# 2.4 嵌入矩阵（Embedding Matrix）

当应用算法来学习词嵌入时，实际上是学习一个**嵌入矩阵**

假设某个词汇库包含了10000个单词，每个单词包含的特征维度为300，那么表征所有单词的**embedding matrix**维度为300 x 10000，用$$E$$来表示。某单词$$w$$的one-hot向量表示为$$O\_w$$，维度为10000 x 1

[![](https://github.com/fengdu78/deeplearning_ai_books/raw/master/images/ad1c7b1e85d39f56756c28787ccef892.png)](https://github.com/fengdu78/deeplearning_ai_books/blob/master/images/ad1c7b1e85d39f56756c28787ccef892.png)

则该单词的嵌入向量(embedding vector)表达式为：

$$
e\_w=E\cdot O\_w
$$

只要知道了embedding matrix$$E$$，就能计算出所有单词的embedding vector $$e\_w$$

不过上述这种矩阵乘积运算$$E\cdot O\_w$$效率并不高，矩阵维度很大，且$$O\_w$$大部分元素为零。通常做法是直接从$$E$$中选取第$$w$$列作为$$e\_w$$


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