প্রিসিশন ও রিকল-এর উৎস দেখুন

{{Orphan|date=মে ২০২১}}

[[File:Precisionrecall.svg|thumb|350px|প্রিসিশন ও রিকল]]
[[pattern recognition|প্যাটার্ন রিকগনেশন]], [[information retrieval|ইনফরমেশন রিট্রিভাল]] ও [[binary classification|বাইনারি ক্লাসিফিকেশন]] এ '''প্রিসিশন''' ([[positive predictive value|পজেটিভ প্রোডাক্টিভ ভ্যালু]]) হলো অনেকগুলো ইন্সট্যান্সের মধ্য থেকে কাছাকাছি ইন্সট্যান্সের কিছু অংশ, অন্য দিকে '''রিকল''' (যেটি [[Sensitivity and specificity|সেন্সিটিভিটি]] নামে পরিচিত) হলো কাছাকাছি ইন্সট্যান্সের অংশ যা সকল কাছাকাছি ইন্সট্যান্স থেকে বের করা হয়। প্রিসেশন ও রিকল দুটোই [[বাস্তবতা]]<nowiki/>র উপর অনুমান ও হিসাবের উপর গঠিত।

ধরুন, একটি কুকুর শনাক্ত করার কম্পিউটার প্রোগ্রামের কথা যেখানে অনেকগুলো ছবির মধ্যে প্রোগ্রামটি ১২টি কুকুরের মধ্যে ৮টি কুকুর শনাক্ত করল আর বাকিগুলো বিড়াল। অসলে, ৮টি কুকুরের মধ্যে সত্যিকার অর্থে ৫টি কুকুর (ট্রু পজেটিভ) ছিল বাকিগুলো বিড়াল (ফলস পজেটিভ)। তাহলে প্রোগ্রামের প্রিসিশন হবে ৫/৮ যেখানে রিকল হবে ৫/১২। যখন আমরা একটি [[সার্চ ইঞ্জিন]] সার্চ করি তখন ৩০টি পেজের মধ্যে ২০টি পেজ বিষয়বস্তু সংশ্লিষ্ট, অন্যদিকে অতিরিক্ত ৪০টি বিষয় সংশ্লিষ্ট পেজ আসতে ব্যর্থ হয়। তখন প্রিসিশন হবে ২০/৩০ যেখানে রিকল ২০/৬০ = ১/৩। কাজেই, প্রিসিশন হলো "সার্চ রেজাল্ট কত ভালো সেটা" আর রিকল হলো "সার্চ রেজাল্ট কয়টা দিতে পারলো সেটা"।

[[পরিসংখ্যান]] অনুযায়ী, যদি [[নাল হাইপোথেসিস]] হয় সমস্ত আইটেম তাহলে সেগুলো ''অসম্পর্কিত'' যেখানে হাইপোথেসিস সিম্পল সাইজের নির্ধারিত সংখ্যার উপর ভিত্তি করে সিদ্ধান্ত নেয়া হয় হাইপো থেসিসটি গৃহীত হবে নাকি বর্জিত হবে, [[টাইপ ওয়ান]] ও [[টাইপ টু ইরর]] (সফল ১০০% [[সেন্সিভিটি আর স্পেসিফিসিটি]]) গুলোতে তুলনামুলকভাবে ধরা হয় সফল প্রিসিশন (ফলস পজেটিভ নেই) এবং সফল প্রিসিশন (ফলস নেগেটিভ নেই)। উপরের প্যাটার্ন রিকগনিশনের উদাহরণ অনুযায়ী ৮ - ৫ = ৩ টাইপ ওয়ান ইরর এবং ১২ - ৫ = ৭ টাইপ টু ইরর। প্রিসিশনে গুনগত মান দেখা হ্য। [[সেন্সিটিভিট আর স্পেচিফিসিটি|সেন্সিটিভিট আর স্পেসিফিসিটি]]<nowiki/>র মধ্যে সম্পর্ক হলো প্রিসিশন মোটের উপর সম্ভব্য সম্ভব্যতার উপর নির্ভর করে।

সহজ কথায়, হাই প্রিসিশন মানে হলো যখন একটি অ্যালগরিদম দূরবর্তীর চেয়ে সবথেকে কাছাকাছি ফলাফল দেয়া, অন্যদিকে হাই রিকল মানে হলে একটি অ্যালগরিদম সবথেকে কাছাকাছি ফলাফল দেবে।

