How to compare the performance of two unsupervised algorithms on same data-set?












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I want to solve an anomaly detection problem on an unlabeled data-set. The only information about this problem is that the anomalies population is lower than 0.1%. It should be notice that the size of the feature vector for each sample is 40. Is there any clear way to compare the performance of unsupervised algorithms?






unsupervised-learning anomaly-detection unbalanced-classes evaluation







share|improve this question











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    5












    $begingroup$


    I want to solve an anomaly detection problem on an unlabeled data-set. The only information about this problem is that the anomalies population is lower than 0.1%. It should be notice that the size of the feature vector for each sample is 40. Is there any clear way to compare the performance of unsupervised algorithms?






    unsupervised-learning anomaly-detection unbalanced-classes evaluation







    share|improve this question











    $endgroup$















      5












      5








      5





      $begingroup$


      I want to solve an anomaly detection problem on an unlabeled data-set. The only information about this problem is that the anomalies population is lower than 0.1%. It should be notice that the size of the feature vector for each sample is 40. Is there any clear way to compare the performance of unsupervised algorithms?






      unsupervised-learning anomaly-detection unbalanced-classes evaluation







      share|improve this question











      $endgroup$




      I want to solve an anomaly detection problem on an unlabeled data-set. The only information about this problem is that the anomalies population is lower than 0.1%. It should be notice that the size of the feature vector for each sample is 40. Is there any clear way to compare the performance of unsupervised algorithms?






      unsupervised-learning anomaly-detection unbalanced-classes evaluation




      unsupervised-learning anomaly-detection unbalanced-classes evaluation






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 18 hours ago







      Alireza Zolanvari

















      asked 19 hours ago









      Alireza ZolanvariAlireza Zolanvari

      35716




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          $begingroup$

          For unlabeled data-sets, unsupervised anomaly detectors can be compared either subjectively or objectively.





          1. Subjective comparison: based on our domain-knowledge and by using some visualizations and statistics, we can compare two detectors and select the one that outputs better anomalies subjectively.




            1. Here is a well-cited survey on unsupervised anomaly detectors that compares the algorithms on labeled data-sets (with known, domain-specific outliers) using AUC, and concludes that local detectors (such as LOF,
              COF, INFLO and LoOP) are not good candidates for global anomaly detection:
              2016 A Comparative Evaluation of Unsupervised Anomaly Detection Algorithms for Multivariate Data



          2. Objective comparison: possible in theory, impossible in practice.



          Requirements for objective comparison:




          1. Anomaly definition: $x$ is an anomaly if $P(x)< t$ for some threshold $t$,


          2. Anomaly detector requirement: $D$ is an anomaly detector if for every detected $x$, $P(x)< t$,


          3. Comparing anomalies: $x_1$ is more anomalous than $x_2$ if $P(x_1)<P(x_2)$ or equivalently $r(x_1, x_2) = P(x_1) / P(x_2) < 1$,


          4. Comparing anomaly detectors: proposal $x_1$ from detector $D_1$ is better than $x_2$ from $D_2$ if $r(x_1, x_2) < 1$,



          As you can see, for qualification and comparison of two detectors we need to know $P(x)$ or at least $r(x_1, x_2)$. But if we know these quantities (which act as a judge $J$) or at least a close enough estimation of them, we have a better anomaly detector $J$ and can throw $D_1$ and $D_2$ away! We plug any observation $x$ or pair of observations $x_1$ and $x_2$ into $J$ and check which one is an anomaly or which one is more anomalous, done! So it is impossible to compare two anomaly detectors objectively unless we have a better anomaly detector (judge). So we should use a subjective comparison.






          share|improve this answer











          $endgroup$













          • $begingroup$
            Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
            $endgroup$
            – Alireza Zolanvari
            18 hours ago











          Your Answer





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          $begingroup$

          For unlabeled data-sets, unsupervised anomaly detectors can be compared either subjectively or objectively.





          1. Subjective comparison: based on our domain-knowledge and by using some visualizations and statistics, we can compare two detectors and select the one that outputs better anomalies subjectively.




