{"id":17554,"date":"2024-05-20T10:55:42","date_gmt":"2024-05-20T14:55:42","guid":{"rendered":"https:\/\/ipullrank.com\/?p=17554"},"modified":"2025-04-26T21:54:35","modified_gmt":"2025-04-27T01:54:35","slug":"cosine-similarity-knn-in-google-sheets","status":"publish","type":"post","link":"https:\/\/ipullrank.com\/cosine-similarity-knn-in-google-sheets","title":{"rendered":"Quick Tip: Cosine Similarity and\u00a0k-Nearest Neighbors in Google Sheets"},"content":{"rendered":"\t\t
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As I discussed in my previous post<\/span><\/a>, vector embeddings have become an indispensable tool, allowing us to go beyond keyword-based strategies and use semantic relevance in content analysis. Many technical SEOs don\u2019t code (no judgment) but are spreadsheet wizards, so let\u2019s talk about leveraging Google Sheets for calculating cosine similarity and k-nearest neighbors with your vector embeddings. Whether you\u2019re enhancing your keyword research, looking for gaps, or clustering related content, integrating these techniques into your Google Sheets workflow can provide powerful, data-driven insights that inform improved rankings.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t

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Writing User-Defined Functions in Google Sheets<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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Google Apps Script is a powerful, cloud-based scripting language that enables users to automate tasks and extend the functionality of Google Workspace applications like Sheets, Docs, and Slides. A form of JavaScript, Apps Script allows for seamless integration and customization across these tools, making it an underrated yet invaluable resource for enhancing productivity in the Google Workspace environment.<\/p>

Cosine Similarity and kNN are not native functions in Sheets, so we\u2019ll need to prepare our own in Apps Script. Here are steps to set it up:<\/p>

  1. Open Google Sheets –<\/b> Open the Google Sheets document where you want to write your script. In our case, we\u2019ll start from a blank sheet.<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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    1. Access the Apps Script Editor – <\/b>Click on Extensions > Apps Scrip to open the code editor.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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      1. Create a New Script –<\/b> In the Apps Script editor, delete any default code in the script file (Code.gs). The default code will look like this when you open it.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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        1. Write Your Function –<\/b> Start by writing your function. For example, let\u2019s write a function to get OpenAI embeddings based on a target cell. This is a good way for us to vectorize keyword data for comparison against page content embeddings collected via Screaming Frog SEO Spider.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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          function GETEMBEDDINGS(input) {\n\u00a0\u00a0const url = 'https:\/\/api.openai.com\/v1\/embeddings';\n\u00a0\u00a0const apiKey = 'YOUR_OPENAI_KEY';\n\n\u00a0\u00a0\u00a0const payload = {\n\u00a0\u00a0\u00a0\u00a0model: 'text-embedding-3-small',\u00a0\n\u00a0\u00a0\u00a0\u00a0input: input\u00a0\u00a0\n\u00a0\u00a0};\n\n\u00a0\u00a0console.log(\"payload: \" + JSON.stringify(payload));\n\u00a0\u00a0const options = {\n\u00a0\u00a0\u00a0\u00a0method: 'post',\n\u00a0\u00a0\u00a0\u00a0contentType: 'application\/json',\n\u00a0\u00a0\u00a0\u00a0headers: {\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0'Authorization': 'Bearer ' + apiKey\n\u00a0\u00a0\u00a0\u00a0},\n\u00a0\u00a0\u00a0\u00a0payload: JSON.stringify(payload),\n\u00a0\u00a0\u00a0\u00a0muteHttpExceptions: true\n\u00a0\u00a0};\n\u00a0\u00a0console.log(\"options:\" + JSON.stringify(options));\n\u00a0\u00a0const response = UrlFetchApp.fetch(url, options);\n\u00a0\u00a0const responseData = JSON.parse(response.getContentText());\n\n\u00a0\u00a0if (responseData.error) {\n\u00a0\u00a0\u00a0\u00a0throw new Error('API Error: ' + responseData.error.message);\n\u00a0\u00a0}\n\n\u00a0\u00a0const embeddings = responseData.data[0].embedding;\n\u00a0\u00a0return JSON.stringify(embeddings);\n}<\/code><\/pre>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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          1. Fill in your OpenAI API Key – <\/b>To generate embeddings, you’ll need an OpenAI API key. You can follow these instructions to get a key<\/span><\/a>.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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            1. Verify it Works – <\/b>The GETEMBEDDINGS() function is written to return data, not to print it to the screen, so we\u2019ll set up a test function that passes text and logs it to the console to make sure everything is working.<\/li><\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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              function testEmbeddings()\n{\n  Logger.log(GETEMBEDDINGS(\"I really need to hire iPullRank for SEO.\"))\n}<\/code><\/pre>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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              1. Save Your Script –<\/b> Click the floppy disk icon or press Ctrl + S to save your script. Name your project appropriately.<\/span>
