> ## Documentation Index
> Fetch the complete documentation index at: https://docs.pinecone.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Run hybrid search on a single legacy vector index

> Run hybrid search on one Pinecone index storing a dense and a sparse vector per record, weighting the two signals client-side with an alpha value.

> [!NOTE]
>
> New projects should use the [Documents API](https://docs.pinecone.io/guides/indexes/create-an-index.md#create-a-document-index). To move an existing index, see [Move to the Documents API](https://docs.pinecone.io/guides/indexes/move-to-the-documents-api.md).

Store a dense vector and a sparse vector on each record in a single Pinecone index, then query both signals in one request. Pinecone combines them server-side. Because sparse (BM25-style) scores are unbounded, you set the balance between the two signals client-side, by scaling the query vectors before the request (an `alpha` weighting). This is the legacy Vectors API single-index hybrid pattern.

## Normalize sparse and dense values

A single index that stores both vector types doesn't reconcile their score ranges. Dense-vector scores fall in a bounded range (roughly `[-1, 1]` for `dotproduct` on unit-norm embeddings), while BM25-style sparse weights are unbounded and can run into double digits. Without explicit weighting, the sparse component dominates the combined score. To make the two signals comparable, apply a **convex combination** at query time using an `alpha` parameter:

* `combined = alpha * dense + (1 - alpha) * sparse`
* `alpha = 1.0` ranks by dense only (pure semantic).
* `alpha = 0.0` ranks by sparse only (pure keyword).
* `alpha = 0.5` weights the two signals equally.

Pinecone applies this weighting by **scaling the query vectors before sending them to the index** (the index itself stores raw values). Use the [`hybrid_score_norm`](#hybrid-single-5-alpha) helper documented in the walkthrough below; it multiplies the dense values by `alpha` and the sparse values by `1 - alpha`, so the underlying dotproduct produces the desired combination.

### Choosing alpha

There's no universal best value — alpha depends on your data and query distribution. Reasonable starting points:

* **`alpha = 0.75`** (dense-leaning) — a good default for natural-language queries on conversational or document-style content.
* **`alpha = 0.5`** (balanced) — useful when keyword and semantic signals contribute equally (e.g., mixed exact-match and synonym queries).
* **`alpha = 0.25`** (sparse-leaning) — good for queries with high keyword specificity (product SKUs, technical IDs, named entities).

We recommend evaluating multiple alpha values against a labeled relevance set drawn from your own workload.

## Set up and search

To perform hybrid search with a single index that stores both dense and sparse vectors, follow these steps:

**1. Create the index**

To store both dense and sparse vectors in a single index, use the [Create an index](https://docs.pinecone.io/reference/api/2026-04/control-plane/create_index.md) operation, setting the `vector_type` to `dense` and the `metric` to `dotproduct`. This is the only combination that supports dense/sparse search on a single index.

```python Python theme={null}
from pinecone.grpc import PineconeGRPC as Pinecone
from pinecone import ServerlessSpec

pc = Pinecone(api_key="YOUR_API_KEY")

index_name = "hybrid-index"

if not pc.has_index(index_name):
    pc.create_index(
        name=index_name,
        vector_type="dense",
        dimension=1024,
        metric="dotproduct",
        spec=ServerlessSpec(
            cloud="aws",
            region="us-east-1"
        )
    )
```

