文章目录
- 1. Machine Translation 机器翻译
- 1.1. 学习目标
- 1.2. 概览
- 1.3. 向量变换
- 1.3.1. F范数
- 1.3.2. 梯度的计算
- 2. 哈希表 Hash tables
- 2.1. locality sensitive hashing
- 2.1.1. 如何判断向量在平面某一侧
- 2.2. Multiple Planes 多平面
- 2.2.1. 多平面的哈希值
- 2.2.2. 一些简单的python实现
- 3. K近邻 K nearest neighbor
- 4. Assignment
- 4.1. 老规矩 引用
- 4.2. 生成变换矩阵Generate embedding and transform matrices
- 4.3. 通过线性变换进行翻译
- 4.3.1. 计算LOSS
- 4.3.2. 计算LOSS的梯度
- 4.3.3. 通过梯度下降找到最优的R
- 4.3.4. 训练变换矩阵R
- 4.4. 测试翻译
- 4.4.1. K近邻
- 4.4.2. 计算accuracy
- 4.4.3. LSH和文档搜索
- 4.4.4. 查询tweets
- 4.4.5. 使用LSH查找最相似的tweet
- 4.4.6. 获取向量hash number
- 4.4.7. 建立hash table
- 4.4.8. 创建所有的hash table
- 4.4.9. Approximate K-NN
1. Machine Translation 机器翻译
1.1. 学习目标
- Transform Vector 向量变换
- “K nearest neightbor” K近邻
- Hash tables 哈希表
- Divide vector space into regions 划分向量
- Locality sensitive hashing 本地敏感哈希
- Approximated nearest neighbors 最近邻估计
1.2. 概览
基本思想为：首先将英语词语和法语词语都转换成向量表示，然后从英语到法语存在一种线性变换使其相互关联。
在翻译时，可以将一个英文单词通过变换变成一个在法语向量空间下的向量，然后找到和这个向量最接近的法语词，即为对应的翻译。
1.3. 向量变换
若想获得最优的矩阵R，应使得XR和Y的distance最小。
- 初始化R
- 在循环中
如果从随机矩阵作为起点，可以通过不断迭代来使其优化。首先通过损失函数对矩阵求导来计算梯度
然后通过减去梯度*学习率来更新矩阵R
1.3.1. F范数
Loss函数中的||·||F代表F范数
其表达式为
在python中可以通过以下方式计算F范数
A_squared = np.square(A)
A_Frobenious = np.sqrt(np.sum(sum(A_squared)))1.3.2. 梯度的计算
2. 哈希表 Hash tables
例：
哈希表可以看作是储存哈希函数结果的表
比如
def basic_hash_table(value_l,n_buckets):
def hash_function(value_l,n_buckets):
return int(value) % n_buckets
hash_table = {i:[] for i in range(n_buckets)}
for value in value_l:
hash_value = hash_function(value,n_buckets)
hash_table[hash_value].append(value)
return hash_table哈希表中就储存了键值所对应的哈希函数值。
在我们的学习资，希望能把相似的单词放到同一个bucket中
2.1. locality sensitive hashing
以圆点来表示向量，划分空间的虚线表示平面(现在是在二维平面里的“面”)
![在这里插入图片描述]() 可以看出灰色向量只在灰色线上方，蓝色向量也只在蓝色线同一侧。 这就相当于我们在划分bucket
分割的平面可以用法向量来表示。
在更高维空间也是如此。
2.1.1. 如何判断向量在平面某一侧
def side_of_plane(P,v):
dotproduct = np.dot(P,v.T)
sign_of_dot_product = np.sign(dotproduct)
sign_of_dot_product_scalar = np.asscalar(sign_of_dot_product)
return sign_of_dot_product_scalar通过投影的符号来判断
2.2. Multiple Planes 多平面
2.2.1. 多平面的哈希值
![在这里插入图片描述]() 通过对每一个平面计算其投影符号，正则为1，负则为2.
