|
F-score
In statistical analysis of binary classification and information retrieval systems, the F-score or F-measure is a measure of predictive performance. It is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all samples predicted to be positive, including those not identified correctly, and the recall is the number of true positive results divided by the number of all samples that should have been identified as positive. Precision is also known as positive predictive value, and recall is also known as sensitivity in diagnostic binary classification. The F1 score is the harmonic mean of the precision and recall. It thus symmetrically represents both precision and recall in one metric. The more generic F_\beta score applies additional weights, valuing one of precision or recall more than the other. The highest possible value of an F-score is 1.0, indicating perfect precision and recall, and the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Informedness
Youden's J statistic (also called Youden's index) is a single statistic that captures the performance of a dichotomous diagnostic test. In meteorology, this statistic is referred to as Peirce Skill Score (PSS), Hanssen–Kuipers Discriminant (HKD), or True Skill Statistic (TSS). (Bookmaker) Informedness is its generalization to the multiclass case and estimates the probability of an informed decision. Definition Youden's ''J'' statistic is : J = \text + \text -1=\text_1 + \text_0 -1 with the two right-hand quantities being sensitivity and specificity. Thus the expanded formula is: :J = \frac+\frac-1 = \frac In this equation, TP is the number of true positives, TN the number of true negatives, FP the number of false positives and FN the number of false negatives. The index was suggested by W. J. Youden in 1950 as a way of summarising the performance of a diagnostic test; however, the formula was earlier published in ''Science'' by C. S. Peirce in 1884. Its value range ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
P4-metric
P4 metric (also known as FS or Symmetric F ) enables performance evaluation of the binary classifier. It is calculated from precision, recall, specificity and NPV (negative predictive value). P4 is designed in similar way to F1 metric, however addressing the criticisms leveled against F1. It may be perceived as its extension. Like the other known metrics, P4 is a function of: TP (true positives), TN (true negatives), FP (false positives), FN (false negatives). Justification The key concept of P4 is to leverage the four key conditional probabilities: :P(+ \mid C) - the probability that the sample is positive, provided the classifier result was positive. :P(C \mid +) - the probability that the classifier result will be positive, provided the sample is positive. :P(C \mid -) - the probability that the classifier result will be negative, provided the sample is negative. :P(- \mid C) - the probability the sample is negative, provided the classifier result was negative. The main ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Precision (information Retrieval)
In pattern recognition, information retrieval, object detection and classification (machine learning), precision and recall are performance metrics that apply to data retrieved from a collection, corpus or sample space. Precision (also called positive predictive value) is the fraction of relevant instances among the retrieved instances. Written as a formula: \text = \frac Recall (also known as sensitivity) is the fraction of relevant instances that were retrieved. Written as a formula: \text = \frac Both precision and recall are therefore based on relevance. Consider a computer program for recognizing dogs (the relevant element) in a digital photograph. Upon processing a picture which contains ten cats and twelve dogs, the program identifies eight dogs. Of the eight elements identified as dogs, only five actually are dogs ( true positives), while the other three are cats ( false positives). Seven dogs were missed ( false negatives), and seven cats were correctly excl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Recall (information Retrieval)
In pattern recognition, information information retrieval, retrieval, object detection and classification (machine learning), precision and recall are performance metrics that apply to data retrieved from a data store, collection, Text_corpus, corpus or sample space. Precision (also called positive predictive value) is the fraction of relevant instances among the retrieved instances. Written as a formula: \text = \frac Recall (also known as Sensitivity and specificity, sensitivity) is the fraction of relevant instances that were retrieved. Written as a formula: \text = \frac Both precision and recall are therefore based on Relevance (information retrieval), relevance. Consider a computer program for recognizing dogs (the relevant element) in a digital photograph. Upon processing a picture which contains ten cats and twelve dogs, the program identifies eight dogs. Of the eight elements identified as dogs, only five actually are dogs (True positive, true positives), while t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sensitivity And Specificity
In medicine and statistics, sensitivity and specificity mathematically describe the accuracy of a test that reports the presence or absence of a medical condition. If individuals who have the condition are considered "positive" and those who do not are considered "negative", then sensitivity is a measure of how well a test can identify true positives and specificity is a measure of how well a test can identify true negatives: * Sensitivity (true positive rate) is the probability of a positive test result, conditioned on the individual truly being positive. * Specificity (true negative rate) is the probability of a negative test result, conditioned on the individual truly being negative. If the true status of the condition cannot be known, sensitivity and specificity can be defined relative to a " gold standard test" which is assumed correct. For all testing, both diagnoses and screening, there is usually a trade-off between sensitivity and specificity, such that higher sensiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Binary Classification