**2. Generate vectors**

Use Pinecone's [hosted embedding models](https://docs.pinecone.io/guides/indexes/index-configuration.md#embedding-models) to [convert data into dense and sparse vectors](https://docs.pinecone.io/reference/api/latest/inference/generate-vectors.md).

```python Python [expandable] theme={null}
# Define the records
data = [
    { "_id": "vec1", "chunk_text": "Apple Inc. issued a $10 billion corporate bond in 2023." },
    { "_id": "vec2", "chunk_text": "ETFs tracking the S&P 500 outperformed active funds last year." },
    { "_id": "vec3", "chunk_text": "Tesla's options volume surged after the latest earnings report." },
    { "_id": "vec4", "chunk_text": "Dividend aristocrats are known for consistently raising payouts." },
    { "_id": "vec5", "chunk_text": "The Federal Reserve raised interest rates by 0.25% to curb inflation." },
    { "_id": "vec6", "chunk_text": "Unemployment hit a record low of 3.7% in Q4 of 2024." },
    { "_id": "vec7", "chunk_text": "The CPI index rose by 6% in July 2024, raising concerns about purchasing power." },
    { "_id": "vec8", "chunk_text": "GDP growth in emerging markets outpaced developed economies." },
    { "_id": "vec9", "chunk_text": "Amazon's acquisition of MGM Studios was valued at $8.45 billion." },
    { "_id": "vec10", "chunk_text": "Alphabet reported a 20% increase in advertising revenue." },
    { "_id": "vec11", "chunk_text": "ExxonMobil announced a special dividend after record profits." },
    { "_id": "vec12", "chunk_text": "Tesla plans a 3-for-1 stock split to attract retail investors." },
    { "_id": "vec13", "chunk_text": "Credit card APRs reached an all-time high of 22.8% in 2024." },
    { "_id": "vec14", "chunk_text": "A 529 college savings plan offers tax advantages for education." },
    { "_id": "vec15", "chunk_text": "Emergency savings should ideally cover 6 months of expenses." },
    { "_id": "vec16", "chunk_text": "The average mortgage rate rose to 7.1% in December." },
    { "_id": "vec17", "chunk_text": "The SEC fined a hedge fund $50 million for insider trading." },
    { "_id": "vec18", "chunk_text": "New ESG regulations require companies to disclose climate risks." },
    { "_id": "vec19", "chunk_text": "The IRS introduced a new tax bracket for high earners." },
    { "_id": "vec20", "chunk_text": "Compliance with GDPR is mandatory for companies operating in Europe." },
    { "_id": "vec21", "chunk_text": "What are the best-performing green bonds in a rising rate environment?" },
    { "_id": "vec22", "chunk_text": "How does inflation impact the real yield of Treasury bonds?" },
    { "_id": "vec23", "chunk_text": "Top SPAC mergers in the technology sector for 2024." },
    { "_id": "vec24", "chunk_text": "Are stablecoins a viable hedge against currency devaluation?" },
    { "_id": "vec25", "chunk_text": "Comparison of Roth IRA vs 401(k) for high-income earners." },
    { "_id": "vec26", "chunk_text": "Stock splits and their effect on investor sentiment." },
    { "_id": "vec27", "chunk_text": "Tech IPOs that disappointed in their first year." },
    { "_id": "vec28", "chunk_text": "Impact of interest rate hikes on bank stocks." },
    { "_id": "vec29", "chunk_text": "Growth vs. value investing strategies in 2024." },
    { "_id": "vec30", "chunk_text": "The role of artificial intelligence in quantitative trading." },
    { "_id": "vec31", "chunk_text": "What are the implications of quantitative tightening on equities?" },
    { "_id": "vec32", "chunk_text": "How does compounding interest affect long-term investments?" },
    { "_id": "vec33", "chunk_text": "What are the best assets to hedge against inflation?" },
    { "_id": "vec34", "chunk_text": "Can ETFs provide better diversification than mutual funds?" },
    { "_id": "vec35", "chunk_text": "Unemployment hit at 2.4% in Q3 of 2024." },
    { "_id": "vec36", "chunk_text": "Unemployment is expected to hit 2.5% in Q3 of 2024." },
    { "_id": "vec37", "chunk_text": "In Q3 2025 unemployment for the prior year was revised to 2.2%"},
    { "_id": "vec38", "chunk_text": "Emerging markets witnessed increased foreign direct investment as global interest rates stabilized." },