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                1. Run Your Function – <\/b>In the Apps Script editor, click the dropdown menu next to the Run button and select your function name. The first time you run the script, you’ll need to authorize it. Follow the prompts to allow necessary permissions.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                  Authorization looks like any other authorization in the Google ecosystem. Don\u2019t be surprised when Apps Script asks for access.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                  1. Test – <\/b>Check the Logs under the Executions menu to debug any issues. If you see a series of decimal numbers print to your screen, then things are working.<\/li>\n<\/ol>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    You can now access your script from your Google Sheet as a function using\n=GETEMBEDDINGS\n(cell)<\/code>. Keep in mind that OpenAI embeddings have a 3191 token input limit. I have not implemented any of the chunking and averaging from the other post in this function because our primary use case here is vectorizing keywords.\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Now, let\u2019s walk through the other functions you\u2019ll need to do vector comparisons.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Convert Strings to Floats<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    First things first, we need to convert our string embeddings to float arrays. Embeddings are often stored as strings<\/span><\/a> (text) if you captured them via Screaming Frog, but to perform mathematical operations like cosine similarity, we need to convert these strings into arrays of floats<\/span><\/a> (decimal numbers). This conversion ensures that each vector’s numerical values can be processed correctly for distance calculations.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    function convertStringToFloatArray(str) {\n  return str.replace(\/[\\[\\]]\/g, '') \/\/ Remove brackets\n            .split(',')             \/\/ Split by commas\n            .map(parseFloat);       \/\/ Convert to floats\n}<\/code><\/pre>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Follow the steps above to add the function to your project in Apps Script.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Cosine Similarity<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Next, let’s define the function to calculate cosine similarity between two vectors. As we previously discussed<\/span><\/a>, cosine similarity measures the cosine of the angle between two vectors, providing a metric for how similar they are in terms of direction. This is particularly useful in SEO for understanding the semantic similarity between different pieces of content, or the relevance of content to a given keyword in this example thereby enabling more nuanced keyword analysis and content clustering.<\/p>
                    Here\u2019s the code:<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    function cosineSimilarity(vecA, vecB) {\n  if (vecA.length !== vecB.length) {\n    throw new Error(\"Vectors must be the same length\");\n  }\n  vecA = convertStringToFloatArray(vecA);\n  vecB = convertStringToFloatArray(vecB);\n  const dotProduct = vecA.reduce((sum, a, idx) => sum + a * vecB[idx], 0);\n  const magnitudeA = Math.sqrt(vecA.reduce((sum, a) => sum + a * a, 0));\n  const magnitudeB = Math.sqrt(vecB.reduce((sum, b) => sum + b * b, 0));\n  return dotProduct \/ (magnitudeA * magnitudeB);\n}<\/code><\/pre>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Here\u2019s an example of the computed similarity in the spreadsheet. We have our embeddings for our keyword pulled via the =GETEMBEDDINGS()<\/code> function and embeddings for the landing page from our Screaming Frog crawl. Then we run our cosine similarity function by passing both vectors.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Follow the steps above to add the cosine similarity function to your project.\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    K-Nearest Neighbors\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    Finally, we compute the nearest neighbors using cosine similarity. The k-nearest neighbors (k-NN) algorithm identifies the k vectors that are most similar to a target vector, based on a chosen distance metric like cosine similarity. In SEO, this can help in finding the most semantically similar keywords or content pieces, aiding in content optimization and internal linking.