diff --git a/src/posts/embedding-benchmark.md b/src/posts/embedding-benchmark.md
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+---
+date: 2025-07-05
+category:
+  - technical
+tag:
+  - AI/ML
+---
+# Text Embedding Benchmark for Recommender Systems
+
+Embedding models encode multimodal information such as images and text into high-dimensional vectors, enabling the calculation of relationships between multimodal information by measuring the distance between embedding vectors in online services like search engines and recommender systems. Text embeddings are the most widely used. Major AI service providers offer text embedding APIs to their users, and there are also many open-source text embedding models available for self-hosting. The current mainstream evaluation standard for text embedding models is [MTEB](https://github.com/embeddings-benchmark/mteb). However, [MTEB](https://github.com/embeddings-benchmark/mteb) does not assess the capabilities of text embedding models in recommender systems, and this post will attempt to evaluate the performance of text embedding models in recommender systems.
+
+## Measurement
+
+Embedding vectors in recommender systems are typically used for similar or related recommendations, with the goal that the distance between embedding vectors accurately reflects the similarity or relevance between items. The de facto relevance or similarity between items does not exist, but in recommender systems, the overlap of users between items, denoted as $s_{ij}$, can be used as an approximate measure of similarity or relevance.
+
+$$
+s_{ij} = \frac{|U_i \cap U_j|}{|U_i \cup U_j|}
+$$
+
+Here, $U_i$ and $U_j$ represent the user sets for items $i$ and $j$, respectively. A higher $s_{ij}$ value indicates greater user overlap between items $i$ and $j$. The distance between embedding vectors can be calculated using Euclidean distance:
+
+$$
+d_{ij} = ||\textbf{v}_i - \textbf{v}_j||
+$$
+
+Here, $\textbf{v}_i$ and $\textbf{v}_j$ represent the embedding vectors for items $i$ and $j$, respectively. To evaluate how well the distance between embedding vectors reflects the similarity or relevance between items, we can use Top-K recall ($Recall@K$). Top-K recall measures the proportion of items among the $K$ items with the smallest embedding vector distance from item $i$ that also appear in the list of $K$ items with the highest user overlap with item $i$. Higher Top-K recall indicates stronger capability of embedding vectors to recommend similar or relevant items.
+
+The dataset used in the experiment is the [MovieLens 1M](https://grouplens.org/datasets/movielens/1m/) dataset, which contains 1 million user ratings for movies. We convert the synopsis of each movie into embedding vectors using a text embedding model. We then calculate the Top-K recall for each movie and take the average of all movies' Top-K recall as the performance measurement for the model in recommender systems.
+
+## Text Embedding Models
+
+For open-source models, we selected the top three models by download count on Ollama:
+
+- [nomic-embed-text](https://ollama.com/library/nomic-embed-text)
+- [mxbai-embed-large](https://ollama.com/library/mxbai-embed-large)
+- [bge-m3](https://ollama.com/library/bge-m3)
+
+For commercial models, we chose the strongest text embedding models from Alibaba Cloud and OpenAI:
+
+- [text-embedding-v4](https://bailian.console.aliyun.com/?spm=5176.29597918.J_SEsSjsNv72yRuRFS2VknO.2.52007ca0kyUn9Q&tab=api#/api/?type=model&url=https%3A%2F%2Fhelp.aliyun.com%2Fdocument_detail%2F2712515.html) (Alibaba Cloud) supports 8 dimensions and over 100 major languages as well as programming languages.
+- [text-embedding-3-large](https://openai.com/index/new-embedding-models-and-api-updates/) (OpenAI) also supports multiple dimensions and languages.
+
+::: note
+
+Testing commercial models incurs costs, and to control expenses, we did not test models from additional service providers. We have open-sourced the [testing script](https://github.com/gorse-cloud/embedding4rec) and welcome to run it with other models.
