Training a classifier when some of the features are unknown Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern) 2019 Moderator Election Q&A - Questionnaire 2019 Community Moderator Election ResultsClassifier ChainsHow to improve an existing (trained) classifier?What is effect when I set up some self defined predisctor variables?Why Matlab neural network classification returns decimal values on prediction dataset?Fitting and transforming text data in training, testing, and validation setsHow to quantify the performance of the classifier (multi-class SVM) using the test data?How do I control for some patients providing multiple samples in my training data?Training and Test setTraining a convolutional neural network for image denoising in MatlabDealing with correlated features when calculating permutation importance

grandmas drink with lemon juice

Can a non-EU citizen traveling with me come with me through the EU passport line?

Biased dice probability question

Typsetting diagram chases (with TikZ?)

What do you call a plan that's an alternative plan in case your initial plan fails?

Stopping real property loss from eroding embankment

How is simplicity better than precision and clarity in prose?

What computer would be fastest for Mathematica Home Edition?

Windows 10: How to Lock (not sleep) laptop on lid close?

Slither Like a Snake

Using "nakedly" instead of "with nothing on"

Was credit for the black hole image misattributed?

Can I add database to AWS RDS MySQL without creating new instance?

Jazz greats knew nothing of modes. Why are they used to improvise on standards?

90's book, teen horror

Can I throw a longsword at someone?

What did Darwin mean by 'squib' here?

When communicating altitude with a '9' in it, should it be pronounced "nine hundred" or "niner hundred"?

Mortgage adviser recommends a longer term than necessary combined with overpayments

How does modal jazz use chord progressions?

Statistical model of ligand substitution

What can I do if my MacBook isn’t charging but already ran out?

Is there a service that would inform me whenever a new direct route is scheduled from a given airport?

Direct Experience of Meditation



Training a classifier when some of the features are unknown



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)
2019 Moderator Election Q&A - Questionnaire
2019 Community Moderator Election ResultsClassifier ChainsHow to improve an existing (trained) classifier?What is effect when I set up some self defined predisctor variables?Why Matlab neural network classification returns decimal values on prediction dataset?Fitting and transforming text data in training, testing, and validation setsHow to quantify the performance of the classifier (multi-class SVM) using the test data?How do I control for some patients providing multiple samples in my training data?Training and Test setTraining a convolutional neural network for image denoising in MatlabDealing with correlated features when calculating permutation importance










2












$begingroup$


I am training a classifier in Matlab with a dataset that I created.
Unfortunately some of the features in the dataset were not recorded.



I currently have the unknown features set as -99999.



So, for example my dataset looks something like this:



class1: 10 1 12 -99999 6 8
class1: 11 2 13 7 6 10
...
class2: 5 -99999 4 3 2 -99999
class2: -99999 16 4 3 1 8
...
class3: 18 2 11 22 7 5
class3: 19 1 9 25 7 5
...


and so on, where the -99999 are the places where the features werent able to be measured. In this case, each class has 6 features.



I don't want to bias my classifier with the unknown features so I thought it would be a good idea to set the unknowns to -99999 so it would be way out of the range of normal features.



I tested the classifier with the -99999's and it was 78% accurate.
Then I changed the -99999 to 0's and tested the classifier again, this time it was 91% accurate.



So my question is, what is a general rule for training a classifier when some of the features were not recorded? Was I right to assume setting the unknowns to a very high negative value? But why was it more accurate when I set the unknowns to 0s?



Thanks for reading!










share|improve this question









New contributor




Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$
















    2












    $begingroup$


    I am training a classifier in Matlab with a dataset that I created.
    Unfortunately some of the features in the dataset were not recorded.



    I currently have the unknown features set as -99999.



    So, for example my dataset looks something like this:



    class1: 10 1 12 -99999 6 8
    class1: 11 2 13 7 6 10
    ...
    class2: 5 -99999 4 3 2 -99999
    class2: -99999 16 4 3 1 8
    ...
    class3: 18 2 11 22 7 5
    class3: 19 1 9 25 7 5
    ...


    and so on, where the -99999 are the places where the features werent able to be measured. In this case, each class has 6 features.