这样可以实现多个平面对应一个哈希值(二进制编码的意思嘛)
def hash_multiple_plane(P_l,v):
hash_value = 0
for i,P in enumerate(P_l):
sign = side_of_plane(P,v)
hash_i = i if sign >= 0 else 0
hash_value += 2**i * hash_i
return hash_value2.2.2. 一些简单的python实现
P = np.array([[1, 2]]) # Define a single plane. You may change the direction
# Get a new plane perpendicular to P. We use a rotation matrix
PT = np.dot([[0, 1], [-1, 0]], P.T).T
fig, ax1 = plt.subplots(figsize=(8, 8)) # Create a plot with custom size
plot_vectors([P], colors=['b'], axes=[2, 2], ax=ax1) # Plot the plane P as a vector
# Plot the plane P as a 2 vectors.
# We scale by 2 just to get the arrows outside the current box
plot_vectors([PT * 4, PT * -4], colors=['k', 'k'], axes=[4, 4], ax=ax1)
# Plot 20 random points.
for i in range(0, 20):
v1 = np.array(np.random.uniform(-4, 4, 2)) # Get a pair of random numbers between -4 and 4
side_of_plane = np.sign(np.dot(P, v1.T)) # Get the sign of the dot product with P
# Color the points depending on the sign of the result of np.dot(P, point.T)
if side_of_plane == 1:
ax1.plot([v1[0]], [v1[1]], 'bo') # Plot a blue point
else:
ax1.plot([v1[0]], [v1[1]], 'ro') # Plot a red point
plt.show()可以获得
3. K近邻 K nearest neighbor
我们的向量从英文空间变换到法文空间后，不一定恰好能落在某个单词向量上，如果发生这种情况需要找到最相似的一个向量。
算了算了这块实在是没讲啥东西，不记了不记了
4. Assignment
4.1. 老规矩 引用
import pdb
import pickle
import string
import time
import gensim
import matplotlib.pyplot as plt
import nltk
import numpy as np
import scipy
import sklearn
from gensim.models import KeyedVectors
from nltk.corpus import stopwords, twitter_samples
from nltk.tokenize import TweetTokenizer
from utils import (cosine_similarity, get_dict,
process_tweet)
from os import getcwd
# add folder, tmp2, from our local workspace containing pre-downloaded corpora files to nltk's data path
filePath = f"{getcwd()}/../tmp2/"
nltk.data.path.append(filePath)若需要下载数据
Google code archive word2vec[https://code.google.com/archive/p/word2vec/]
并解压
French embeddings[https://github.com/vjstark/crosslingual_text_classification]
在终端输入
curl -o ./wiki.multi.fr.vec https://dl.fbaipublicfiles.com/arrival/vectors/wiki.multi.fr.vec然后运行
# Use this code to download and process the full dataset on your local computer
from gensim.models import KeyedVectors
en_embeddings = KeyedVectors.load_word2vec_format('./GoogleNews-vectors-negative300.bin', binary = True)
fr_embeddings = KeyedVectors.load_word2vec_format('./wiki.multi.fr.vec')
# loading the english to french dictionaries
en_fr_train = get_dict('en-fr.train.txt')
print('The length of the english to french training dictionary is', len(en_fr_train))
en_fr_test = get_dict('en-fr.test.txt')
print('The length of the english to french test dictionary is', len(en_fr_train))
english_set = set(en_embeddings.vocab)
french_set = set(fr_embeddings.vocab)
en_embeddings_subset = {}
fr_embeddings_subset = {}
french_words = set(en_fr_train.values())
for en_word in en_fr_train.keys():
fr_word = en_fr_train[en_word]
if fr_word in french_set and en_word in english_set:
en_embeddings_subset[en_word] = en_embeddings[en_word]
fr_embeddings_subset[fr_word] = fr_embeddings[fr_word]
for en_word in en_fr_test.keys():
fr_word = en_fr_test[en_word]
if fr_word in french_set and en_word in english_set:
en_embeddings_subset[en_word] = en_embeddings[en_word]
fr_embeddings_subset[fr_word] = fr_embeddings[fr_word]
pickle.dump( en_embeddings_subset, open( "en_embeddings.p", "wb" ) )
pickle.dump( fr_embeddings_subset, open( "fr_embeddings.p", "wb" ) )- 然后导入数据
en_embeddings_subset = pickle.load(open("en_embeddings.p", "rb"))
fr_embeddings_subset = pickle.load(open("fr_embeddings.p", "rb"))
# loading the english to french dictionaries
en_fr_train = get_dict('en-fr.train.txt')
print('The length of the English to French training dictionary is', len(en_fr_train))
en_fr_test = get_dict('en-fr.test.txt')
print('The length of the English to French test dictionary is', len(en_fr_train))4.2. 生成变换矩阵Generate embedding and transform matrices
# UNQ_C1 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def get_matrices(en_fr, french_vecs, english_vecs):
"""
Input:
en_fr: English to French dictionary
french_vecs: French words to their corresponding word embeddings.
english_vecs: English words to their corresponding word embeddings.
