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


Clustering with Replicator Neural NetworkH2o autoencoder anomaly detection for multivariate time series datahow to compare different sets of time series dataUnsupervised Anomaly Detection in ImagesHow would I apply anomaly detection to time series data in LSTM?Anomaly detection on time seriesAnomaly detection in nominal big dataAnomaly Detection: Model Creation & ImplementationVariable Importance in unsupervised anomaly detection algorithms













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?










share|improve this question











$endgroup$











  • $begingroup$
    How do you measure performance of single model?
    $endgroup$
    – mikalai
    2 days ago










  • $begingroup$
    @mikalai It is exactly what I have asked
    $endgroup$
    – Alireza Zolanvari
    2 days ago















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?










share|improve this question











$endgroup$











  • $begingroup$
    How do you measure performance of single model?
    $endgroup$
    – mikalai
    2 days ago










  • $begingroup$
    @mikalai It is exactly what I have asked
    $endgroup$
    – Alireza Zolanvari
    2 days ago













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?










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






share|improve this question















share|improve this question













share|improve this question




share|improve this question








edited Mar 20 at 11:07







Alireza Zolanvari

















asked Mar 20 at 9:52









Alireza ZolanvariAlireza Zolanvari

35716




35716











  • $begingroup$
    How do you measure performance of single model?
    $endgroup$
    – mikalai
    2 days ago










  • $begingroup$
    @mikalai It is exactly what I have asked
    $endgroup$
    – Alireza Zolanvari
    2 days ago
















  • $begingroup$
    How do you measure performance of single model?
    $endgroup$
    – mikalai
    2 days ago










  • $begingroup$
    @mikalai It is exactly what I have asked
    $endgroup$
    – Alireza Zolanvari
    2 days ago















$begingroup$
How do you measure performance of single model?
$endgroup$
– mikalai
2 days ago




$begingroup$
How do you measure performance of single model?
$endgroup$
– mikalai
2 days ago












$begingroup$
@mikalai It is exactly what I have asked
$endgroup$
– Alireza Zolanvari
2 days ago




$begingroup$
@mikalai It is exactly what I have asked
$endgroup$
– Alireza Zolanvari
2 days ago










1 Answer
1






active

oldest

votes


















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
    Mar 20 at 11:04










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









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
    Mar 20 at 11:04















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
    Mar 20 at 11:04













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 Mar 20 at 14:21

























answered Mar 20 at 10:57









EsmailianEsmailian

1,696115




1,696115











  • $begingroup$
    Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
    $endgroup$
    – Alireza Zolanvari
    Mar 20 at 11:04
















  • $begingroup$
    Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
    $endgroup$
    – Alireza Zolanvari
    Mar 20 at 11:04















$begingroup$
Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
$endgroup$
– Alireza Zolanvari
Mar 20 at 11:04




$begingroup$
Please check the question update. Each sample has about 40 features and subjective comparison is not very practical.
$endgroup$
– Alireza Zolanvari
Mar 20 at 11:04

















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