Binary classification is the task of classifying the elements of a set into one of two groups (each called ''class''). Typical binary classification problems include: * Medical testing to determine if a patient has a certain disease or not; * Quality control in industry, deciding whether a specification has been met; * In information retrieval, deciding whether a page should be in the result set of a search or not * In administration, deciding whether someone should be issued with a driving licence or not * In cognition, deciding whether an object is food or not food. When measuring the accuracy of a binary classifier, the simplest way is to count the errors. But in the real world often one of the two classes is more important, so that the number of both of the different types of errors is of interest. For example, in medical testing, detecting a disease when it is not present (a '' false positive'') is considered differently from not detecting a disease when it is present (a '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Harmonic Mean
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rate (mathematics), rates such as speeds, and is normally only used for positive arguments. The harmonic mean is the multiplicative inverse, reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f(x) = \frac. For example, the harmonic mean of 1, 4, and 4 is :\left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is :H(x_1, x_2, \ldots, x_n) = \frac = \frac. It is the reciprocal of the arithmetic mean of the reciprocals, and vice versa: :\begin H(x_1, x_2, \ldots, x_n) &= \frac, \\ A(x_1, x_2, \ldots, x_n) &= \frac, \end where the arithmetic mean is A(x_1, x_2, \ldots, x_n) = \tfrac1n \sum_^n x_i. The harmonic mean is a Schur-concave function, and is greater than or equal to the minimum of its arguments: for positive a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Multiclass Classification
In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whether an image is showing a banana, peach, orange, or an apple is a multiclass classification problem, with four possible classes (banana, peach, orange, apple), while deciding on whether an image contains an apple or not is a binary classification problem (with the two possible classes being: apple, no apple). While many classification algorithms (notably multinomial logistic regression) naturally permit the use of more than two classes, some are by nature binary algorithms; these can, however, be turned into multinomial classifiers by a variety of strategies. Multiclass classification should not be confused with multi-label classification, where multiple labels are to be predicted for each i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Matthews Correlation Coefficient
In statistics, the phi coefficient, or mean square contingency coefficient, denoted by ''φ'' or ''r''''φ'', is a measure of association for two binary variables. In machine learning, it is known as the Matthews correlation coefficient (MCC) and used as a measure of the quality of binary (two-class) classifications, introduced by biochemist Brian W. Matthews in 1975. Introduced by Karl Pearson,Cramer, H. (1946). ''Mathematical Methods of Statistics''. Princeton: Princeton University Press, p. 282 (second paragraph). https://archive.org/details/in.ernet.dli.2015.223699 and also known as the ''Yule phi coefficient'' from its introduction by Udny Yule in 1912 this measure is similar to the Pearson correlation coefficient in its interpretation. In meteorology, the phi coefficient, or its square (the latter aligning with M. H. Doolittle's original proposition from 1885), is referred to as the Doolittle Skill Score or the Doolittle Measure of Association. Definition A Pear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Harmonic Mean
In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rate (mathematics), rates such as speeds, and is normally only used for positive arguments. The harmonic mean is the multiplicative inverse, reciprocal of the arithmetic mean of the reciprocals of the numbers, that is, the generalized f-mean with f(x) = \frac. For example, the harmonic mean of 1, 4, and 4 is :\left(\frac\right)^ = \frac = \frac = 2\,. Definition The harmonic mean ''H'' of the positive real numbers x_1, x_2, \ldots, x_n is :H(x_1, x_2, \ldots, x_n) = \frac = \frac. It is the reciprocal of the arithmetic mean of the reciprocals, and vice versa: :\begin H(x_1, x_2, \ldots, x_n) &= \frac, \\ A(x_1, x_2, \ldots, x_n) &= \frac, \end where the arithmetic mean is A(x_1, x_2, \ldots, x_n) = \tfrac1n \sum_^n x_i. The harmonic mean is a Schur-concave function, and is greater than or equal to the minimum of its arguments: for positive a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Fowlkes–Mallows Index
The Fowlkes–Mallows index is an external evaluation method that is used to determine the similarity between two clusterings (clusters obtained after a clustering algorithm), and also a metric to measure confusion matrices. This measure of similarity could be either between two hierarchical clusterings or a clustering and a benchmark classification. A higher value for the Fowlkes–Mallows index indicates a greater similarity between the clusters and the benchmark classifications. It was invented by Bell Labs statisticians Edward Fowlkes and Collin Mallows in 1983. Preliminaries The Fowlkes–Mallows index, when results of two clustering algorithms are used to evaluate the results, is defined as : FM = \sqrt= \sqrt where TP is the number of true positives, FP is the number of false positives, and FN is the number of false negatives. TPR is the ''true positive rate'', also called '' sensitivity'' or ''recall'', and PPV is the ''positive predictive rate'', also known as '' p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Geometric Mean
In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean of numbers is the Nth root, th root of their product (mathematics), product, i.e., for a collection of numbers , the geometric mean is defined as : \sqrt[n]. When the collection of numbers and their geometric mean are plotted in logarithmic scale, the geometric mean is transformed into an arithmetic mean, so the geometric mean can equivalently be calculated by taking the natural logarithm of each number, finding the arithmetic mean of the logarithms, and then returning the result to linear scale using the exponential function , :\sqrt[n] = \exp \left( \frac \right). The geometric mean of two numbers is the square root of their product, for example with numbers and the geometric mean is \textstyle \sqrt = The geometric mean o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