+
+:::
+
+## Results  
+
+::: echarts Text Embedding Benchmark for Recommender Systems
+
+```json
+{
+  "legend": {
+    "data": ["text-embedding-v4", "text-embedding-3-large", "nomic-embed-text", "mxbai-embed-large", "bge-m3"]
+  },
+  "xAxis": {
+    "name": "Dimension",
+    "data": [64, 128, 256, 512, 768, 1024, 2048, 3072]
+  },
+  "yAxis": {
+    "name": "Recall@100",
+    "type": "value",
+    "min": 0.1
+  },
+  "tooltip": {
+    "trigger": "item",
+    "formatter": "{c}"
+  },
+  "series": [
+    {
+      "name": "text-embedding-v4",
+      "data": [0.11969, 0.13873, 0.15280, 0.1627, 0.16674, 0.16946, 0.17262],
+      "type": "line",
+      "smooth": true
+    },
+    {
+      "name": "text-embedding-3-large",
+      "data": [0.11272, 0.13769, 0.15086, 0.16362, 0.16610, 0.17026, 0.17241, 0.17395],
+      "type": "line",
+      "smooth": true
+    },
+    {
+      "name": "nomic-embed-text",
+      "data": [null, null, null, null, 0.15161],
+      "type": "line"
+    },
+    {
+      "name": "mxbai-embed-large",
+      "data": [null, null, null, null, null, 0.16595],
+      "type": "line"
+    },
+    {
+      "name": "bge-m3",
+      "data": [null, null, null, null, null, 0.11492],
+      "type": "line"
+    }
+  ]
+}
+```
+
+:::
+
+Based on the results, the following conclusions can be drawn:  
+
+1. Under the same dimension, commercial models such as [text-embedding-v4](https://bailian.console.aliyun.com/?spm=5176.29597918.J_SEsSjsNv72yRuRFS2VknO.2.52007ca0kyUn9Q&tab=api#/api/?type=model&url=https%3A%2F%2Fhelp.aliyun.com%2Fdocument_detail%2F2712515.html) and [text-embedding-3-large](https://openai.com/index/new-embedding-models-and-api-updates/) generally outperform open-source models, while the differences between commercial models are minimal.  
+2. Among open-source models, [mxbai-embed-large](https://ollama.com/library/mxbai-embed-large) performs the best and can be the preferred choice for self-hosting.
+3. Dimensionality significantly impacts model performance. As the dimension increases, the Top-K recall of the models generally improves, but the rate of improvement gradually diminishes. It is necessary to balance recommendation precision with computational and storage costs to select an appropriate dimension.  
+
+::: tip  
+
+Unless there are strict computational or storage resource limits, it is recommended to use vector lengths of 512 or higher to achieve better recommendation precision.  
+
+:::  
+
+In addition to quantitative comparisons, we can also intuitively evaluate model performance through recommendation results. Below are lists of similar movies recommended for ["Vertigo"](https://www.imdb.com/title/tt0052357/) using embeddings of two different dimensions from [text-embedding-v4](https://bailian.console.aliyun.com/?spm=5176.29597918.J_SEsSjsNv72yRuRFS2VknO.2.52007ca0kyUn9Q&tab=api#/api/?type=model&url=https%3A%2F%2Fhelp.aliyun.com%2Fdocument_detail%2F2712515.html):  
+
+::: tabs
+
+@tab 2048
+