Output:
X: a matrix where the columns are the English embeddings.
Y: a matrix where the columns correspong to the French embeddings.
R: the projection matrix that minimizes the F norm ||X R -Y||^2.
"""
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# X_l and Y_l are lists of the english and french word embeddings
X_l = list()
Y_l = list()
# get the english words (the keys in the dictionary) and store in a set()
english_set = set(english_vecs.keys())
# get the french words (keys in the dictionary) and store in a set()
french_set = set(french_vecs.keys())
# store the french words that are part of the english-french dictionary (these are the values of the dictionary)
french_words = set(en_fr.values())
# loop through all english, french word pairs in the english french dictionary
for en_word, fr_word in en_fr.items():
# check that the french word has an embedding and that the english word has an embedding
if fr_word in french_set and en_word in english_set:
# get the english embedding
en_vec = english_vecs[en_word]
# get the french embedding
fr_vec = french_vecs[fr_word]
# add the english embedding to the list
X_l.append(en_vec)
# add the french embedding to the list
Y_l.append(fr_vec)
# stack the vectors of X_l into a matrix X
X = np.array(X_l)
# stack the vectors of Y_l into a matrix Y
Y = np.array(Y_l)
### END CODE HERE ###
return X, Y4.3. 通过线性变换进行翻译
4.3.1. 计算LOSS
# UNQ_C3 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def compute_loss(X, Y, R):
'''
Inputs:
X: a matrix of dimension (m,n) where the columns are the English embeddings.
Y: a matrix of dimension (m,n) where the columns correspong to the French embeddings.
R: a matrix of dimension (n,n) - transformation matrix from English to French vector space embeddings.
Outputs:
L: a matrix of dimension (m,n) - the value of the loss function for given X, Y and R.
'''
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# m is the number of rows in X
m = len(X)
# diff is XR - Y
diff = np.dot(X,R) - Y
# diff_squared is the element-wise square of the difference
diff_squared = np.square(diff)
# sum_diff_squared is the sum of the squared elements
sum_diff_squared = sum(sum(diff_squared))
# loss i the sum_diff_squard divided by the number of examples (m)
loss = sum_diff_squared/m
### END CODE HERE ###
return loss4.3.2. 计算LOSS的梯度
# UNQ_C4 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def compute_gradient(X, Y, R):
'''
Inputs:
X: a matrix of dimension (m,n) where the columns are the English embeddings.
Y: a matrix of dimension (m,n) where the columns correspong to the French embeddings.
R: a matrix of dimension (n,n) - transformation matrix from English to French vector space embeddings.
Outputs:
g: a matrix of dimension (n,n) - gradient of the loss function L for given X, Y and R.
'''
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# m is the number of rows in X
m = len(X)
# gradient is X^T(XR - Y) * 2/m
gradient = 2/m* (np.dot(X.transpose(), np.dot(X,R)-Y ))
### END CODE HERE ###
return gradient4.3.3. 通过梯度下降找到最优的R
# UNQ_C5 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def align_embeddings(X, Y, train_steps=100, learning_rate=0.0003):
'''
Inputs:
X: a matrix of dimension (m,n) where the columns are the English embeddings.
Y: a matrix of dimension (m,n) where the columns correspong to the French embeddings.
train_steps: positive int - describes how many steps will gradient descent algorithm do.
learning_rate: positive float - describes how big steps will gradient descent algorithm do.
Outputs:
R: a matrix of dimension (n,n) - the projection matrix that minimizes the F norm ||X R -Y||^2
'''
np.random.seed(129)
# the number of columns in X is the number of dimensions for a word vector (e.g. 300)
# R is a square matrix with length equal to the number of dimensions in th word embedding
R = np.random.rand(X.shape[1], X.shape[1])
for i in range(train_steps):
if i % 25 == 0:
print("loss at iteration ",i," is:", compute_loss(X, Y, R))
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# use the function that you defined to compute the gradient
gradient = compute_gradient(X, Y, R)