            1. Here is a well-cited survey on unsupervised anomaly detectors that compares the algorithms on labeled data-sets (with known, domain-specific outliers) using AUC, and concludes that local detectors (such as LOF,
              COF, INFLO and LoOP) are not good candidates for global anomaly detection:
              2016 A Comparative Evaluation of Unsupervised Anomaly Detection Algorithms for Multivariate Data



          2. Objective comparison: possible in theory, impossible in practice.



          Requirements for objective comparison:




          1. Anomaly definition: $x$ is an anomaly if $P(x)< t$ for some threshold $t$,


          2. Anomaly detector requirement: $D$ is an anomaly detector if for every detected $x$, $P(x)< t$,


          3. Comparing anomalies: $x_1$ is more anomalous than $x_2$ if $P(x_1)<P(x_2)$ or equivalently $r(x_1, x_2) = P(x_1) / P(x_2) < 1$,


          4. Comparing anomaly detectors: proposal $x_1$ from detector $D_1$ is better than $x_2$ from $D_2$ if $r(x_1, x_2) < 1$,



          As you can see, for qualification and comparison of two detectors we need to know $P(x)$ or at least $r(x_1, x_2)$. But if we know these quantities (which act as a judge $J$) or at least a close enough estimation of them, we have a better anomaly detector $J$ and can throw $D_1$ and $D_2$ away! We plug any observation $x$ or pair of observations $x_1$ and $x_2$ into $J$ and check which one is an anomaly or which one is more anomalous, done! So it is impossible to compare two anomaly detectors objectively unless we have a better anomaly detector (judge). So we should use a subjective comparison.






          share|improve this answer











          $endgroup$













          • $begingroup$
            Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
            $endgroup$
            – Alireza Zolanvari
            18 hours ago
















          1












          $begingroup$

          For unlabeled data-sets, unsupervised anomaly detectors can be compared either subjectively or objectively.





          1. Subjective comparison: based on our domain-knowledge and by using some visualizations and statistics, we can compare two detectors and select the one that outputs better anomalies subjectively.




            1. Here is a well-cited survey on unsupervised anomaly detectors that compares the algorithms on labeled data-sets (with known, domain-specific outliers) using AUC, and concludes that local detectors (such as LOF,
              COF, INFLO and LoOP) are not good candidates for global anomaly detection:
              2016 A Comparative Evaluation of Unsupervised Anomaly Detection Algorithms for Multivariate Data



          2. Objective comparison: possible in theory, impossible in practice.



          Requirements for objective comparison:




          1. Anomaly definition: $x$ is an anomaly if $P(x)< t$ for some threshold $t$,


          2. Anomaly detector requirement: $D$ is an anomaly detector if for every detected $x$, $P(x)< t$,


          3. Comparing anomalies: $x_1$ is more anomalous than $x_2$ if $P(x_1)<P(x_2)$ or equivalently $r(x_1, x_2) = P(x_1) / P(x_2) < 1$,


          4. Comparing anomaly detectors: proposal $x_1$ from detector $D_1$ is better than $x_2$ from $D_2$ if $r(x_1, x_2) < 1$,



          As you can see, for qualification and comparison of two detectors we need to know $P(x)$ or at least $r(x_1, x_2)$. But if we know these quantities (which act as a judge $J$) or at least a close enough estimation of them, we have a better anomaly detector $J$ and can throw $D_1$ and $D_2$ away! We plug any observation $x$ or pair of observations $x_1$ and $x_2$ into $J$ and check which one is an anomaly or which one is more anomalous, done! So it is impossible to compare two anomaly detectors objectively unless we have a better anomaly detector (judge). So we should use a subjective comparison.






          share|improve this answer











          $endgroup$













          • $begingroup$
            Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
            $endgroup$
            – Alireza Zolanvari
            18 hours ago














          1












          1








          1





          $begingroup$

          For unlabeled data-sets, unsupervised anomaly detectors can be compared either subjectively or objectively.





          1. Subjective comparison: based on our domain-knowledge and by using some visualizations and statistics, we can compare two detectors and select the one that outputs better anomalies subjectively.