+| Movie                                     | Year | Director         | Genre                         |
+|-------------------------------------------|------|------------------|-------------------------------|
+| Rear Window                               | 1954 | Alfred Hitchcock | Suspenseful Thriller          |
+| Spellbound                                | 1945 | Alfred Hitchcock | Psychological Thriller        |
+| Psycho                                    | 1960 | Alfred Hitchcock | Psychological Thriller/Horror |
+| North by Northwest                        | 1959 | Alfred Hitchcock | Suspense Thriller             |
+| Stage Fright                              | 1950 | Alfred Hitchcock | Mystery Thriller              |
+| Dial M for Murder                         | 1954 | Alfred Hitchcock | Mystery Thriller              |
+| The Spiral Staircase                      | 1946 | Robert Siodmak   | Psychological Thriller/Noir   |
+| The Hitch-Hiker                           | 1953 | Ida Lupino       | Noir Thriller                 |
+| Shadow of a Doubt                         | 1943 | Alfred Hitchcock | Suspense Thriller             |
+| Woman on the Verge of a Nervous Breakdown | 1988 | Pedro Almodóvar  | Dark Comedy/Drama             |
+
+@tab 64
+
+| Movie                                     | Year | Director         | Genre                  |
+|-------------------------------------------|------|------------------|------------------------|
+| Pi                                        | 1998 | Darren Aronofsky | Psychological Thriller |
+| Silent Fall                               | 1994 | Bruce Beresford  | Psychological Thriller |
+| Woman on the Verge of a Nervous Breakdown | 1988 | Pedro Almodóvar  | Dark Comedy/Drama      |
+| Crash                                     | 1996 | David Cronenberg | Psychological Drama    |
+| Eyes Wide Shut                            | 1999 | Stanley Kubrick  | Drama/Thriller         |
+| Psycho                                    | 1960 | Alfred Hitchcock | Psychological Horror   |
+| Windows                                   | 1980 | Herb Freed       | Psychological Thriller |
+| The Morning After                         | 1986 | Sidney Lumet     | Suspense Drama         |
+| North by Northwest                        | 1959 | Alfred Hitchcock | Suspense Thriller      |
+| Peeping Tom                               | 1960 | Michael Powell   | Psychological Horror   |
+
+:::
+
+For users who have just watched *Vertigo*, the movies recommended by the 2048-dimensional embedding vectors exhibit higher relevance and similarity to *Vertigo*.
+
+## Conclusion  
+
+This post evaluates the performance of text embedding models in recommender systems. The results indicate that commercial models generally outperform open-source models, with [mxbai-embed-large](https://ollama.com/library/mxbai-embed-large) standing out among open-source models. Dimensionality significantly affects model performance, and it is recommended to use vector lengths of 512 or higher for better recommendation results.