    { "_id": "vec39", "chunk_text": "The rise in energy prices significantly impacted inflation trends during the first half of 2024." },
    { "_id": "vec40", "chunk_text": "Labor market trends show a declining participation rate despite record low unemployment in 2024." },
    { "_id": "vec41", "chunk_text": "Forecasts of global supply chain disruptions eased in late 2024, but consumer prices remained elevated due to persistent demand." },
    { "_id": "vec42", "chunk_text": "Tech sector layoffs in Q3 2024 have reshaped hiring trends across high-growth industries." },
    { "_id": "vec43", "chunk_text": "The U.S. dollar weakened against a basket of currencies as the global economy adjusted to shifting trade balances." },
    { "_id": "vec44", "chunk_text": "Central banks worldwide increased gold reserves to hedge against geopolitical and economic instability." },
    { "_id": "vec45", "chunk_text": "Corporate earnings in Q4 2024 were largely impacted by rising raw material costs and currency fluctuations." },
    { "_id": "vec46", "chunk_text": "Economic recovery in Q2 2024 relied heavily on government spending in infrastructure and green energy projects." },
    { "_id": "vec47", "chunk_text": "The housing market saw a rebound in late 2024, driven by falling mortgage rates and pent-up demand." },
    { "_id": "vec48", "chunk_text": "Wage growth outpaced inflation for the first time in years, signaling improved purchasing power in 2024." },
    { "_id": "vec49", "chunk_text": "China's economic growth in 2024 slowed to its lowest level in decades due to structural reforms and weak exports." },
    { "_id": "vec50", "chunk_text": "AI-driven automation in the manufacturing sector boosted productivity but raised concerns about job displacement." },
    { "_id": "vec51", "chunk_text": "The European Union introduced new fiscal policies in 2024 aimed at reducing public debt without stifling growth." },
    { "_id": "vec52", "chunk_text": "Record-breaking weather events in early 2024 have highlighted the growing economic impact of climate change." },
    { "_id": "vec53", "chunk_text": "Cryptocurrencies faced regulatory scrutiny in 2024, leading to volatility and reduced market capitalization." },
    { "_id": "vec54", "chunk_text": "The global tourism sector showed signs of recovery in late 2024 after years of pandemic-related setbacks." },
    { "_id": "vec55", "chunk_text": "Trade tensions between the U.S. and China escalated in 2024, impacting global supply chains and investment flows." },
    { "_id": "vec56", "chunk_text": "Consumer confidence indices remained resilient in Q2 2024 despite fears of an impending recession." },
    { "_id": "vec57", "chunk_text": "Startups in 2024 faced tighter funding conditions as venture capitalists focused on profitability over growth." },
    { "_id": "vec58", "chunk_text": "Oil production cuts in Q1 2024 by OPEC nations drove prices higher, influencing global energy policies." },
    { "_id": "vec59", "chunk_text": "The adoption of digital currencies by central banks increased in 2024, reshaping monetary policy frameworks." },
    { "_id": "vec60", "chunk_text": "Healthcare spending in 2024 surged as governments expanded access to preventive care and pandemic preparedness." },
    { "_id": "vec61", "chunk_text": "The World Bank reported declining poverty rates globally, but regional disparities persisted." },
    { "_id": "vec62", "chunk_text": "Private equity activity in 2024 focused on renewable energy and technology sectors amid shifting investor priorities." },
    { "_id": "vec63", "chunk_text": "Population aging emerged as a critical economic issue in 2024, especially in advanced economies." },
    { "_id": "vec64", "chunk_text": "Rising commodity prices in 2024 strained emerging markets dependent on imports of raw materials." },
    { "_id": "vec65", "chunk_text": "The global shipping industry experienced declining freight rates in 2024 due to overcapacity and reduced demand." },
    { "_id": "vec66", "chunk_text": "Bank lending to small and medium-sized enterprises surged in 2024 as governments incentivized entrepreneurship." },
    { "_id": "vec67", "chunk_text": "Renewable energy projects accounted for a record share of global infrastructure investment in 2024." },