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    function computeNearestNeighbors(targetCell, embeddingsColumn, dataColumn, numNeighbors,showScores=0) {\n\u00a0\u00a0const sheet = SpreadsheetApp.getActiveSpreadsheet().getActiveSheet();\n\n\u00a0\u00a0\/\/ Get target embedding from target cell\n\u00a0\u00a0const targetEmbeddingString = targetCell;\n\u00a0\u00a0const targetEmbedding = convertStringToFloatArray(targetEmbeddingString);\n\n\u00a0\u00a0\/\/ Get embeddings and associated data from specified columns\n\u00a0\u00a0const embeddingsRange = sheet.getRange(`${embeddingsColumn}2:${embeddingsColumn}`).getValues();\n\u00a0\u00a0const dataRange = sheet.getRange(`${dataColumn}2:${dataColumn}`).getValues();\n\n\u00a0\u00a0const embeddingsValues = embeddingsRange.filter(row => row[0] !== \"\");\n\u00a0\u00a0const dataValues = dataRange.filter(row => row[0] !== \"\");\n\n\u00a0\u00a0\/\/ Compute distances using cosine similarity\n\u00a0\u00a0const distances = embeddingsValues.map((row, index) => {\n\u00a0\u00a0\u00a0\u00a0const embedding = convertStringToFloatArray(row[0]);\n\u00a0\u00a0\u00a0\u00a0return {\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0index: index + 2, \/\/ +2 to match row number in sheet (since we start from row 2)\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0distance: cosineSimilarity(targetEmbedding, embedding),\n\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0data: dataValues[index][0]\n\u00a0\u00a0\u00a0\u00a0};\n\u00a0\u00a0});\n\n\u00a0\u00a0\/\/ Sort by distance\n\u00a0\u00a0distances.sort((a, b) => b.distance - a.distance); \/\/ Descending order for cosine similarity\n\n\u00a0\u00a0\/\/ Output nearest neighbors\n\u00a0\u00a0const nearestNeighbors = distances.slice(0, numNeighbors);\n\n\u00a0\u00a0var results = nearestNeighbors.map(neighbor => neighbor.data);\n\n\u00a0\u00a0if (showScores !=0){\n\u00a0\u00a0\u00a0\u00a0results = nearestNeighbors.map(neighbor => `Data: ${neighbor.data}, Score: ${neighbor.distance.toFixed(4)}`);\n\u00a0\u00a0}\n\n\u00a0\u00a0return results.join(\", \");\n}<\/code><\/pre>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                    This function is a bit more complex to use because you need to provide the lookup embeddings and the list of embeddings and the column you want to pull results from.<\/p>\n\n
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                    1. Place the data and set the range – <\/b>Copy your data whether pulled via Screaming Frog or otherwise. Ensure your embeddings that you want to compare against are in the specified column, starting from row 2.<\/li>\n \t
                    2. Function Parameters – <\/b>Call the computeNearestNeighbors()<\/code> function with the following parameters:\n
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                      1. targetCell –<\/b> The cell containing the embedding you want (e.g., B2).<\/li>\n \t
                      2. embeddingsColumn – <\/b>The column containing the embeddings (e.g.,\u00a0 \u201cK\u201d).<\/li>\n \t
                      3. dataColumn – <\/b>the column containing the data that you want returned based on the match. In our case this will be the URL column. (E.g. \u201cL\u201d)<\/li>\n \t
                      4. numNeighbors –<\/b> The number of nearest neighbors to return (e.g., 5).<\/li>\n \t
                      5. showScores –<\/b> this is an optional flag that returns the cosine similarity scores<\/li>\n<\/ol>\n<\/li>\n \t
                      6. Run the Function – using =computeNearestNeighbors()<\/code> in a cell.<\/li>\n<\/ol>\n
                        If we want a single match we run the function with numNeighbors set to 1 as follows: =computeNearestNeighbors(B2,\"L\",\"K\",1)<\/code>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                        If we want three matches, we set numNeighbors to 3 like so: =computeNearestNeighbors(B2,\"L\",\"K\",3)<\/code>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                        If we want three matches and the scores cosine similarity scores, we use the optional 5th parameter =computeNearestNeighbors(B2,\"L\",\"K\",3,1)<\/code>.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                        Download our Workbook<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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                        If you’re in a rush and just want to get to the analysis instead of setting everything up, go ahead and download our Google Sheets workbook by filling out this form.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t
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