# update R by subtracting the learning rate times gradient
R -= learning_rate * gradient
### END CODE HERE ###
return R验证有
# UNQ_C6 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
# Testing your implementation.
np.random.seed(129)
m = 10
n = 5
X = np.random.rand(m, n)
Y = np.random.rand(m, n) * .1
R = align_embeddings(X, Y)4.3.4. 训练变换矩阵R
# UNQ_C7 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
R_train = align_embeddings(X_train, Y_train, train_steps=400, learning_rate=0.8)这个在jupyterbook里跑了蛮久的
4.4. 测试翻译
4.4.1. K近邻
# UNQ_C8 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def nearest_neighbor(v, candidates, k=1):
"""
Input:
- v, the vector you are going find the nearest neighbor for
- candidates: a set of vectors where we will find the neighbors
- k: top k nearest neighbors to find
Output:
- k_idx: the indices of the top k closest vectors in sorted form
"""
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
similarity_l = []
# for each candidate vector...
for row in candidates:
# get the cosine similarity
cos_similarity = np.dot(row,v)/(np.linalg.norm(row)*np.linalg.norm(v))
# append the similarity to the list
similarity_l.append(cos_similarity)
# sort the similarity list and get the indices of the sorted list
sorted_ids = np.argsort(similarity_l)
# get the indices of the k most similar candidate vectors
k_idx = sorted_ids[k-1:]
### END CODE HERE ###
return k_idx可进行简单测试
# UNQ_C9 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
# Test your implementation:
v = np.array([1, 0, 1])
candidates = np.array([[1, 0, 5], [-2, 5, 3], [2, 0, 1], [6, -9, 5], [9, 9, 9]])
print(candidates[nearest_neighbor(v, candidates, 3)])4.4.2. 计算accuracy
# UNQ_C10 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def test_vocabulary(X, Y, R):
'''
Input:
X: a matrix where the columns are the English embeddings.
Y: a matrix where the columns correspong to the French embeddings.
R: the transform matrix which translates word embeddings from
English to French word vector space.
Output:
accuracy: for the English to French capitals
'''
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# The prediction is X times R
pred = np.dot(X,R)
# initialize the number correct to zero
num_correct = 0
# loop through each row in pred (each transformed embedding)
for i in range(len(pred)):
# get the index of the nearest neighbor of pred at row 'i'; also pass in the candidates in Y
pred_idx = nearest_neighbor(X[i], Y, k=1)[-1]
# if the index of the nearest neighbor equals the row of i... \
if pred_idx == i:
# increment the number correct by 1.
num_correct += 1
# accuracy is the number correct divided by the number of rows in 'pred' (also number of rows in X)
accuracy = num_correct/len(X)
### END CODE HERE ###
return accuracy4.4.3. LSH和文档搜索
获取数据
# get the positive and negative tweets
all_positive_tweets = twitter_samples.strings('positive_tweets.json')
all_negative_tweets = twitter_samples.strings('negative_tweets.json')
all_tweets = all_positive_tweets + all_negative_tweets文档向量
# UNQ_C12 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def get_document_embedding(tweet, en_embeddings):
'''
Input:
- tweet: a string
- en_embeddings: a dictionary of word embeddings
Output:
- doc_embedding: sum of all word embeddings in the tweet
'''
doc_embedding = np.zeros(300)
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# process the document into a list of words (process the tweet)
processed_doc = process_tweet(tweet)
for word in processed_doc:
# add the word embedding to the running total for the document embedding
if word in en_embeddings.keys():
doc_embedding += en_embeddings[word]
### END CODE HERE ###
return doc_embedding
# UNQ_C13 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
# testing your function
custom_tweet = "RT @Twitter @chapagain Hello There! Have a great day. :) #good #morning http://chapagain.com.np"
tweet_embedding = get_document_embedding(custom_tweet, en_embeddings_subset)
tweet_embedding[-5:]获得文档向量
# UNQ_C14 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def get_document_vecs(all_docs, en_embeddings):
'''
Input:
- all_docs: list of strings - all tweets in our dataset.
- en_embeddings: dictionary with words as the keys and their embeddings as the values.
Output:
- document_vec_matrix: matrix of tweet embeddings.
- ind2Doc_dict: dictionary with indices of tweets in vecs as keys and their embeddings as the values.
'''
# the dictionary's key is an index (integer) that identifies a specific tweet
# the value is the document embedding for that document
ind2Doc_dict = {}
# this is list that will store the document vectors
document_vec_l = []
for i, doc in enumerate(all_docs):
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# get the document embedding of the tweet
doc_embedding = get_document_embedding(doc, en_embeddings)
# save the document embedding into the ind2Tweet dictionary at index i
ind2Doc_dict[i] = doc_embedding
# append the document embedding to the list of document vectors
document_vec_l.append(doc_embedding)
### END CODE HERE ###
# convert the list of document vectors into a 2D array (each row is a document vector)
document_vec_matrix = np.vstack(document_vec_l)
return document_vec_matrix, ind2Doc_dict4.4.4. 查询tweets
my_tweet = 'i am sad'
process_tweet(my_tweet)
tweet_embedding = get_document_embedding(my_tweet, en_embeddings_subset)
# UNQ_C16 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
# this gives you a similar tweet as your input.
# this implementation is vectorized...
idx = np.argmax(cosine_similarity(document_vecs, tweet_embedding))
print(all_tweets[idx])4.4.5. 使用LSH查找最相似的tweet
N_VECS = len(all_tweets) # This many vectors.