    I don't want to bias my classifier with the unknown features so I thought it would be a good idea to set the unknowns to -99999 so it would be way out of the range of normal features.



    I tested the classifier with the -99999's and it was 78% accurate.
    Then I changed the -99999 to 0's and tested the classifier again, this time it was 91% accurate.



    So my question is, what is a general rule for training a classifier when some of the features were not recorded? Was I right to assume setting the unknowns to a very high negative value? But why was it more accurate when I set the unknowns to 0s?



    Thanks for reading!










    share|improve this question









    New contributor




    Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
    Check out our Code of Conduct.







    $endgroup$














      2












      2








      2





      $begingroup$


      I am training a classifier in Matlab with a dataset that I created.
      Unfortunately some of the features in the dataset were not recorded.



      I currently have the unknown features set as -99999.



      So, for example my dataset looks something like this:



      class1: 10 1 12 -99999 6 8
      class1: 11 2 13 7 6 10
      ...
      class2: 5 -99999 4 3 2 -99999
      class2: -99999 16 4 3 1 8
      ...
      class3: 18 2 11 22 7 5
      class3: 19 1 9 25 7 5
      ...


      and so on, where the -99999 are the places where the features werent able to be measured. In this case, each class has 6 features.



      I don't want to bias my classifier with the unknown features so I thought it would be a good idea to set the unknowns to -99999 so it would be way out of the range of normal features.



      I tested the classifier with the -99999's and it was 78% accurate.
      Then I changed the -99999 to 0's and tested the classifier again, this time it was 91% accurate.



      So my question is, what is a general rule for training a classifier when some of the features were not recorded? Was I right to assume setting the unknowns to a very high negative value? But why was it more accurate when I set the unknowns to 0s?



      Thanks for reading!










      share|improve this question









      New contributor




      Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.







      $endgroup$




      I am training a classifier in Matlab with a dataset that I created.
      Unfortunately some of the features in the dataset were not recorded.



      I currently have the unknown features set as -99999.



      So, for example my dataset looks something like this:



      class1: 10 1 12 -99999 6 8
      class1: 11 2 13 7 6 10
      ...
      class2: 5 -99999 4 3 2 -99999
      class2: -99999 16 4 3 1 8
      ...
      class3: 18 2 11 22 7 5
      class3: 19 1 9 25 7 5
      ...


      and so on, where the -99999 are the places where the features werent able to be measured. In this case, each class has 6 features.



      I don't want to bias my classifier with the unknown features so I thought it would be a good idea to set the unknowns to -99999 so it would be way out of the range of normal features.



      I tested the classifier with the -99999's and it was 78% accurate.
      Then I changed the -99999 to 0's and tested the classifier again, this time it was 91% accurate.



      So my question is, what is a general rule for training a classifier when some of the features were not recorded? Was I right to assume setting the unknowns to a very high negative value? But why was it more accurate when I set the unknowns to 0s?



      Thanks for reading!







      machine-learning classification dataset matlab






      share|improve this question









      New contributor




      Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.











      share|improve this question









      New contributor




      Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      share|improve this question




      share|improve this question








      edited 2 hours ago







      Darklink9110













      New contributor




      Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.









      asked 2 hours ago









      Darklink9110Darklink9110

      113




      113




      New contributor




      Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.





      New contributor





      Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.






      Darklink9110 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
      Check out our Code of Conduct.




















          1 Answer
          1






          active

          oldest

          votes


















          1












          $begingroup$

          Welcome to Data Science SE!



          Well, we say that most of our jobs is to wrangle with data, and that is because data is usually trying to deceive us... jokes aside:



          You have a missing data problem



          that means your have to clean your data and fill those missing values. To perform this cleaning process your must take the most classic statistician inside of you and ask:



          • Why is this data missing?

          • How much data is missing?

          There are many reasons for a specific information to be unavailable. This will demand you to make assumptions and decide how to deal with this.



          Jeff Sauro posted at MeasuringU: 7 Ways to Handle Missing Data, some which I list here:



          • Delete corrupted samples:

          If you have a large dataset and there is not much data missing, you can simply remove those corrupted data points and go on with life



          • Recover the values:

          Some problems will allow you to go back and get missing information.



