一个视频：https://www.bilibili.com/video/BV1mb4y1y7EB/?spm_id_from=333.337.search-card.all.click&vd_source=7a1a0bc74158c6993c7355c5490fc600

这里有个视频，讲解得更加生动形象一些

总得来说，词袋模型(Bow, bag-of-words) 是最简单的 “文本 —> 矢量”(把文本转为矢量) 模型

二元分类和多元分类的两个例子放在末尾

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以下是 Claude3 的解释，我们慢慢看

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The bag-of-words model is a simplifying representation used in natural language processing (NLP). In this representation, a text (such as a sentence or a document) is represented as an unordered collection of words, disregarding grammar and word order.

bag-of-words 模型是 NLP领域 里的一个简化表示方法。在这种表示方法里，一个文本(比如一个句子或者是一个文档) 会被表示成一个乱序的单词集合，无视里面的语法和单词顺序。

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Here’s how it works:

1. A vocabulary of known words is created from the corpus of texts.
2. Each text is represented as a vector, with one dimension for each word in the vocabulary.
3. If a word appears in the text, its value in the vector is non-zero (typically 1 or a number representing frequency); otherwise, it is zero.

For example, if the vocabulary is [“hello”, “goodbye”, “computer”], then the sentence “hello hello computer” would be represented by the vector [2, 0, 1].

如下，是 bag-of-words 的工作方法：

1. 一堆已知单词的词汇表是从语料库里创建出来的
2. 每一个文本都可以使用一个向量表示，词汇表中的每一个单词都可以使用一个一维向量来表示
3. 如果一个单词在文本中出现，它在矢量中的值是 non-zero，否则就是 0。

举个例子，如果词汇表是 [“hello”, “goodbye”, “computer”]，那么这句 “hello hello computer” 就可以用矢量 [2, 0, 1] 表示

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The advantages of this model are its simplicity and the fact that it allows for straightforward application of techniques from fields like machine learning and information retrieval.

However, the bag-of-words model has several shortcomings:

1. It disregards word order and grammar, which can be very important in natural language.
2. It assumes that all words are equally important, ignoring semantics.
3. For large vocabularies, the resulting vector can be very high-dimensional and sparse.

Despite these limitations, the bag-of-words model can serve as a baseline for more advanced NLP techniques and may still have some uses in simple applications.

这个模型的优点是：很简单，并且它允许直接应用来自机器学习和信息检索等领域的技术。

然而，bag-of-words 模型也有几个缺点：

1. 它忽略了单词的顺序和语法结构,而这在自然语言中是非常重要的。 （单词向量无法展示单词顺序和语法结构）
2. 它假设所有单词同等重要,忽视了词义语义信息。 （假设所有单词同等重要）
3. 对于大型词汇表,生成的向量往往是非常高维且稀疏的。 （大型词汇表中，向量高维且稀疏）

尽管有这些限制，bag-of-words 模型仍然可以作为一些先进的 NLP技术的 baseline，并且在一些简单的应用中都是有用例的

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In modern NLP systems, more advanced techniques like word embeddings (e.g., Word2Vec, GloVe, BERT) are commonly used to capture richer semantic and syntactic information.

在现代NLP系统中,通常采用更先进的技术,如词嵌入(例如Word2Vec、GloVe、BERT)来捕获更丰富的语义和语法信息。

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二元分类和多元分类的两个例子放在末尾

二元分类：

多元分类：