N_DIMS = len(ind2Tweet[1]) # Vector dimensionality.
print(f"Number of vectors is {N_VECS} and each has {N_DIMS} dimensions.")
# The number of planes. We use log2(256) to have ~16 vectors/bucket.
N_PLANES = 10
# Number of times to repeat the hashing to improve the search.
N_UNIVERSES = 254.4.6. 获取向量hash number
np.random.seed(0)
planes_l = [np.random.normal(size=(N_DIMS, N_PLANES))
for _ in range(N_UNIVERSES)]计算向量的hash value
# UNQ_C17 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
def hash_value_of_vector(v, planes):
"""Create a hash for a vector; hash_id says which random hash to use.
Input:
- v: vector of tweet. It's dimension is (1, N_DIMS)
- planes: matrix of dimension (N_DIMS, N_PLANES) - the set of planes that divide up the region
Output:
- res: a number which is used as a hash for your vector
"""
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# for the set of planes,
# calculate the dot product between the vector and the matrix containing the planes
# remember that planes has shape (300, 10)
# The dot product will have the shape (1,10)
dot_product = np.dot(v,planes)
# get the sign of the dot product (1,10) shaped vector
sign_of_dot_product = np.sign(dot_product)
sign_of_dot_product = np.squeeze(sign_of_dot_product)
# set h to be false (eqivalent to 0 when used in operations) if the sign is negative,
# and true (equivalent to 1) if the sign is positive (1,10) shaped vector
h = [0 if i<0 else 1 for i in sign_of_dot_product]
# remove extra un-used dimensions (convert this from a 2D to a 1D array)
h = np.squeeze(h)
# initialize the hash value to 0
hash_value = 0
n_planes = planes.shape[1]
for i in range(n_planes):
# increment the hash value by 2^i * h_i
hash_value += 2**i*h[i]
### END CODE HERE ###
# cast hash_value as an integer
hash_value = int(hash_value)
return hash_value
# UNQ_C18 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
np.random.seed(0)
idx = 0
planes = planes_l[idx] # get one 'universe' of planes to test the function
vec = np.random.rand(1, 300)
print(f" The hash value for this vector,",
f"and the set of planes at index {idx},",
f"is {hash_value_of_vector(vec, planes)}")4.4.7. 建立hash table
# UNQ_C19 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# This is the code used to create a hash table: feel free to read over it
def make_hash_table(vecs, planes):
"""
Input:
- vecs: list of vectors to be hashed.
- planes: the matrix of planes in a single "universe", with shape (embedding dimensions, number of planes).
Output:
- hash_table: dictionary - keys are hashes, values are lists of vectors (hash buckets)
- id_table: dictionary - keys are hashes, values are list of vectors id's
(it's used to know which tweet corresponds to the hashed vector)
"""
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# number of planes is the number of columns in the planes matrix
num_of_planes = len(planes[0])
# number of buckets is 2^(number of planes)
num_buckets = 2**num_of_planes
# create the hash table as a dictionary.
# Keys are integers (0,1,2.. number of buckets)
# Values are empty lists
hash_table = {i:[] for i in range(num_buckets)}
# create the id table as a dictionary.
# Keys are integers (0,1,2... number of buckets)
# Values are empty lists
id_table = {i:[] for i in range(num_buckets)}
# for each vector in 'vecs'
for i, v in enumerate(vecs):
# calculate the hash value for the vector
h = hash_value_of_vector(v, planes)
# store the vector into hash_table at key h,
# by appending the vector v to the list at key h
hash_table[h].append(v)
