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Intersection Over Union
The Jaccard index is a statistic used for gauging the Similarity measure, similarity and diversity index, diversity of Sample (statistics), sample sets. It is defined in general taking the ratio of two sizes (areas or volumes), the intersection size divided by the union size, also called intersection over union (IoU). It was developed by Grove Karl Gilbert in 1884 as his ratio of verification (v) and now is often called the critical success index in meteorology. It was later developed independently by Paul Jaccard, originally giving the French name (coefficient of community), and independently formulated again by Taffee Tadashi Tanimoto. Thus, it is also called Tanimoto index or Tanimoto coefficient in some fields. Overview The Jaccard index measures similarity between finite non-empty sample sets and is defined as the size of the intersection (set theory), intersection divided by the size of the Union (set theory), union of the sample sets: : J(A, B) = \frac = \frac. Note t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Object Detection
Object detection is a computer technology related to computer vision and image processing that deals with detecting instances of semantic objects of a certain class (such as humans, buildings, or cars) in digital images and videos. Well-researched domains of object detection include face detection and pedestrian detection. Object detection has applications in many areas of computer vision, including image retrieval and video surveillance. Uses It is widely used in computer vision tasks such as image annotation, vehicle counting, activity recognition, face detection, face recognition, video object co-segmentation. It is also used in tracking objects, for example tracking a ball during a football match, tracking movement of a cricket bat, or tracking a person in a video. Often, the test images are sampled from a different data distribution, making the object detection task significantly more difficult. To address the challenges caused by the domain gap between training and test ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Measure
In mathematics, a probability measure is a real-valued function defined on a set of events in a σ-algebra that satisfies Measure (mathematics), measure properties such as ''countable additivity''. The difference between a probability measure and the more general notion of measure (which includes concepts like area or volume) is that a probability measure must assign value 1 to the entire space. Intuitively, the additivity property says that the probability assigned to the union of two disjoint (mutually exclusive) events by the measure should be the sum of the probabilities of the events; for example, the value assigned to the outcome "1 or 2" in a throw of a dice should be the sum of the values assigned to the outcomes "1" and "2". Probability measures have applications in diverse fields, from physics to finance and biology. Definition The requirements for a set function \mu to be a probability measure on a σ-algebra are that: * \mu must return results in the unit interval ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geometric Interpretation Of The Probability Jaccard Index As Simplices
Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. Originally developed to model the physical world, geometry has applications in almost all sciences, and also in art, architecture, and other activities that are related to graphics. Geometry also has applications in areas of mathematics that are apparently unrelated. For example, methods of algebraic geometry are fundamental in Wiles's proof of Fermat's Last Theorem, a problem that was stated in terms of elementary arithmetic, and remained unsolved for several centuries. During t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indicator Function
In mathematics, an indicator function or a characteristic function of a subset of a set is a function that maps elements of the subset to one, and all other elements to zero. That is, if is a subset of some set , then the indicator function of is the function \mathbf_A defined by \mathbf_\!(x) = 1 if x \in A, and \mathbf_\!(x) = 0 otherwise. Other common notations are and \chi_A. The indicator function of is the Iverson bracket of the property of belonging to ; that is, \mathbf_(x) = \left x\in A\ \right For example, the Dirichlet function is the indicator function of the rational numbers as a subset of the real numbers. Definition Given an arbitrary set , the indicator function of a subset of is the function \mathbf_A \colon X \mapsto \ defined by \operatorname\mathbf_A\!( x ) = \begin 1 & \text x \in A \\ 0 & \text x \notin A \,. \end The Iverson bracket provides the equivalent notation \left x\in A\ \right/math> or that can be used instead of \mathbf_\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dummy Variable (statistics)
In regression analysis, a dummy variable (also known as indicator variable or just dummy) is one that takes a binary value (0 or 1) to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. For example, if we were studying the relationship between biological sex and income, we could use a dummy variable to represent the sex of each individual in the study. The variable could take on a value of 1 for males and 0 for females (or vice versa). In machine learning this is known as one-hot encoding. Dummy variables are commonly used in regression analysis to represent categorical variables that have more than two levels, such as education level or occupation. In this case, multiple dummy variables would be created to represent each level of the variable, and only one dummy variable would take on a value of 1 for each observation. Dummy variables are useful because they allow us to include categorical variables in our analysis, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affinity Analysis