    { "_id": "vec68", "chunk_text": "Cybersecurity spending reached new highs in 2024, reflecting the growing threat of digital attacks on infrastructure." },
    { "_id": "vec69", "chunk_text": "The agricultural sector faced challenges in 2024 due to extreme weather and rising input costs." },
    { "_id": "vec70", "chunk_text": "Consumer spending patterns shifted in 2024, with a greater focus on experiences over goods." },
    { "_id": "vec71", "chunk_text": "The economic impact of the 2008 financial crisis was mitigated by quantitative easing policies." },
    { "_id": "vec72", "chunk_text": "In early 2024, global GDP growth slowed, driven by weaker exports in Asia and Europe." },
    { "_id": "vec73", "chunk_text": "The historical relationship between inflation and unemployment is explained by the Phillips Curve." },
    { "_id": "vec74", "chunk_text": "The World Trade Organization's role in resolving disputes was tested in 2024." },
    { "_id": "vec75", "chunk_text": "The collapse of Silicon Valley Bank raised questions about regulatory oversight in 2024." },
    { "_id": "vec76", "chunk_text": "The cost of living crisis has been exacerbated by stagnant wage growth and rising inflation." },
    { "_id": "vec77", "chunk_text": "Supply chain resilience became a top priority for multinational corporations in 2024." },
    { "_id": "vec78", "chunk_text": "Consumer sentiment surveys in 2024 reflected optimism despite high interest rates." },
    { "_id": "vec79", "chunk_text": "The resurgence of industrial policy in Q1 2024 focused on decoupling critical supply chains." },
    { "_id": "vec80", "chunk_text": "Technological innovation in the fintech sector disrupted traditional banking in 2024." },
    { "_id": "vec81", "chunk_text": "The link between climate change and migration patterns is increasingly recognized." },
    { "_id": "vec82", "chunk_text": "Renewable energy subsidies in 2024 reduced the global reliance on fossil fuels." },
    { "_id": "vec83", "chunk_text": "The economic fallout of geopolitical tensions was evident in rising defense budgets worldwide." },
    { "_id": "vec84", "chunk_text": "The IMF's 2024 global outlook highlighted risks of stagflation in emerging markets." },
    { "_id": "vec85", "chunk_text": "Declining birth rates in advanced economies pose long-term challenges for labor markets." },
    { "_id": "vec86", "chunk_text": "Digital transformation initiatives in 2024 drove productivity gains in the services sector." },
    { "_id": "vec87", "chunk_text": "The U.S. labor market's resilience in 2024 defied predictions of a severe recession." },
    { "_id": "vec88", "chunk_text": "New fiscal measures in the European Union aimed to stabilize debt levels post-pandemic." },
    { "_id": "vec89", "chunk_text": "Venture capital investments in 2024 leaned heavily toward AI and automation startups." },
    { "_id": "vec90", "chunk_text": "The surge in e-commerce in 2024 was facilitated by advancements in logistics technology." },
    { "_id": "vec91", "chunk_text": "The impact of ESG investing on corporate strategies has been a major focus in 2024." },
    { "_id": "vec92", "chunk_text": "Income inequality widened in 2024 despite strong economic growth in developed nations." },
    { "_id": "vec93", "chunk_text": "The collapse of FTX highlighted the volatility and risks associated with cryptocurrencies." },
    { "_id": "vec94", "chunk_text": "Cyberattacks targeting financial institutions in 2024 led to record cybersecurity spending." },
    { "_id": "vec95", "chunk_text": "Automation in agriculture in 2024 increased yields but displaced rural workers." },
    { "_id": "vec96", "chunk_text": "New trade agreements signed 2022 will make an impact in 2024"},
]
```

```python Python theme={null}
# Convert the chunk_text into dense vectors
dense_embeddings = pc.inference.embed(
    model="llama-text-embed-v2",
    inputs=[d['chunk_text'] for d in data],
    parameters={"input_type": "passage", "truncate": "END"}
)

# Convert the chunk_text into sparse vectors
sparse_embeddings = pc.inference.embed(
    model="pinecone-sparse-english-v0",
    inputs=[d['chunk_text'] for d in data],
    parameters={"input_type": "passage", "truncate": "END"}
)
```