==পরিচিতি==
[[Information retrieval|information retrieval (IR)]] চিত্রে, ইনস্ট্যান্সগুলো ডকুমেন্ট আর টাস্কটি উল্লিখিত সার্চ টার্মের কাছাকাছি অথবা সমান, ডকুমেন্টগুলোর একটি সেট রিটার্ন করে; প্রত্যেক ডকুমেন্টের দুটি ক্যাটাগরির একটিতে, হয় "কাছাকাছি" আর না হয় "কাছাকাছি নয়" এসাইন করে। In this case, the "relevant" documents are simply those that belong to the "relevant" category.  Recall is defined as the ''number of relevant documents'' retrieved by a search ''divided by the total number of existing relevant documents'', while precision is defined as the ''number of relevant documents'' retrieved by a search ''divided by the total number of documents retrieved'' by that search.

In a [[classification (machine learning)|classification]] task, the precision for a class is the ''number of true positives'' (i.e. the number of items correctly labeled as belonging to the positive class) ''divided by the total number of elements labeled as belonging to the positive class'' (i.e. the sum of true positives and [[Type I and type II errors|false positives]], which are items incorrectly labeled as belonging to the class).  Recall in this context is defined as the ''number of true positives divided by the total number of elements that actually belong to the positive class'' (i.e. the sum of true positives and [[Type I and type II errors|false negatives]], which are items which were not labeled as belonging to the positive class but should have been).

In information retrieval, a perfect precision score of 1.0 means that every result retrieved by a search was relevant (but says nothing about whether all relevant documents were retrieved) whereas a perfect recall score of 1.0 means that all relevant documents were retrieved by the search (but says nothing about how many irrelevant documents were also retrieved).

In a classification task, a precision score of 1.0 for a class C means that every item labeled as belonging to class C does indeed belong to class C (but says nothing about the number of items from class C that were not labeled correctly) whereas a recall of 1.0 means that every item from class C was labeled as belonging to class C (but says nothing about how many other items were incorrectly also labeled as belonging to class C).{{Clarify |post-text=Which items?|date=March 2019}}

Often, there is an inverse relationship between precision and recall, where it is possible to increase one at the cost of reducing the other. Brain surgery provides an illustrative example of the tradeoff.  Consider a brain surgeon tasked with removing a cancerous tumor from a patient’s brain. The surgeon needs to remove all of the tumor cells since any remaining cancer cells will regenerate the tumor. Conversely, the surgeon must not remove healthy brain cells since that would leave the patient with impaired brain function. The surgeon may be more liberal in the area of the brain he removes to ensure he has extracted all the cancer cells. This decision increases recall but reduces precision.  On the other hand, the surgeon may be more conservative in the brain he removes to ensure he extracts only cancer cells. This decision increases precision but reduces recall. That is to say, greater recall increases the chances of removing healthy cells (negative outcome) and increases the chances of removing all cancer cells (positive outcome).  Greater precision decreases the chances of removing healthy cells (positive outcome) but also decreases the chances of removing all cancer cells (negative outcome).

Usually, precision and recall scores are not discussed in isolation. Instead, either values for one measure are compared for a fixed level at the other measure (e.g. ''precision at a recall level of 0.75'') or both are combined into a single measure. Examples of measures that are a combination of precision and recall are the [[Precision and recall#F-measure|F-measure]] (the weighted [[harmonic mean]] of precision and recall), or the [[Matthews correlation coefficient]], which is a [[geometric mean]] of the chance-corrected variants: the [[regression coefficient]]s [[Informedness]] (DeltaP') and [[Markedness]] (DeltaP).<ref name="Powers2011" /><ref>{{সাময়িকী উদ্ধৃতি |প্রথমাংশ১=P. |শেষাংশ১=Perruchet |প্রথমাংশ২=R. |শেষাংশ২=Peereman |বছর=2004 |শিরোনাম=The exploitation of distributional information in syllable processing |সাময়িকী=J. Neurolinguistics |খণ্ড=17 |সংখ্যা নং=2–3 |পাতাসমূহ=97–119 |ডিওআই=10.1016/s0911-6044(03)00059-9}}</ref> [[Accuracy and precision#In binary classification|Accuracy]] is a weighted arithmetic mean of Precision and Inverse Precision (weighted by Bias) as well as a weighted arithmetic mean of Recall and Inverse Recall (weighted by Prevalence).<ref name="Powers2011"/> Inverse Precision and Inverse Recall are simply the Precision and Recall of the inverse problem where positive and negative labels are exchanged (for both real classes and prediction labels).  Recall and Inverse Recall, or equivalently true positive rate and false positive rate, are frequently plotted against each other as [[Receiver operating characteristic|ROC]] curves and provide a principled mechanism to explore operating point tradeoffs. Outside of Information Retrieval, the application of Recall, Precision and F-measure are argued to be flawed as they ignore the true negative cell of the contingency table, and they are easily manipulated by biasing the predictions.<ref name="Powers2011"/>  The first problem is 'solved' by using [[Accuracy and precision#In binary classification|Accuracy]] and the second problem is 'solved' by discounting the chance component and renormalizing to [[Cohen's kappa]], but this no longer affords the opportunity to explore tradeoffs graphically. However, [[Informedness]] and [[Markedness]] are Kappa-like renormalizations of Recall and Precision,<ref>{{cite conference |first=David M. W. |last=Powers |date=2012 |title=The Problem with Kappa |booktitle=Conference of the European Chapter of the Association for Computational Linguistics (EACL2012) Joint ROBUS-UNSUP Workshop}}</ref> and their geometric mean [[Matthews correlation coefficient]] thus acts like a debiased F-measure.