diff --git a/src/zh/posts/embedding-benchmark.md b/src/zh/posts/embedding-benchmark.md
new file mode 100644
index 0000000..2d1c5ad
--- /dev/null
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+---
+icon: zhinengsuanfa
+date: 2025-07-05
+category:
+  - 技术分享
+tag:
+  - 机器学习
+---
+# 推荐场景下文本嵌入模型性能对比
+
+向量嵌入技术可以将图片、文字等信息转换为高维向量，从而能够在搜素推荐等场景下，通过计算向量之间的距离来计算图片、文本等原始内容之间的相关性。其中本文嵌入用到最多，市面上主要的AI服务商都会为他们的用户提供本文嵌入API，另外也有很多开源文本嵌入模型可供自行部署使用。目前主流的文本嵌入模型的评估标准为[MTEB](https://github.com/embeddings-benchmark/mteb)，但是[MTEB](https://github.com/embeddings-benchmark/mteb)并没有评估文本嵌入模型在推荐系统中的能力，而本文将尝试评估文本嵌入模型在推荐场景下的表现。
+
+## 实验指标
+
+嵌入向量在推荐系统中通常用于相似推荐或者相关推荐，希望嵌入向量之间的距离能够很好地表达推荐物料之前的相似性和相关性。物料之间的相关性和相似度实际上不存在标准答案，在推荐系统中可以使用物料之间用户的重叠程度$s_{ij}$来近似地衡量物料之间的相似度或者相关性。
+
+$$
+s_{ij} = \frac{|U_i \cap U_j|}{|U_i \cup U_j|}
+$$
+
+其中$U_i$和$U_j$分别表示物料$i$和$j$的用户集合，$s_{ij}$的值越大，表示物料$i$和$j$之间的用户重叠度越高。而向量之间的距离可以使用欧式距离计算：
+
+$$
+d_{ij} = ||\textbf{v}_i - \textbf{v}_j||
+$$
+
+其中$\textbf{v}_i$和$\textbf{v}_j$分别表示物料$i$和$j$的嵌入向量。为了衡量嵌入向量之间的距离反馈物料相似度或者相关度的能力，我们可以使用Top-K准确率（$Recall@K$），Top-K准确率表示在与物料$i$的向量距离最小的$K$个物料中，有多少比例的物料也在与物料$i$用户重合度最高的$K$个物料列表中。Top-K准确率越高，意味着嵌入向量推荐相似或者相关物料的能力越强。
+
+实验使用的数据集为[MovieLens 1M](https://grouplens.org/datasets/movielens/1m/)数据集，包含100万条用户对电影的评分数据。我们将每个电影的简介作为文本内容，使用文本嵌入模型将其转换为向量。然后计算每个电影上的Top-K准确率，最后对所有电影的Top-K准确率取平均值，作为模型在推荐场景下的性能指标。
+
+## 文本嵌入模型
+
+开源模型我们选择了Ollama下载量前三的模型，它们分别是：
+
+- [nomic-embed-text](https://ollama.com/library/nomic-embed-text)
+- [mxbai-embed-large](https://ollama.com/library/mxbai-embed-large)
+- [bge-m3](https://ollama.com/library/bge-m3)
+
+商业模型我们选择了阿里云和OpneAI各自的最强文本嵌入模型：
+
+- [text-embedding-v4](https://bailian.console.aliyun.com/?spm=5176.29597918.J_SEsSjsNv72yRuRFS2VknO.2.52007ca0kyUn9Q&tab=api#/api/?type=model&url=https%3A%2F%2Fhelp.aliyun.com%2Fdocument_detail%2F2712515.html)（阿里云）支持8种向量维度，支持100+主流语种及多种编程语言
+- [text-embedding-3-large](https://openai.com/index/new-embedding-models-and-api-updates/)（OpenAI）同样支持多种向量维度和多种语言
+
+::: note
+
+测试商业模型他需要花费一定的费用，为了控制成本，我们没有测试来自更多服务商的模型。我们开源了[测试脚本](https://github.com/gorse-cloud/embedding4rec)，欢迎大家在自己的环境中运行测试脚本来获取更多模型的性能数据。
+
+:::
+
+## 实验结果
+
+
+::: echarts 推荐场景下文本嵌入模型性能对比
+
+```json
+{
+  "legend": {
+    "data": ["text-embedding-v4", "text-embedding-3-large", "nomic-embed-text", "mxbai-embed-large", "bge-m3"]
+  },
+  "xAxis": {
+    "name": "向量长度",
+    "data": [64, 128, 256, 512, 768, 1024, 2048, 3072]
+  },
+  "yAxis": {
+    "name": "准确率@100",
+    "type": "value",
+    "min": 0.1
+  },
+  "tooltip": {
+    "trigger": "item",
+    "formatter": "{c}"
+  },
+  "series": [
+    {
+      "name": "text-embedding-v4",
+      "data": [0.11969, 0.13873, 0.15280, 0.1627, 0.16674, 0.16946, 0.17262],
+      "type": "line",
+      "smooth": true
+    },
+    {
+      "name": "text-embedding-3-large",
+      "data": [0.11272, 0.13769, 0.15086, 0.16362, 0.16610, 0.17026, 0.17241, 0.17395],
+      "type": "line",
+      "smooth": true
+    },
+    {
+      "name": "nomic-embed-text",