**3. Upsert records with dense and sparse vectors**

Use the [Upsert records](https://docs.pinecone.io/reference/api/latest/data-plane/upsert.md) operation, specifying dense values in the `value` parameter and sparse values in the `sparse_values` parameter.

> [!NOTE]
>
> Only indexes that store dense vectors with the [dotproduct distance metric](https://docs.pinecone.io/guides/indexes/indexing-overview.md#dotproduct) accept records that also have sparse vectors. Upserting such records into an index with a different distance metric will succeed, but querying will return an error.

```Python Python theme={null}
# Target the index
# To get the unique host for an index, 
# see https://docs.pinecone.io/guides/indexes/target-an-index
index = pc.index(host="INDEX_HOST", grpc=True)

# Each record contains an ID, a dense vector, a sparse vector, and the original text as metadata
records = []
for d, de, se in zip(data, dense_embeddings, sparse_embeddings):
    records.append({
        "id": d['_id'],
        "values": de['values'],
        "sparse_values": {'indices': se['sparse_indices'], 'values': se['sparse_values']},
        "metadata": {'text': d['chunk_text']}
    })

# Upsert the records into the index
index.upsert(
    vectors=records,
    namespace="example-namespace"
)
```

**4. Search the index**

Use the [Generate vectors](https://docs.pinecone.io/reference/api/latest/inference/generate-vectors.md) operation to convert your query into a dense vector and a sparse vector, and then use the [Search with a vector](https://docs.pinecone.io/reference/api/latest/data-plane/query.md) operation to search the index for the 40 most relevant records.

```Python Python theme={null}
query = "Q3 2024 us economic data"

# Convert the query into a dense vector
dense_query_embedding = pc.inference.embed(
    model="llama-text-embed-v2",
    inputs=query,
    parameters={"input_type": "query", "truncate": "END"}
)

# Convert the query into a sparse vector
sparse_query_embedding = pc.inference.embed(
    model="pinecone-sparse-english-v0",
    inputs=query,
    parameters={"input_type": "query", "truncate": "END"}
)

for d, s in zip(dense_query_embedding, sparse_query_embedding):
    query_response = index.query(
        namespace="example-namespace",
        top_k=40,
        vector=d['values'],
        sparse_vector={'indices': s['sparse_indices'], 'values': s['sparse_values']},
        include_values=False,
        include_metadata=True
    )
    print(query_response)
```

```python Response [expandable] theme={null}
{'matches': [{'id': 'vec35',
              'metadata': {'text': 'Unemployment hit at 2.4% in Q3 of 2024.'},
              'score': 7.92519569,
              'values': []},
             {'id': 'vec46',
              'metadata': {'text': 'Economic recovery in Q2 2024 relied '
                                   'heavily on government spending in '
                                   'infrastructure and green energy projects.'},
              'score': 7.86733627,
              'values': []},
             {'id': 'vec36',
              'metadata': {'text': 'Unemployment is expected to hit 2.5% in Q3 '
                                   'of 2024.'},
              'score': 7.82636,
              'values': []},
             {'id': 'vec42',
              'metadata': {'text': 'Tech sector layoffs in Q3 2024 have '
                                   'reshaped hiring trends across high-growth '
                                   'industries.'},
              'score': 7.79465914,
              'values': []},
             {'id': 'vec49',
              'metadata': {'text': "China's economic growth in 2024 slowed to "
                                   'its lowest level in decades due to '
                                   'structural reforms and weak exports.'},
              'score': 7.46323156,
              'values': []},
             {'id': 'vec63',
              'metadata': {'text': 'Population aging emerged as a critical '
                                   'economic issue in 2024, especially in '
                                   'advanced economies.'},
              'score': 7.29055929,
              'values': []},
             {'id': 'vec92',
              'metadata': {'text': 'Income inequality widened in 2024 despite '
                                   'strong economic growth in developed '
                                   'nations.'},
              'score': 6.51210213,
              'values': []},
             {'id': 'vec52',
              'metadata': {'text': 'Record-breaking weather events in early '
                                   '2024 have highlighted the growing economic '
                                   'impact of climate change.'},
              'score': 6.4125514,
              'values': []},
             {'id': 'vec62',
              'metadata': {'text': 'Private equity activity in 2024 focused on '
                                   'renewable energy and technology sectors '
                                   'amid shifting investor priorities.'},
              'score': 4.8084693,
              'values': []},
             {'id': 'vec89',
              'metadata': {'text': 'Venture capital investments in 2024 leaned '
                                   'heavily toward AI and automation '
                                   'startups.'},
              'score': 4.7974205,
              'values': []},
             {'id': 'vec57',
              'metadata': {'text': 'Startups in 2024 faced tighter funding '
                                   'conditions as venture capitalists focused '
                                   'on profitability over growth.'},
              'score': 4.72518444,
              'values': []},
             {'id': 'vec37',
              'metadata': {'text': 'In Q3 2025 unemployment for the prior year '
                                   'was revised to 2.2%'},
              'score': 4.71824408,
              'values': []},
             {'id': 'vec69',
              'metadata': {'text': 'The agricultural sector faced challenges '
                                   'in 2024 due to extreme weather and rising '
                                   'input costs.'},
              'score': 4.66726208,
              'values': []},
             {'id': 'vec60',
              'metadata': {'text': 'Healthcare spending in 2024 surged as '
                                   'governments expanded access to preventive '
                                   'care and pandemic preparedness.'},
              'score': 4.62045908,
              'values': []},
             {'id': 'vec55',
              'metadata': {'text': 'Trade tensions between the U.S. and China '
                                   'escalated in 2024, impacting global supply '
                                   'chains and investment flows.'},
              'score': 4.59764862,
              'values': []},
             {'id': 'vec51',
              'metadata': {'text': 'The European Union introduced new fiscal '
                                   'policies in 2024 aimed at reducing public '
                                   'debt without stifling growth.'},