== সংজ্ঞা (ইনফরমেশন রিট্রিভাল কনটেক্সট)) ==

In [[information retrieval]] contexts, precision and recall are defined in terms of a set of ''retrieved documents'' (e.g. the list of documents produced by a [[web search engine]] for a query) and a set of ''relevant documents'' (e.g. the list of all documents on the internet that are relevant for a certain topic), cf. [[relevance]]. The measures were defined in {{harvtxt|Perry|Kent|Berry|1955}}.

===প্রিসিশন===

In the field of [[information retrieval]], precision is the fraction of retrieved documents that are [[Relevance (information retrieval)|relevant]] to the query:

<math display="block"> \text{precision}=\frac{|\{\text{relevant documents}\}\cap\{\text{retrieved documents}\}|}{|\{\text{retrieved documents}\}|} </math>

For example, for a text search on a set of documents, precision is the number of correct results divided by the number of all returned results.

Precision takes all retrieved documents into account, but it can also be evaluated at a given cut-off rank, considering only the topmost results returned by the system. This measure is called ''precision at n'' or ''P@n''.

Precision is used with [[recall (information retrieval)|recall]], the percent of ''all'' relevant documents that is returned by the search. The two measures are sometimes used together in the [[F1 Score]] (or f-measure) to provide a single measurement for a system.

Note that the meaning and usage of "precision" in the field of information retrieval differs from the definition of [[accuracy and precision]] within other branches of science and technology.

===রিকল===

In information retrieval, recall is the fraction of the relevant documents that are successfully retrieved.

<math display="block"> \text{recall}=\frac{|\{\text{relevant documents}\}\cap\{\text{retrieved documents}\}|}{|\{\text{relevant documents}\}|} </math>

For example, for a text search on a set of documents, recall is the number of correct results divided by the number of results that should have been returned.

In binary classification, recall is called [[Sensitivity and specificity#Sensitivity|sensitivity]]. It can be viewed as the probability that a relevant document is retrieved by the query.

It is trivial to achieve recall of 100% by returning all documents in response to any query. Therefore, recall alone is not enough but one needs to measure the number of non-relevant documents also, for example by also computing the precision.

== সংজ্ঞা (classification context) ==
For classification tasks, the terms ''true positives'', ''true negatives'', ''false positives'', and ''false negatives'' (see [[Type I and type II errors]] for definitions) compare the results of the classifier under test with trusted external judgments.  The terms ''positive'' and ''negative'' refer to the classifier's prediction (sometimes known as the ''expectation''), and the terms ''true'' and ''false'' refer to whether that prediction corresponds to the external judgment (sometimes known as the ''observation'').

Let us define an experiment from ''P'' positive instances and ''N'' negative instances for some condition. The four outcomes can be formulated in a 2×2 [[contingency table]] or [[confusion matrix]], as follows:

{{DiagnosticTesting_Diagram}}
{{Confusion matrix terms}}

<!--
{| border="0" align="center" style="text-align: center; background: #FFFFFF;"
|+
!
! colspan="2" style="background: #ddffdd;"|actual class <br/> (observation)
|-
!
|-----
|+
! rowspan="2" style="background: #ffdddd;"|predicted class <br/> (expectation)
| '''tp''' <br> (true positive) <br/> Correct result
| '''fp''' <br> (false positive) <br/> Unexpected result
|-bgcolor="#EFEFEF"
| '''fn''' <br> (false negative) <br/> Missing result
| '''tn''' <br> (true negative) <br/> Correct absence of result
|+
|}