Affinity analysis falls under the umbrella term of data mining which uncovers meaningful correlations between different entities according to their co-occurrence in a data set. In almost all systems and processes, the application of affinity analysis can extract significant knowledge about the unexpected trends . In fact, affinity analysis takes advantages of studying attributes that go together which helps uncover the hidden patterns in a big data through generating association rules. Association rules mining procedure is two-fold: first, it finds all frequent attributes in a data set and, then generates association rules satisfying some predefined criteria, support and confidence, to identify the most important relationships in the frequent itemset. The first step in the process is to count the co-occurrence of attributes in the data set. Next, a subset is created called the frequent itemset. The association rules mining takes the form of ''if'' a condition or feature (A) is prese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Matching Coefficient
The simple matching coefficient (SMC) or Rand similarity coefficient is a statistic used for comparing the similarity and diversity of sample sets. Given two objects, A and B, each with ''n'' binary attributes, SMC is defined as: \begin \text & = \frac \\ pt& = \frac \end where *M_ is the total number of attributes where ''A'' and ''B'' both have a value of 0, *M_ is the total number of attributes where ''A'' and ''B'' both have a value of 1, *M_ is the total number of attributes where ''A'' has value 0 and ''B'' has value 1, and *M_ is the total number of attributes where ''A'' has value 1 and ''B'' has value 0. The simple matching distance (SMD), which measures dissimilarity between sample sets, is given by 1 - \text. SMC is linearly related to Hamann similarity: \text = (\text+1) / 2. Also, \text = 1 - D^2/n, where D^2 is the squared Euclidean distance between the two objects (binary vectors) and is the number of attributes. The SMC is very similar to the more popular J ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multinomial Distribution
In probability theory, the multinomial distribution is a generalization of the binomial distribution. For example, it models the probability of counts for each side of a ''k''-sided die rolled ''n'' times. For ''n'' statistical independence, independent trials each of which leads to a success for exactly one of ''k'' categories, with each category having a given fixed success probability, the multinomial distribution gives the probability of any particular combination of numbers of successes for the various categories. When ''k'' is 2 and ''n'' is 1, the multinomial distribution is the Bernoulli distribution. When ''k'' is 2 and ''n'' is bigger than 1, it is the binomial distribution. When ''k'' is bigger than 2 and ''n'' is 1, it is the categorical distribution. The term "multinoulli" is sometimes used for the categorical distribution to emphasize this four-way relationship (so ''n'' determines the suffix, and ''k'' the prefix). The Bernoulli distribution models the outcome of a si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Significance
In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by \alpha, is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value, ''p''-value of a result, ''p'', is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is said to be ''statistically significant'', by the standards of the study, when p \le \alpha. The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study. In any experiment or Observational study, observation that involves drawing a Sampling (statistics), sample from a Statistical population, population, there is always the possibility that an observed effect would have occurred due to sampling error al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Numeral System
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method for representing numbers that uses only two symbols for the natural numbers: typically "0" ( zero) and "1" ( one). A ''binary number'' may also refer to a rational number that has a finite representation in the binary numeral system, that is, the quotient of an integer by a power of two. The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harrio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hash Function
A hash function is any Function (mathematics), function that can be used to map data (computing), data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called ''hash values'', ''hash codes'', (''hash/message'') ''digests'', or simply ''hashes''. The values are usually used to index a fixed-size table called a ''hash table''. Use of a hash function to index a hash table is called ''hashing'' or ''scatter-storage addressing''. Hash functions and their associated hash tables are used in data storage and retrieval applications to access data in a small and nearly constant time per retrieval. They require an amount of storage space only fractionally greater than the total space required for the data or records themselves. Hashing is a computationally- and storage-space-efficient form of data access that avoids the non-constant access time of ordered and unordered lists and s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