              'score': 4.57397079,
              'values': []},
             {'id': 'vec70',
              'metadata': {'text': 'Consumer spending patterns shifted in '
                                   '2024, with a greater focus on experiences '
                                   'over goods.'},
              'score': 4.55043507,
              'values': []},
             {'id': 'vec87',
              'metadata': {'text': "The U.S. labor market's resilience in 2024 "
                                   'defied predictions of a severe recession.'},
              'score': 4.51785707,
              'values': []},
             {'id': 'vec90',
              'metadata': {'text': 'The surge in e-commerce in 2024 was '
                                   'facilitated by advancements in logistics '
                                   'technology.'},
              'score': 4.47754288,
              'values': []},
             {'id': 'vec78',
              'metadata': {'text': 'Consumer sentiment surveys in 2024 '
                                   'reflected optimism despite high interest '
                                   'rates.'},
              'score': 4.46246624,
              'values': []},
             {'id': 'vec53',
              'metadata': {'text': 'Cryptocurrencies faced regulatory scrutiny '
                                   'in 2024, leading to volatility and reduced '
                                   'market capitalization.'},
              'score': 4.4435873,
              'values': []},
             {'id': 'vec45',
              'metadata': {'text': 'Corporate earnings in Q4 2024 were largely '
                                   'impacted by rising raw material costs and '
                                   'currency fluctuations.'},
              'score': 4.43836403,
              'values': []},
             {'id': 'vec82',
              'metadata': {'text': 'Renewable energy subsidies in 2024 reduced '
                                   'the global reliance on fossil fuels.'},
              'score': 4.43601322,
              'values': []},
             {'id': 'vec94',
              'metadata': {'text': 'Cyberattacks targeting financial '
                                   'institutions in 2024 led to record '
                                   'cybersecurity spending.'},
              'score': 4.41334057,
              'values': []},
             {'id': 'vec47',
              'metadata': {'text': 'The housing market saw a rebound in late '
                                   '2024, driven by falling mortgage rates and '
                                   'pent-up demand.'},
              'score': 4.39900732,
              'values': []},
             {'id': 'vec41',
              'metadata': {'text': 'Forecasts of global supply chain '
                                   'disruptions eased in late 2024, but '
                                   'consumer prices remained elevated due to '
                                   'persistent demand.'},
              'score': 4.37389421,
              'values': []},
             {'id': 'vec84',
              'metadata': {'text': "The IMF's 2024 global outlook highlighted "
                                   'risks of stagflation in emerging markets.'},
              'score': 4.37335157,
              'values': []},
             {'id': 'vec96',
              'metadata': {'text': 'New trade agreements signed 2022 will make '
                                   'an impact in 2024'},
              'score': 4.33860636,
              'values': []},
             {'id': 'vec79',
              'metadata': {'text': 'The resurgence of industrial policy in Q1 '
                                   '2024 focused on decoupling critical supply '
                                   'chains.'},
              'score': 4.33784199,
              'values': []},
             {'id': 'vec6',
              'metadata': {'text': 'Unemployment hit a record low of 3.7% in '
                                   'Q4 of 2024.'},
              'score': 4.33008051,
              'values': []},
             {'id': 'vec65',
              'metadata': {'text': 'The global shipping industry experienced '
                                   'declining freight rates in 2024 due to '
                                   'overcapacity and reduced demand.'},
              'score': 4.3228569,
              'values': []},
             {'id': 'vec64',
              'metadata': {'text': 'Rising commodity prices in 2024 strained '
                                   'emerging markets dependent on imports of '
                                   'raw materials.'},
              'score': 4.32269621,
              'values': []},
             {'id': 'vec95',
              'metadata': {'text': 'Automation in agriculture in 2024 '
                                   'increased yields but displaced rural '
                                   'workers.'},
              'score': 4.31127262,
              'values': []},
             {'id': 'vec86',
              'metadata': {'text': 'Digital transformation initiatives in 2024 '
                                   'drove productivity gains in the services '
                                   'sector.'},
              'score': 4.30181122,
              'values': []},
             {'id': 'vec66',
              'metadata': {'text': 'Bank lending to small and medium-sized '
                                   'enterprises surged in 2024 as governments '
                                   'incentivized entrepreneurship.'},
              'score': 4.27241945,
              'values': []},
             {'id': 'vec58',
              'metadata': {'text': 'Oil production cuts in Q1 2024 by OPEC '
                                   'nations drove prices higher, influencing '
                                   'global energy policies.'},
              'score': 4.21715498,
              'values': []},
             {'id': 'vec80',
              'metadata': {'text': 'Technological innovation in the fintech '
                                   'sector disrupted traditional banking in '
                                   '2024.'},
              'score': 4.17712116,
              'values': []},
             {'id': 'vec75',
              'metadata': {'text': 'The collapse of Silicon Valley Bank raised '
                                   'questions about regulatory oversight in '
                                   '2024.'},
              'score': 4.16192341,
              'values': []},
             {'id': 'vec56',
              'metadata': {'text': 'Consumer confidence indices remained '
                                   'resilient in Q2 2024 despite fears of an '
                                   'impending recession.'},
              'score': 4.15782213,
              'values': []},
             {'id': 'vec67',
              'metadata': {'text': 'Renewable energy projects accounted for a '
                                   'record share of global infrastructure '
                                   'investment in 2024.'},
              'score': 4.14623,
              'values': []}],
 'namespace': 'example-namespace',
 'usage': {'read_units': 9}}
```

