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POEuclidean Distance or cosine similarity?
 

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    <p>I was reading <a href="http://semanticvoid.com/blog/2007/02/23/similarity-measure-cosine-similarity-or-euclidean-distance-or-both/" rel="nofollow">Similarity Measure</a> and suddenly my whole world was falling apart. I have implemented a search engine using Clustering Technique. For Clustering , I used K Means which has distance measure as Euclidean distance.I also used cosine similarity to display results. I was getting amazingly accurate results.But now that i read this, what i did was normalize the document vectors and calculated the euclidean distance between two vectors and hence i have not considered magnitude anywhere.</p> <p>Am i doing something wrong ?</p> <p>Although i think that a higher term frequency would make up for a higher tf-idf value and a higher normalized tf-idf value and hence would be appropriately ranked high. Thanks</p> <p>Results( Using not normalized vectors , the figures are euclidean distances)</p> <pre><code>61.79689257425985 222Proposed Research Details.doc 144.15451315901478 and_Integrated_Assessment_of__Natural_resources_and_evolution_of_alternate_sustainable_land_management_options_for_tribal_dominated_watersheds_RRPS_24.doc 72.61392308146608 done_Developing live fencing systems for soil &amp; water conservation_NATIP-RNPS-3 SKN Math).doc 72.96125277156261 done_Management strategies for impriing rabi (SKN Math).doc 65.51734241367222 done_RPFIII_dr.dogra.doc 66.72042766100921 Evaluation of crops and their varieties (SKN Math).doc 418.8868087170988 P. VIJAYA KUMAR (DSS).doc 140.3914521621597 RPF - I PIMS-ICAR project proposal for IASRI.doc 72.95414421468679 RPF-III__Indo-US_project.doc 82.25126123574397 220Introduction and objectives.doc </code></pre> <p>Results(With normalized vectors , the figures are euclidean distances)</p> <pre><code>1.3435369899385359 222Proposed Research Details.doc 1.1277471087250086 and_Integrated_Assessment_of__Natural_resources_and_evolution_of_alternate_sustainable_land_management_options_for_tribal_dominated_watersheds_RRPS_24.doc 1.2741267093494966 done_Developing live fencing systems for soil &amp; water conservation_NATIP-RNPS-3 SKN Math).doc 1.264154265747389 done_Management strategies for impriing rabi (SKN Math).doc 1.2902191708899362 done_RPFIII_dr.dogra.doc 1.3128744973475515 Evaluation of crops and their varieties (SKN Math).doc 0.4924243033927417 P. VIJAYA KUMAR (DSS).doc 1.1747048933792805 RPF - I PIMS-ICAR project proposal for IASRI.doc 1.29150899172647 RPF-III__Indo-US_project.doc 1.318016051789028 220Introduction and objectives.doc </code></pre> <p>Results(figures are cosine similarity)</p> <pre><code>0.09745417833344654 222Proposed Research Details.doc 0.36409322938119104 and_Integrated_Assessment_of__Natural_resources_and_evolution_of_alternate_sustainable_land_management_options_for_tribal_dominated_watersheds_RRPS_24.doc 0.1883005642611103 done_Developing live fencing systems for soil &amp; water conservation_NATIP-RNPS-3 SKN Math).doc 0.2009569961963377 done_Management strategies for impriing rabi (SKN Math).doc 0.16766724553404047 done_RPFIII_dr.dogra.doc 0.13818027710720598 Evaluation of crops and their varieties (SKN Math).doc 0.8787591527140649 P. VIJAYA KUMAR (DSS).doc 0.3100342067353838 RPF - I PIMS-ICAR project proposal for IASRI.doc 0.16600226214483405 RPF-III__Indo-US_project.doc 0.13141684361322944 220Introduction and objectives.doc </code></pre> <p>The results 1 and 2 do not agree with each other while 2 and 3 strongly do. More similarity,lesser distance. The distances are taken between cluster centroid vector and the document vectors of each of the document.</p> <p>Infact the most weird result is the document with a euclidean distance of 418 and having the most similarity of 0.87. while normalized distance becomes 0.49 and agrees with similarity.</p>
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    1. COOn stats: http://stats.stackexchange.com/questions/35076/euclidean-distance-euclidean-distance-between-unit-vectors-or-cosine-similarity
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    2. COThis question has been cross-posted on [Cross Validated](http://stats.stackexchange.com/questions/35076/euclidean-distance-b-t-unit-vectors-or-cosine-similarity-where-vectors-are-docum), where it is better suited.
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