http://blog.base2.io/2014/02/25/autocomplete-and-the-three-algorithms/

brands_controller.rb

# app/controllers/api/v1/brands_controller.rb
module Api
  module V1
    class BrandsController < ApiController
      def search
        @results = SimilarBrandsQuery.new.similar_to(params.require(:q)).limit(10)

        render json: @results, status: 200
      end
    end
  end
end

levenshtein.sql

SELECT *, levenshtein(name, 'hazienda') AS distance FROM brands ORDER BY distance ASC, name LIMIT 10;

similar_brands_query.rb

# app/queries/similar_brands_query.rb
class SimilarBrandsQuery
  attr_reader :relation

  def initialize(relation = Brand.all)
    @relation = relation
  end

  def similar_to(name)
    @relation.select('*', "similarity(name, #{ActiveRecord::Base.sanitize(name)}) AS similarity").order('similarity DESC, name')
  end
end

soundex.sql

SELECT *, difference(name, 'hazienda') AS similarity FROM brands ORDER BY similarity DESC, name LIMIT 10;

trigram.sql

SELECT *, similarity(name, 'hazienda') AS similarity FROM brands ORDER BY similarity DESC, name LIMIT 10;