Path finding algorithms

There are many algorithms for finding the shortest path between two points, but few are better known than Dijkstra’s algorithm and the A* algorithm.

Dijkstra’s algorithm

• 

Dijkstra’s algorithm is often described as being “shortest-path first”. This is a greedy approach that isn’t suitable for large graphs.

Source: wikimedia.org

A* search algorithm

• 

• 

A*, Weighted A*. Source: wikimedia.org

A* is a best-first search algorithm. In cases when it is available, it uses a heuristic to prioritize search. The resulting speed-up has made the A* search algorithm very popular.

Applying A* to word vectors

In my last post, I discussed how word2vec can be used to qualitatively fingerprint sets of items. Since word vectors can be thought of as spatial coordinates, then a shortest path of word vectors can be found between any two words.

After training on the IMDB Movie Reviews Dataset, this is the result:

animated -> carrying
Explored: 68, Frontier: 169, Cost: 3.356

animated
…scripted
…written
…played
…plays
…playing
…working
carrying

know -> tasty
Explored: 11166, Frontier: 2618, Cost: 7.393

know
…think
…thought
…felt
…feeling
…idea
…explanation
…answers
…food
…coffee
…dinner
…breakfast
…bread
tasty

tasty -> boxing
Explored: 461, Frontier: 1305, Cost: 4.298

tasty
…aesthetic
…artistic
…cinematic
…visual
…technical
…chess
boxing

threaten -> restore
Explored: 4820, Frontier: 2992, Cost: 6.216

threaten
…manages
…fails
…failed
…died
…killed
…kidnapped
…kidnapping
…manipulation
…drawing
…painting
restore

Code

Setup

The following is a snippet from Word segmentation in Python and Building a recommendation system using product embeddings.

name = 'reviews'
vocab_size = 12000
epochs = 100

if not os.path.isfile('{0}.model'.format(name)):
    spm.SentencePieceTrainer.Train('--input={0}.txt --model_prefix={0} --vocab_size={1} --split_by_whitespace=True'.format(name,vocab_size))

sp = spm.SentencePieceProcessor()
sp.load('{0}.model'.format(name))

if not os.path.isfile('./checkpoints/{0}-{1}.w2v'.format(name,epochs-1)):
    if not os.path.isfile('{0}_tokenized.tsv'.format(name)):
        with open('{0}_tokenized.tsv'.format(name),'w+') as f:
            for i,line in enumerate(open('{0}.txt'.format(name))):
                ids = sp.EncodeAsIds(line)
                if len(ids) > 10:
                    f.write('{0}\t{1}\n'.format(i,' '.join(str(x) for x in ids)))

    model = Doc2Vec(vector_size=300, window=8, min_count=3, negative=5, workers=16, epochs=1)

    documents = get_documents('{0}_tokenized.tsv'.format(name),name)
    model.build_vocab(documents)
    model = train_model(model,documents,name,epochs)

model = Doc2Vec.load('./checkpoints/{0}-{1}.w2v'.format(name,epochs-1))

A* search algorithm

Adapted from WikiClassify, a project that would later become the Chrome extension WikiPopularity.

import heapq

class elem_t:
    def __init__(self,value,parent=None,cost=None):
        self.value = value
        self.cost = cost
        self.column_offset = 0
        self.parent = parent

class PriorityQueue:
    def __init__(self):
        self._queue = []
        self._index = 0

    def push(self,item):
        heapq.heappush(self._queue, (item.cost,self._index,item) )
        self._index += 1

    def pop(self):
        index,item = heapq.heappop(self._queue)[1:]
        return item

    def length(self):
        return len(self._queue)

def get_transition_cost(word1,word2,doc2vec_model):
    return 1.0-float(doc2vec_model.similarity(word1,word2))

def a_star_search(start_word, end_word, doc2vec_model, branching_factor=60, weight=4.):

    cost_list = {start_word:0}

    frontier = PriorityQueue()
    start_elem = elem_t(start_word,parent=None,cost=get_transition_cost(start_word,end_word,doc2vec_model))
    frontier.push(start_elem)

    path_end = start_elem
    explored = []
    while True:

        if frontier.length() == 0:
            break

        current_node = frontier.pop()
        current_word = current_node.value
        explored.append(current_word)

        if current_word == end_word:
            path_end = current_node
            break

        neighbors = [x[0] for x in doc2vec_model.most_similar(current_word,topn=branching_factor) if x!=current_word]
        if neighbors == None:
            continue

        base_cost = cost_list[current_word]

        for neighbor_word in neighbors:
            if current_word == neighbor_word:
                continue
            cost = base_cost + get_transition_cost(current_word,neighbor_word,doc2vec_model)
            new_elem = elem_t(neighbor_word,parent=current_node,cost=cost)
            new_elem.column_offset = neighbors.index(neighbor_word)
            if (neighbor_word not in cost_list or cost<cost_list[neighbor_word]) and neighbor_word not in explored:
                cost_list[neighbor_word] = cost
                new_elem.cost = cost + weight*get_transition_cost(neighbor_word,end_word,doc2vec_model)
                frontier.push(new_elem)
        print("Explored: "+str(len(explored))+", Frontier: "+str(frontier.length())+", Cost: "+str(base_cost)[:5],end='\r')
    print('')
    path = [path_end.value]
    cur = path_end
    while cur:
        cur = cur.parent
        if cur:
            path.append(cur.value)
    return path[::-1]