            1. Here is a well-cited survey on unsupervised anomaly detectors that compares the algorithms on labeled data-sets (with known, domain-specific outliers) using AUC, and concludes that local detectors (such as LOF,
              COF, INFLO and LoOP) are not good candidates for global anomaly detection:
              2016 A Comparative Evaluation of Unsupervised Anomaly Detection Algorithms for Multivariate Data



          2. Objective comparison: possible in theory, impossible in practice.



          Requirements for objective comparison:




          1. Anomaly definition: $x$ is an anomaly if $P(x)< t$ for some threshold $t$,


          2. Anomaly detector requirement: $D$ is an anomaly detector if for every detected $x$, $P(x)< t$,


          3. Comparing anomalies: $x_1$ is more anomalous than $x_2$ if $P(x_1)<P(x_2)$ or equivalently $r(x_1, x_2) = P(x_1) / P(x_2) < 1$,


          4. Comparing anomaly detectors: proposal $x_1$ from detector $D_1$ is better than $x_2$ from $D_2$ if $r(x_1, x_2) < 1$,



          As you can see, for qualification and comparison of two detectors we need to know $P(x)$ or at least $r(x_1, x_2)$. But if we know these quantities (which act as a judge $J$) or at least a close enough estimation of them, we have a better anomaly detector $J$ and can throw $D_1$ and $D_2$ away! We plug any observation $x$ or pair of observations $x_1$ and $x_2$ into $J$ and check which one is an anomaly or which one is more anomalous, done! So it is impossible to compare two anomaly detectors objectively unless we have a better anomaly detector (judge). So we should use a subjective comparison.






          share|improve this answer











          $endgroup$



          For unlabeled data-sets, unsupervised anomaly detectors can be compared either subjectively or objectively.





          1. Subjective comparison: based on our domain-knowledge and by using some visualizations and statistics, we can compare two detectors and select the one that outputs better anomalies subjectively.




            1. Here is a well-cited survey on unsupervised anomaly detectors that compares the algorithms on labeled data-sets (with known, domain-specific outliers) using AUC, and concludes that local detectors (such as LOF,
              COF, INFLO and LoOP) are not good candidates for global anomaly detection:
              2016 A Comparative Evaluation of Unsupervised Anomaly Detection Algorithms for Multivariate Data



          2. Objective comparison: possible in theory, impossible in practice.



          Requirements for objective comparison:




          1. Anomaly definition: $x$ is an anomaly if $P(x)< t$ for some threshold $t$,


          2. Anomaly detector requirement: $D$ is an anomaly detector if for every detected $x$, $P(x)< t$,


          3. Comparing anomalies: $x_1$ is more anomalous than $x_2$ if $P(x_1)<P(x_2)$ or equivalently $r(x_1, x_2) = P(x_1) / P(x_2) < 1$,


          4. Comparing anomaly detectors: proposal $x_1$ from detector $D_1$ is better than $x_2$ from $D_2$ if $r(x_1, x_2) < 1$,



          As you can see, for qualification and comparison of two detectors we need to know $P(x)$ or at least $r(x_1, x_2)$. But if we know these quantities (which act as a judge $J$) or at least a close enough estimation of them, we have a better anomaly detector $J$ and can throw $D_1$ and $D_2$ away! We plug any observation $x$ or pair of observations $x_1$ and $x_2$ into $J$ and check which one is an anomaly or which one is more anomalous, done! So it is impossible to compare two anomaly detectors objectively unless we have a better anomaly detector (judge). So we should use a subjective comparison.







          share|improve this answer














          share|improve this answer



          share|improve this answer








          edited 15 hours ago

























          answered 18 hours ago









          EsmailianEsmailian

          1,601114




          1,601114












          • $begingroup$
            Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
            $endgroup$
            – Alireza Zolanvari
            18 hours ago


















          • $begingroup$
            Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
            $endgroup$
            – Alireza Zolanvari
            18 hours ago
















          $begingroup$
          Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
          $endgroup$
          – Alireza Zolanvari
          18 hours ago




          $begingroup$
          Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
          $endgroup$
          – Alireza Zolanvari
          18 hours ago


















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