+      "data": [null, null, null, null, 0.15161],
+      "type": "line"
+    },
+    {
+      "name": "mxbai-embed-large",
+      "data": [null, null, null, null, null, 0.16595],
+      "type": "line"
+    },
+    {
+      "name": "bge-m3",
+      "data": [null, null, null, null, null, 0.11492],
+      "type": "line"
+    }
+  ]
+}
+```
+
+:::
+
+根据实验结果可以得出一下结论：
+
+1. 在相同维度下，商业模型[text-embedding-v4](https://bailian.console.aliyun.com/?spm=5176.29597918.J_SEsSjsNv72yRuRFS2VknO.2.52007ca0kyUn9Q&tab=api#/api/?type=model&url=https%3A%2F%2Fhelp.aliyun.com%2Fdocument_detail%2F2712515.html)和[text-embedding-3-large](https://openai.com/index/new-embedding-models-and-api-updates/)的性能普遍优于开源模型，而商业模型之间的差异并不大。
+2. 在开源模型中，[mxbai-embed-large](https://ollama.com/library/mxbai-embed-large)的表现最好，可以作为自行部署的首选模型。
+3. 向量维度对模型表现有显著影响，随着向量维度的增加，模型的Top-K准确率普遍提高，但是提高的幅度逐渐减小。需要权衡推荐准确率和计算存储成本，选择合适的向量维度。
+
+::: tip
+
+除非有严苛的计算存储资源限制，否则建议使用512维以上的向量长度，从而获得较好的推荐准确率。
+
+:::
+
+除了量化对比，我们还可以通过推荐结果来直观地感受模型的表现。以下是使用[text-embedding-v4](https://bailian.console.aliyun.com/?spm=5176.29597918.J_SEsSjsNv72yRuRFS2VknO.2.52007ca0kyUn9Q&tab=api#/api/?type=model&url=https%3A%2F%2Fhelp.aliyun.com%2Fdocument_detail%2F2712515.html)两种维度嵌入向量为[《迷魂记》](https://movie.douban.com/subject/1297294/)推荐的相似电影列表：
+
+::: tabs
+
+@tab 2048
+
+| 电影名称         | 发布年份 | 导演                | 电影类型            |
+|----------------|----------|-------------------|------------------|
+| 《后窗》           | 1954     | 阿尔弗雷德·希区柯克 | 惊悚片/悬疑         |
+| 《爱德华大夫》     | 1945     | 阿尔弗雷德·希区柯克 | 心理惊悚片          |
+| 《惊魂记》         | 1960     | 阿尔弗雷德·希区柯克 | 心理惊悚片/恐怖     |
+| 《西北偏北》       | 1959     | 阿尔弗雷德·希区柯克 | 悬疑惊悚片          |
+| 《欲海惊魂》       | 1950     | 阿尔弗雷德·希区柯克 | 悬疑片              |
+| 《电话谋杀案》     | 1954     | 阿尔弗雷德·希区柯克 | 悬疑/犯罪           |
+| 《哑女惊魂记》     | 1946     | 罗伯特·西奥德马克   | 心理惊悚片/黑色电影 |
+| 《搭便车的人》     | 1953     | 艾达·卢皮诺         | 黑色电影            |
+| 《辣手摧花》       | 1943     | 阿尔弗雷德·希区柯克 | 悬疑/惊悚           |
+| 《崩溃边缘的女人》 | 1988     | 佩德罗·阿莫多瓦     | 剧情/喜剧/社会讽刺  |
+
+@tab 64
+
+| 电影名称         | 发布年份 | 导演                | 电影类型          |
+|-----------------|----------|---------------------|---------------|
+| 《死亡密码》       | 1998     | 达伦·阿罗诺夫斯基   | 心理惊悚片        |
+| 《沉默的陷阱》     | 1994     | -                   | 心理悬疑          |
+| 《崩溃边缘的女人》 | 1988     | 佩德罗·阿莫多瓦     | 黑色喜剧          |
+| 《欲望号快车》     | 1996     | 大卫·柯南伯格       | 先锋电影/心理惊悚 |
+| 《大开眼戒》       | 1999     | 斯坦利·库布里克     | 心理惊悚/剧情     |
+| 《惊魂记》         | 1960     | 阿尔弗雷德·希区柯克 | 恐怖/心理惊悚     |
+| 《窗》             | 1980     | 赫伯·弗里德         | 心理惊悚          |
+| 《含冤莫白酒醒时》 | 1986     | -                   | 悬疑/黑色电影     |
+| 《西北偏北》       | 1959     | 阿尔弗雷德·希区柯克 | 悬疑/冒险         |
+| 《偷窥狂》         | 1960     | 迈克尔·鲍威尔       | 心理惊悚/元电影   |
+
+:::
+
+对于刚看完《迷魂记》的用户来说，2048维的向量推荐的电影和《迷魂记》有着更高的相关性和相似度。
+
+## 总结
+
+本文对文本嵌入模型在推荐场景下的性能进行了评估，结果表明商业模型在推荐准确率上普遍优于开源模型，而开源模型中[mxbai-embed-large](https://ollama.com/library/mxbai-embed-large)表现较好。向量维度对模型性能有显著影响，建议使用512维以上的向量长度以获得较好的推荐效果。