          We usually ain't that lucky, then you can



          • Educated Guessing:

          Sometimes, you can infer what would be the feature value by simply looking their pears. That is a bit arbitrary but it might work.



          • Average:

          This is the most common approach, simply use the average of that value whenever it is missing. This might artificially reduce your variance but so does using 0 or -9999... for every missing value.



          • Regression Substitution:

          You can use a multiple regression to infer the missing value from the available values for each candidate.



          Some references on missing data are:



          • Allison, Paul D. 2001. Missing Data. Sage University Papers
            Series on Quantitative Applications in the Social Sciences.
            Thousand Oaks: Sage.

          • Enders, Craig. 2010. Applied Missing Data Analysis.
            Guilford Press: New York.

          • Little, Roderick J., Donald Rubin. 2002. Statistical Analysis
            with Missing Data. John Wiley & Sons, Inc: Hoboken.

          • Schafer, Joseph L., John W. Graham. 2002. “Missing Data:
            Our View of the State of the Art.” Psychological Methods.


          About your experiment:



          Adding -99... is creating outliers and that bit of information is heavy (numerically speaking, it is huge) and will affect parameter tuning. For example, suppose you have this data:



          | Feature1 | Feature2 | 
          |----------|----------|
          | 0 | 8 |
          | -1 | 7 |
          | 1 | - |
          | - | 8 |


          And you try filling the missing values with -99, now try to fit a linear regression trough the data. Can you see that you don't be able to fit it properly?



          The brown line



          The line won't fit, and this will yield bad performance.



          Adding 0 values on the other hand will give a slightly better line:



          The yellow line



          It is still not good, but slightly better since the scale of the parameters will be more realistic.



          Now, using average, is this case will give you even better curve, but using regression will give you a perfect fitting line:



          The perfect line



          Note: I need to remake those images, but these should do until I have the time for it.






          share|improve this answer











          $endgroup$













            Your Answer








            StackExchange.ready(function()
            var channelOptions =
            tags: "".split(" "),
            id: "557"
            ;
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function()
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled)
            StackExchange.using("snippets", function()
            createEditor();
            );

            else
            createEditor();

            );

            function createEditor()
            StackExchange.prepareEditor(
            heartbeatType: 'answer',
            autoActivateHeartbeat: false,
            convertImagesToLinks: false,
            noModals: true,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: null,
            bindNavPrevention: true,
            postfix: "",
            imageUploader:
            brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
            contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
            allowUrls: true
            ,
            onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            );



            );






            Darklink9110 is a new contributor. Be nice, and check out our Code of Conduct.









            draft saved

            draft discarded


















            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdatascience.stackexchange.com%2fquestions%2f49298%2ftraining-a-classifier-when-some-of-the-features-are-unknown%23new-answer', 'question_page');

            );

            Post as a guest















            Required, but never shown

























            1 Answer
            1






            active

            oldest

            votes








            1 Answer
            1






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes









            1












            $begingroup$

            Welcome to Data Science SE!



            Well, we say that most of our jobs is to wrangle with data, and that is because data is usually trying to deceive us... jokes aside:



            You have a missing data problem



            that means your have to clean your data and fill those missing values. To perform this cleaning process your must take the most classic statistician inside of you and ask:



            • Why is this data missing?

            • How much data is missing?

            There are many reasons for a specific information to be unavailable. This will demand you to make assumptions and decide how to deal with this.



            Jeff Sauro posted at MeasuringU: 7 Ways to Handle Missing Data, some which I list here:



            • Delete corrupted samples:

            If you have a large dataset and there is not much data missing, you can simply remove those corrupted data points and go on with life



            • Recover the values:

            Some problems will allow you to go back and get missing information.



            We usually ain't that lucky, then you can



            • Educated Guessing:

            Sometimes, you can infer what would be the feature value by simply looking their pears. That is a bit arbitrary but it might work.



            • Average:

            This is the most common approach, simply use the average of that value whenever it is missing. This might artificially reduce your variance but so does using 0 or -9999... for every missing value.



            • Regression Substitution:

            You can use a multiple regression to infer the missing value from the available values for each candidate.



