Implementing Ranking Algorithms

In a search engine, ranking algorithms are fundamental for sorting and displaying the most relevant results based on keywords or queries. Different search engines often use different ranking algorithms. Some commonly used algorithms in the field are PageRank, TF-IDF, and BM25. We will focus on a simplified version of the PageRank algorithm for our search engine implementation.

PageRank is a popular ranking algorithm developed by the founders of Google, Larry Page and Sergey Brin. It calculates the importance of web pages based on the quantity and quality of inbound links. The concept behind PageRank is assuming a random user following links: the probability the user lands on a specific page gives the page a rank.

In our search engine, we can implement a simple version of the PageRank algorithm for ranking our indexed documents. We will define a utility function to calculate the PageRank for a document and use it as a ranking criterion. Below is a simplified Python implementation:

This algorithm helps sort out the results in a relevant way, enhancing the accuracy of the search engine. This becomes incredibly relevant in domains such as AI and finance, where accessing the most pertinent information efficiently can be crucial in decision-making processes.

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if __name__ == "__main__":

  def page_rank(document, links):

    dangling_nodes = 0

    for link in links.values():

      if not link:

        dangling_nodes += 1

    rank = defaultdict(int)

    rank = {node: 1 / len(links.keys()) for node in links.keys()}

​

    damping_factor = 0.85

    for _ in range(20):

      new_rank = {node: (1 - damping_factor) / len(links) for node in links}

      for node in links:

        for end_node in links[node]:

            new_rank[end_node] += damping_factor * (rank[node] / len(links[node]))

      rank = new_rank

    return rank[document]

​

  links = { # for illustration

  'Page_A': ['Page_B', 'Page_C', 'Page_E', 'Page_F'],

  'Page_B': ['Page_C', 'Page_E'],

  'Page_C': ['Page_A'],

  'Page_D': ['Page_C', 'Page_F', 'Page_A'],

  'Page_E': [],

  'Page_F': ['Page_B', 'Page_A', 'Page_C'],

  }

  print(page_rank('Page_A', links))