# store the vector's index 'i' (each document is given a unique integer 0,1,2...)
# the key is the h, and the 'i' is appended to the list at key h
id_table[h].append(i)
### END CODE HERE ###
return hash_table, id_table
### 验证
# UNQ_C20 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
np.random.seed(0)
planes = planes_l[0] # get one 'universe' of planes to test the function
vec = np.random.rand(1, 300)
tmp_hash_table, tmp_id_table = make_hash_table(document_vecs, planes)
print(f"The hash table at key 0 has {len(tmp_hash_table[0])} document vectors")
print(f"The id table at key 0 has {len(tmp_id_table[0])}")
print(f"The first 5 document indices stored at key 0 of are {tmp_id_table[0][0:5]}")4.4.8. 创建所有的hash table
# Creating the hashtables
hash_tables = []
id_tables = []
for universe_id in range(N_UNIVERSES): # there are 25 hashes
print('working on hash universe #:', universe_id)
planes = planes_l[universe_id]
hash_table, id_table = make_hash_table(document_vecs, planes)
hash_tables.append(hash_table)
id_tables.append(id_table)4.4.9. Approximate K-NN
# UNQ_C21 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# This is the code used to do the fast nearest neighbor search. Feel free to go over it
def approximate_knn(doc_id, v, planes_l, k=1, num_universes_to_use=N_UNIVERSES):
"""Search for k-NN using hashes."""
assert num_universes_to_use <= N_UNIVERSES
# Vectors that will be checked as possible nearest neighbor
vecs_to_consider_l = list()
# list of document IDs
ids_to_consider_l = list()
# create a set for ids to consider, for faster checking if a document ID already exists in the set
ids_to_consider_set = set()
# loop through the universes of planes
for universe_id in range(num_universes_to_use):
# get the set of planes from the planes_l list, for this particular universe_id
planes = planes_l[universe_id]
# get the hash value of the vector for this set of planes
hash_value = hash_value_of_vector(v, planes)
# get the hash table for this particular universe_id
hash_table = hash_tables[universe_id]
# get the list of document vectors for this hash table, where the key is the hash_value
document_vectors_l = hash_table[hash_value]
# get the id_table for this particular universe_id
id_table = id_tables[universe_id]
# get the subset of documents to consider as nearest neighbors from this id_table dictionary
new_ids_to_consider = id_table[hash_value]
### START CODE HERE (REPLACE INSTANCES OF 'None' with your code) ###
# remove the id of the document that we're searching
if doc_id in new_ids_to_consider:
new_ids_to_consider.remove(doc_id)
print(f"removed doc_id {doc_id} of input vector from new_ids_to_search")
# loop through the subset of document vectors to consider
for i, new_id in enumerate(new_ids_to_consider):
# if the document ID is not yet in the set ids_to_consider...
if new_id not in ids_to_consider_set:
# access document_vectors_l list at index i to get the embedding
# then append it to the list of vectors to consider as possible nearest neighbors
document_vector_at_i = document_vectors_l[i]
vecs_to_consider_l.append(document_vector_at_i)
# append the new_id (the index for the document) to the list of ids to consider
ids_to_consider_l.append(new_id)
# also add the new_id to the set of ids to consider
# (use this to check if new_id is not already in the IDs to consider)
ids_to_consider_set.add(new_id)
### END CODE HERE ###
# Now run k-NN on the smaller set of vecs-to-consider.
print("Fast considering %d vecs" % len(vecs_to_consider_l))
# convert the vecs to consider set to a list, then to a numpy array
vecs_to_consider_arr = np.array(vecs_to_consider_l)
# call nearest neighbors on the reduced list of candidate vectors
nearest_neighbor_idx_l = nearest_neighbor(v, vecs_to_consider_arr, k=k)
# Use the nearest neighbor index list as indices into the ids to consider
# create a list of nearest neighbors by the document ids
nearest_neighbor_ids = [ids_to_consider_l[idx]
for idx in nearest_neighbor_idx_l]
return nearest_neighbor_ids测试代码
#document_vecs, ind2Tweet
doc_id = 0
doc_to_search = all_tweets[doc_id]
vec_to_search = document_vecs[doc_id]
# UNQ_C22 (UNIQUE CELL IDENTIFIER, DO NOT EDIT)
# You do not have to input any code in this cell, but it is relevant to grading, so please do not change anything
# Sample
nearest_neighbor_ids = approximate_knn(
doc_id, vec_to_search, planes_l, k=3, num_universes_to_use=5)
print(f"Nearest neighbors for document {doc_id}")
print(f"Document contents: {doc_to_search}")
print("")
for neighbor_id in nearest_neighbor_ids:
print(f"Nearest neighbor at document id {neighbor_id}")
print(f"document contents: {all_tweets[neighbor_id]}")
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