            Some references on missing data are:



            • Allison, Paul D. 2001. Missing Data. Sage University Papers
              Series on Quantitative Applications in the Social Sciences.
              Thousand Oaks: Sage.

            • Enders, Craig. 2010. Applied Missing Data Analysis.
              Guilford Press: New York.

            • Little, Roderick J., Donald Rubin. 2002. Statistical Analysis
              with Missing Data. John Wiley & Sons, Inc: Hoboken.

            • Schafer, Joseph L., John W. Graham. 2002. “Missing Data:
              Our View of the State of the Art.” Psychological Methods.


            About your experiment:



            Adding -99... is creating outliers and that bit of information is heavy (numerically speaking, it is huge) and will affect parameter tuning. For example, suppose you have this data:



            | Feature1 | Feature2 | 
            |----------|----------|
            | 0 | 8 |
            | -1 | 7 |
            | 1 | - |
            | - | 8 |


            And you try filling the missing values with -99, now try to fit a linear regression trough the data. Can you see that you don't be able to fit it properly?



            The brown line



            The line won't fit, and this will yield bad performance.



            Adding 0 values on the other hand will give a slightly better line:



            The yellow line



            It is still not good, but slightly better since the scale of the parameters will be more realistic.



            Now, using average, is this case will give you even better curve, but using regression will give you a perfect fitting line:



            The perfect line



            Note: I need to remake those images, but these should do until I have the time for it.






            share|improve this answer











            $endgroup$

















              1












              $begingroup$

              Welcome to Data Science SE!



              Well, we say that most of our jobs is to wrangle with data, and that is because data is usually trying to deceive us... jokes aside:



              You have a missing data problem



              that means your have to clean your data and fill those missing values. To perform this cleaning process your must take the most classic statistician inside of you and ask:



              • Why is this data missing?

              • How much data is missing?

              There are many reasons for a specific information to be unavailable. This will demand you to make assumptions and decide how to deal with this.



              Jeff Sauro posted at MeasuringU: 7 Ways to Handle Missing Data, some which I list here:



              • Delete corrupted samples:

              If you have a large dataset and there is not much data missing, you can simply remove those corrupted data points and go on with life



              • Recover the values:

              Some problems will allow you to go back and get missing information.



              We usually ain't that lucky, then you can



              • Educated Guessing:

              Sometimes, you can infer what would be the feature value by simply looking their pears. That is a bit arbitrary but it might work.



              • Average:

              This is the most common approach, simply use the average of that value whenever it is missing. This might artificially reduce your variance but so does using 0 or -9999... for every missing value.



              • Regression Substitution:

              You can use a multiple regression to infer the missing value from the available values for each candidate.



              Some references on missing data are:



              • Allison, Paul D. 2001. Missing Data. Sage University Papers
                Series on Quantitative Applications in the Social Sciences.
                Thousand Oaks: Sage.

              • Enders, Craig. 2010. Applied Missing Data Analysis.
                Guilford Press: New York.

              • Little, Roderick J., Donald Rubin. 2002. Statistical Analysis
                with Missing Data. John Wiley & Sons, Inc: Hoboken.

              • Schafer, Joseph L., John W. Graham. 2002. “Missing Data:
                Our View of the State of the Art.” Psychological Methods.


              About your experiment:



              Adding -99... is creating outliers and that bit of information is heavy (numerically speaking, it is huge) and will affect parameter tuning. For example, suppose you have this data:



              | Feature1 | Feature2 | 
              |----------|----------|
              | 0 | 8 |
              | -1 | 7 |
              | 1 | - |
              | - | 8 |


              And you try filling the missing values with -99, now try to fit a linear regression trough the data. Can you see that you don't be able to fit it properly?



              The brown line



              The line won't fit, and this will yield bad performance.



              Adding 0 values on the other hand will give a slightly better line:



              The yellow line



              It is still not good, but slightly better since the scale of the parameters will be more realistic.



              Now, using average, is this case will give you even better curve, but using regression will give you a perfect fitting line:



              The perfect line



              Note: I need to remake those images, but these should do until I have the time for it.






              share|improve this answer











              $endgroup$















                1












                1








                1





                $begingroup$

                Welcome to Data Science SE!