**5. Search the index with explicit weighting**

For a conceptual overview of why this normalization is needed, see [Normalize sparse and dense values](#normalize-sparse-and-dense-values).

Because Pinecone views your sparse-dense vector as a single vector, it doesn't offer a built-in parameter to adjust the weight of a query's dense part against its sparse part; the index is agnostic to density or sparsity of coordinates in your vectors. You may, however, incorporate a linear weighting scheme by customizing your query vector, as demonstrated in the function below.

The following example transforms vector values using an alpha parameter.

```Python Python theme={null}
def hybrid_score_norm(dense, sparse, alpha: float):
    """Hybrid score using a convex combination

    alpha * dense + (1 - alpha) * sparse

    Args:
        dense: Array of floats representing
        sparse: a dict of `indices` and `values`
        alpha: scale between 0 and 1
    """
    if alpha < 0 or alpha > 1:
        raise ValueError("Alpha must be between 0 and 1")
    hs = {
        'indices': sparse['indices'],
        'values':  [v * (1 - alpha) for v in sparse['values']]
    }
    return [v * alpha for v in dense], hs
```

The following example transforms a vector using the above function, then queries a Pinecone index.

```Python Python theme={null}
sparse_vector = {
   'indices': [10, 45, 16],
   'values':  [0.5, 0.5, 0.2]
}
dense_vector = [0.1, 0.2, 0.3]

hdense, hsparse = hybrid_score_norm(dense_vector, sparse_vector, alpha=0.75)

query_response = index.query(
    namespace="example-namespace",
    top_k=10,
    vector=hdense,
    sparse_vector=hsparse
)
```