fix: Add vector database doc (#4165)

docs/reference/alpha-vector-database.md

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+# [Alpha] Vector Database
+**Warning**: This is an _experimental_ feature. To our knowledge, this is stable, but there are still rough edges in the experience. Contributions are welcome!
+
+## Overview
+Vector database allows user to store and retrieve embeddings. Feast provides general APIs to store and retrieve embeddings.
+
+## Integration
+Below are supported vector databases and implemented features:
+
+| Vector Database | Retrieval | Indexing |
+|-----------------|-----------|----------|
+| Pgvector        | [x]       | [ ]      |
+| Elasticsearch   | [ ]       | [ ]      |
+| Milvus          | [ ]       | [ ]      |
+| Faiss           | [ ]       | [ ]      |
+
+
+## Example
+
+See [https://github.com/feast-dev/feast-workshop/blob/rag/module_4_rag](https://github.com/feast-dev/feast-workshop/blob/rag/module_4_rag) for an example on how to use vector database.
+
+### **Prepare offline embedding dataset**
+Run the following commands to prepare the embedding dataset:
+```shell
+python pull_states.py
+python batch_score_documents.py
+```
+The output will be stored in `data/city_wikipedia_summaries.csv.`
+
+### **Initialize Feast feature store and materialize the data to the online store**
+Use the feature_tore.yaml file to initialize the feature store. This will use the data as offline store, and Pgvector as online store.
+
+```yaml
+project: feast_demo_local
+provider: local
+registry:
+  registry_type: sql
+  path: postgresql://@localhost:5432/feast
+online_store:
+  type: postgres
+  pgvector_enabled: true
+  vector_len: 384
+  host: 127.0.0.1
+  port: 5432
+  database: feast
+  user: ""
+  password: ""
+
+
+offline_store:
+  type: file
+entity_key_serialization_version: 2
+```
+Run the following command in terminal to apply the feature store configuration:
+
+```shell
+feast apply
+```
+
+Note that when you run `feast apply` you are going to apply the following Feature View that we will use for retrieval later:  
+
+```python
+city_embeddings_feature_view = FeatureView(
+    name="city_embeddings",
+    entities=[item],
+    schema=[
+        Field(name="Embeddings", dtype=Array(Float32)),
+    ],
+    source=source,
+    ttl=timedelta(hours=2),
+)
+```
+
+Then run the following command in the terminal to materialize the data to the online store:  
+
+```shell  
+CURRENT_TIME=$(date -u +"%Y-%m-%dT%H:%M:%S")  
+feast materialize-incremental $CURRENT_TIME  
+```
+
+### **Prepare a query embedding**
+```python
+from batch_score_documents import run_model, TOKENIZER, MODEL
+from transformers import AutoTokenizer, AutoModel
+
+question = "the most populous city in the U.S. state of Texas?"
+
+tokenizer = AutoTokenizer.from_pretrained(TOKENIZER)
+model = AutoModel.from_pretrained(MODEL)
+query_embedding = run_model(question, tokenizer, model)
+query = query_embedding.detach().cpu().numpy().tolist()[0]
+```
+
+### **Retrieve the top 5 similar documents**
+First create a feature store instance, and use the `retrieve_online_documents` API to retrieve the top 5 similar documents to the specified query.
+
+```python
+from feast import FeatureStore
+store = FeatureStore(repo_path=".")
+features = store.retrieve_online_documents(
+    feature="city_embeddings:Embeddings",
+    query=query,
+    top_k=5
+).to_dict()
+
+def print_online_features(features):
+    for key, value in sorted(features.items()):
+        print(key, " : ", value)
+
+print_online_features(features)
+```