                Well, we say that most of our jobs is to wrangle with data, and that is because data is usually trying to deceive us... jokes aside:



                You have a missing data problem



                that means your have to clean your data and fill those missing values. To perform this cleaning process your must take the most classic statistician inside of you and ask:



                • Why is this data missing?

                • How much data is missing?

                There are many reasons for a specific information to be unavailable. This will demand you to make assumptions and decide how to deal with this.



                Jeff Sauro posted at MeasuringU: 7 Ways to Handle Missing Data, some which I list here:



                • Delete corrupted samples:

                If you have a large dataset and there is not much data missing, you can simply remove those corrupted data points and go on with life



                • Recover the values:

                Some problems will allow you to go back and get missing information.



                We usually ain't that lucky, then you can



                • Educated Guessing:

                Sometimes, you can infer what would be the feature value by simply looking their pears. That is a bit arbitrary but it might work.



                • Average:

                This is the most common approach, simply use the average of that value whenever it is missing. This might artificially reduce your variance but so does using 0 or -9999... for every missing value.



                • Regression Substitution:

                You can use a multiple regression to infer the missing value from the available values for each candidate.



                Some references on missing data are:



                • Allison, Paul D. 2001. Missing Data. Sage University Papers
                  Series on Quantitative Applications in the Social Sciences.
                  Thousand Oaks: Sage.

                • Enders, Craig. 2010. Applied Missing Data Analysis.
                  Guilford Press: New York.

                • Little, Roderick J., Donald Rubin. 2002. Statistical Analysis
                  with Missing Data. John Wiley & Sons, Inc: Hoboken.

                • Schafer, Joseph L., John W. Graham. 2002. “Missing Data:
                  Our View of the State of the Art.” Psychological Methods.


                About your experiment:



                Adding -99... is creating outliers and that bit of information is heavy (numerically speaking, it is huge) and will affect parameter tuning. For example, suppose you have this data:



                | Feature1 | Feature2 | 
                |----------|----------|
                | 0 | 8 |
                | -1 | 7 |
                | 1 | - |
                | - | 8 |


                And you try filling the missing values with -99, now try to fit a linear regression trough the data. Can you see that you don't be able to fit it properly?



                The brown line



                The line won't fit, and this will yield bad performance.



                Adding 0 values on the other hand will give a slightly better line:



                The yellow line



                It is still not good, but slightly better since the scale of the parameters will be more realistic.



                Now, using average, is this case will give you even better curve, but using regression will give you a perfect fitting line:



                The perfect line



                Note: I need to remake those images, but these should do until I have the time for it.






                share|improve this answer











                $endgroup$



                Welcome to Data Science SE!



                Well, we say that most of our jobs is to wrangle with data, and that is because data is usually trying to deceive us... jokes aside:



                You have a missing data problem



                that means your have to clean your data and fill those missing values. To perform this cleaning process your must take the most classic statistician inside of you and ask:



                • Why is this data missing?

                • How much data is missing?

                There are many reasons for a specific information to be unavailable. This will demand you to make assumptions and decide how to deal with this.



                Jeff Sauro posted at MeasuringU: 7 Ways to Handle Missing Data, some which I list here:



                • Delete corrupted samples:

                If you have a large dataset and there is not much data missing, you can simply remove those corrupted data points and go on with life



                • Recover the values:

                Some problems will allow you to go back and get missing information.



                We usually ain't that lucky, then you can



                • Educated Guessing:

                Sometimes, you can infer what would be the feature value by simply looking their pears. That is a bit arbitrary but it might work.



                • Average:

                This is the most common approach, simply use the average of that value whenever it is missing. This might artificially reduce your variance but so does using 0 or -9999... for every missing value.



                • Regression Substitution:

                You can use a multiple regression to infer the missing value from the available values for each candidate.



                Some references on missing data are:



                • Allison, Paul D. 2001. Missing Data. Sage University Papers
                  Series on Quantitative Applications in the Social Sciences.
                  Thousand Oaks: Sage.

                • Enders, Craig. 2010. Applied Missing Data Analysis.
                  Guilford Press: New York.