-->
<!--Precision and recall are then defined as:<ref name="OlsonDelen">Olson, David L.; and Delen, Dursun (2008); ''Advanced Data Mining Techniques'', Springer, 1st edition (February 1, 2008), page 138, {{ISBN|3-540-76916-1}}</ref>

<math display="block">\text{Precision}=\frac{tp}{tp+fp} \, </math>

<math display="block">\text{Recall}=\frac{tp}{tp+fn} \, </math>

Recall in this context is also referred to as the true positive rate or [[Sensitivity and specificity|sensitivity]], and precision is also referred to as [[positive predictive value]] (PPV); other related measures used in classification include true negative rate and [[Accuracy and precision#In binary classification|accuracy]].<ref name="OlsonDelen" /> True negative rate is also called [[Specificity (tests)#Specificity|specificity]].

<math display="block">\text{True negative rate}=\frac{tn}{tn+fp} \, </math>

<math display="block">\text{Accuracy}=\frac{tp+tn}{tp+tn+fp+fn} \, </math>

Accuracy does not perform well with imbalanced data sets. For example, if you have 95 negative and 5 positive samples, classifying all as negative gives 0.95 accuracy score. Balanced Accuracy <ref>{{সাময়িকী উদ্ধৃতি|শেষাংশ=Mower|প্রথমাংশ=Jeffrey P.|তারিখ=2005-04-12|শিরোনাম=PREP-Mt: predictive RNA editor for plant mitochondrial genes|সাময়িকী=BMC Bioinformatics|খণ্ড=6|পাতাসমূহ=96|ডিওআই=10.1186/1471-2105-6-96|issn=1471-2105|pmc=1087475|pmid=15826309}}</ref> (bACC) overcomes this problem, by normalizing true positive and true negative predictions by the number of positive and negative samples, respectively, and divides their sum into two. This is equivalent to the following formula:
  
<math display="block">\text{Balanced Accuracy}= \frac{TPR + TNR}{2}\, </math>

Regarding the previous example (95 negative and 5 positive samples), classifying all as negative gives 0.5 balanced accuracy score out of the maximum bACC one, which is equivalent to the expected value of a random guess of a balanced data. Balanced Accuracy is suggested to use to measure how accurate is the overall performance of a model is, considering both positive and negative classes without worrying about the  imbalance of a data set. Since most of the real data sets are imbalanced, Balanced Accuracy metric is suggested instead of Accuracy metric.

Additionally, the predicted positive condition rate (PPCR) identifies the percentage of the total population that is flagged; for example, for a search engine returning 30 results (retrieved documents) out of 1,000,000 documents, the PPCR is 0.003%. <math display="block">\text{Predicted positive condition rate}=\frac{tp+fp}{tp+fp+tn+fn} \, </math>

== Probabilistic interpretation ==

It is possible to interpret precision and recall not as ratios but as probabilities:

* Precision is the probability that a (randomly selected) retrieved document is relevant.
* Recall is the probability that a (randomly selected) relevant document is retrieved in a search.

Note that the random selection refers to a uniform distribution over the appropriate pool of documents; i.e. by ''randomly selected retrieved document'', we mean selecting a document from the set of retrieved documents in a random fashion. The random selection should be such that all documents in the set are equally likely to be selected.

Note that, in a typical classification system, the probability that a retrieved document is relevant depends on the document. The above interpretation extends to that scenario also (needs explanation).

Another interpretation for precision and recall is as follows. Precision is the average probability of relevant retrieval. Recall is the average probability of complete retrieval. Here we average over multiple retrieval queries.

== এফ-মেজার ==
{{মূল নিবন্ধ|F1 score}}
A measure that combines precision and recall is the [[harmonic mean]] of precision and recall, the traditional F-measure or balanced F-score:

<math display="block">F = 2 \cdot \frac{\mathrm{precision} \cdot \mathrm{recall}}{ \mathrm{precision} + \mathrm{recall}}</math>

This measure is approximately the average of the two when they are close, and is more generally the [[harmonic mean]], which, for the case of two numbers, coincides with the square of the [[geometric mean]] divided by the [[arithmetic mean]]. There are several reasons that the F-score can be criticized in particular circumstances due to its bias as an evaluation metric.<ref name="Powers2011" /> This is also known as the <math>F_1</math> measure, because recall and precision are evenly weighted.

