聽說GNN大有可為,從這篇開始學以致用

總結

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