                • Little, Roderick J., Donald Rubin. 2002. Statistical Analysis
                  with Missing Data. John Wiley & Sons, Inc: Hoboken.

                • Schafer, Joseph L., John W. Graham. 2002. “Missing Data:
                  Our View of the State of the Art.” Psychological Methods.


                About your experiment:



                Adding -99... is creating outliers and that bit of information is heavy (numerically speaking, it is huge) and will affect parameter tuning. For example, suppose you have this data:



                | Feature1 | Feature2 | 
                |----------|----------|
                | 0 | 8 |
                | -1 | 7 |
                | 1 | - |
                | - | 8 |


                And you try filling the missing values with -99, now try to fit a linear regression trough the data. Can you see that you don't be able to fit it properly?



                The brown line



                The line won't fit, and this will yield bad performance.



                Adding 0 values on the other hand will give a slightly better line:



                The yellow line



                It is still not good, but slightly better since the scale of the parameters will be more realistic.



                Now, using average, is this case will give you even better curve, but using regression will give you a perfect fitting line:



                The perfect line



                Note: I need to remake those images, but these should do until I have the time for it.







                share|improve this answer














                share|improve this answer



                share|improve this answer








                edited 1 hour ago

























                answered 2 hours ago









                Pedro Henrique MonfortePedro Henrique Monforte

                466114




                466114




















                    Darklink9110 is a new contributor. Be nice, and check out our Code of Conduct.









                    draft saved

                    draft discarded


















                    Darklink9110 is a new contributor. Be nice, and check out our Code of Conduct.












                    Darklink9110 is a new contributor. Be nice, and check out our Code of Conduct.











                    Darklink9110 is a new contributor. Be nice, and check out our Code of Conduct.














                    Thanks for contributing an answer to Data Science Stack Exchange!


                    • Please be sure to answer the question. Provide details and share your research!

                    But avoid


                    • Asking for help, clarification, or responding to other answers.

                    • Making statements based on opinion; back them up with references or personal experience.

                    Use MathJax to format equations. MathJax reference.


                    To learn more, see our tips on writing great answers.




                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function ()
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fdatascience.stackexchange.com%2fquestions%2f49298%2ftraining-a-classifier-when-some-of-the-features-are-unknown%23new-answer', 'question_page');

                    );

                    Post as a guest















                    Required, but never shown





















































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown

































                    Required, but never shown














                    Required, but never shown












                    Required, but never shown







                    Required, but never shown







                    Popular posts from this blog

                    名間水力發電廠 目录 沿革 設施 鄰近設施 註釋 外部連結 导航菜单23°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.7113923°50′10″N 120°42′41″E / 23.83611°N 120.71139°E / 23.83611; 120.71139計畫概要原始内容臺灣第一座BOT 模式開發的水力發電廠-名間水力電廠名間水力發電廠 水利署首件BOT案原始内容《小檔案》名間電廠 首座BOT水力發電廠原始内容名間電廠BOT - 經濟部水利署中區水資源局

                    Prove that NP is closed under karp reduction?Space(n) not closed under Karp reductions - what about NTime(n)?Class P is closed under rotation?Prove or disprove that $NL$ is closed under polynomial many-one reductions$mathbfNC_2$ is closed under log-space reductionOn Karp reductionwhen can I know if a class (complexity) is closed under reduction (cook/karp)Check if class $PSPACE$ is closed under polyonomially space reductionIs NPSPACE also closed under polynomial-time reduction and under log-space reduction?Prove PSPACE is closed under complement?Prove PSPACE is closed under union?

                    Is my guitar’s action too high? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 23, 2019 at 23:30 UTC (7:30pm US/Eastern)Strings too stiff on a recently purchased acoustic guitar | Cort AD880CEIs the action of my guitar really high?Μy little finger is too weak to play guitarWith guitar, how long should I give my fingers to strengthen / callous?When playing a fret the guitar sounds mutedPlaying (Barre) chords up the guitar neckI think my guitar strings are wound too tight and I can't play barre chordsF barre chord on an SG guitarHow to find to the right strings of a barre chord by feel?High action on higher fret on my steel acoustic guitar