It is a special case of the general <math>F_\beta</math> measure (for non-negative real values of&nbsp;<math>\beta</math>):

<math display="block">F_\beta = (1 + \beta^2) \cdot \frac{\mathrm{precision} \cdot \mathrm{recall} }{ \beta^2 \cdot \mathrm{precision} + \mathrm{recall}}</math>

Two other commonly used <math>F</math> measures are the <math>F_2</math> measure, which weights recall higher than precision, and the <math>F_{0.5}</math> measure, which puts more emphasis on precision than recall.

The F-measure was derived by van Rijsbergen (1979) so that <math>F_\beta</math> "measures the effectiveness of retrieval with respect to a user who attaches <math>\beta</math> times as much importance to recall as precision".  It is based on van Rijsbergen's effectiveness measure <math>E_{\alpha} = 1 - \frac{1}{\frac{\alpha}{P} + \frac{1-\alpha}{R}}</math>, the second term being the weighted harmonic mean of precision and recall with weights <math>(\alpha, 1-\alpha)</math>.  Their relationship is <math>F_\beta = 1 - E_{\alpha}</math> where <math>\alpha=\frac{1}{1 + \beta^2}</math>.

==Limitations as goals==
There are other parameters and strategies for performance metric of information retrieval system, such as the area under the ROC curve (AUC).<ref>Zygmunt Zając. What you wanted to know about AUC.  http://fastml.com/what-you-wanted-to-know-about-auc/</ref>

For [[web document]] retrieval, if the user's objectives are not clear, the  precision and recall can't be optimized{{Disputed inline|date=October 2017}}. As summarized by Lopresti,<ref>Lopresti, Daniel (2001); [http://www.csc.liv.ac.uk/~wda2001/Panel_Presentations/Lopresti/Lopresti_files/v3_document.htm ''WDA 2001 panel'']</ref>
{{quote|[[Browsing]] is a comfortable and powerful paradigm (the [[Serendipity|serendipity effect]]).
* Search results don't have to be very good. {{Disputed inline|date=October 2017}}
* Recall?    Not important (as long as you get at least some good hits).{{Disputed inline|date=October 2017}}
* Precision? Not important (as long as at least some of the hits on the first page you return are good).{{Disputed inline|date=October 2017}}}}

==See also==
* [[Uncertainty coefficient]], also called ''proficiency''
* [[Sensitivity and specificity]]
-->

==তথ্যসূত্র==
{{সূত্র তালিকা}}

{{refbegin}}
* Baeza-Yates, Ricardo; Ribeiro-Neto, Berthier (1999). ''Modern Information Retrieval''. New York, NY: ACM Press, Addison-Wesley, Seiten 75 ff. {{ISBN|0-201-39829-X}}
* Hjørland, Birger (2010); ''The foundation of the concept of relevance'', Journal of the American Society for Information Science and Technology, 61(2), 217-237
* [[John Makhoul|Makhoul, John]]; Kubala, Francis; Schwartz, Richard; and Weischedel, Ralph (1999); [http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.27.4637 ''Performance measures for information extraction''], in ''Proceedings of DARPA Broadcast News Workshop, Herndon, VA, February 1999''
* {{সাময়িকী উদ্ধৃতি |শিরোনাম=Machine literature searching X. Machine language; factors underlying its design and development |ইউআরএল=https://archive.org/details/sim_american-documentation_1955-10_6_4/page/242 |সাময়িকী=American Documentation |খণ্ড=6 |সংখ্যা নং=4 |পাতাসমূহ=242 |বছর=1955 |ডিওআই=10.1002/asi.5090060411|শেষাংশ১=Perry |প্রথমাংশ১=James W. |শেষাংশ২=Kent |প্রথমাংশ২=Allen |শেষাংশ৩=Berry |প্রথমাংশ৩=Madeline M. }}
* van Rijsbergen, Cornelis Joost "Keith" (1979); ''Information Retrieval'', London, GB; Boston, MA: Butterworth, 2nd Edition, {{ISBN|0-408-70929-4}}
{{refend}}

==বহিঃসংযোগ==
* [http://www.dcs.gla.ac.uk/Keith/Preface.html Information Retrieval – C. J. van Rijsbergen 1979]
* [http://www.text-analytics101.com/2014/10/computing-precision-and-recall-for.html Computing Precision and Recall for a Multi-class Classification Problem]

[[বিষয়শ্রেণী:Information retrieval evaluation]]
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