Obsessive–compulsive personality disorderObsessive–compulsive personality disorder (OCPD) is a cluster C personality disorder marked by a spectrum of obsessions with rules, lists, schedules, and order, among other things. Symptoms are usually present by the time a person reaches adulthood, and are visible in a variety of situations. The cause of OCPD is thought to involve a combination of genetic and environmental factors, namely problems with attachment. Obsessive–compulsive personality disorder is distinct from obsessive–compulsive disorder (OCD), and the relation between the two is contentious.
Antisocial personality disorderAntisocial personality disorder (ASPD or APD) is a personality disorder characterized by a limited capacity for empathy and a long-term pattern of disregard or violation of the rights of others. Other notable symptoms include impulsivity and reckless behavior (including substance abuse), a lack of remorse after hurting others, deceitfulness, irresponsibility, and aggressive behavior. Symptoms of ASPD must be present before the age of 15 to receive a diagnosis.
Borderline personality disorderBorderline personality disorder (BPD), also known as emotionally unstable personality disorder (EUPD), is a personality disorder characterized by a long-term pattern of intense and unstable interpersonal relationships, distorted sense of self, and strong emotional reactions. Those affected often engage in self-harm and other dangerous behaviors, often due to their difficulty with returning their emotional level to a healthy or normal baseline. They may also struggle with a feeling of emptiness, fear of abandonment, and dissociation.
Dependent personality disorderDependent personality disorder (DPD) is characterized by a pervasive psychological dependence on other people. This personality disorder is a long-term condition in which people depend on others to meet their emotional and physical needs, with only a minority achieving normal levels of independence. Dependent personality disorder is a cluster C personality disorder, which is characterized by excessive fear and anxiety. It begins prior to early adulthood, and it is present in a variety of contexts and is associated with inadequate functioning.
Metric spaceIn mathematics, a metric space is a set together with a notion of distance between its elements, usually called points. The distance is measured by a function called a metric or distance function. Metric spaces are the most general setting for studying many of the concepts of mathematical analysis and geometry. The most familiar example of a metric space is 3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic plane.
Correlation clusteringClustering is the problem of partitioning data points into groups based on their similarity. Correlation clustering provides a method for clustering a set of objects into the optimum number of clusters without specifying that number in advance. Cluster analysis In machine learning, correlation clustering or cluster editing operates in a scenario where the relationships between the objects are known instead of the actual representations of the objects.
Complete metric spaceIn mathematical analysis, a metric space M is called complete (or a Cauchy space) if every Cauchy sequence of points in M has a limit that is also in M. Intuitively, a space is complete if there are no "points missing" from it (inside or at the boundary). For instance, the set of rational numbers is not complete, because e.g. is "missing" from it, even though one can construct a Cauchy sequence of rational numbers that converges to it (see further examples below).
Multiclass classificationIn 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). 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.
Pseudometric spaceIn mathematics, a pseudometric space is a generalization of a metric space in which the distance between two distinct points can be zero. Pseudometric spaces were introduced by Đuro Kurepa in 1934. In the same way as every normed space is a metric space, every seminormed space is a pseudometric space. Because of this analogy the term semimetric space (which has a different meaning in topology) is sometimes used as a synonym, especially in functional analysis. When a topology is generated using a family of pseudometrics, the space is called a gauge space.
Hierarchical clusteringIn data mining and statistics, hierarchical clustering (also called hierarchical cluster analysis or HCA) is a method of cluster analysis that seeks to build a hierarchy of clusters. Strategies for hierarchical clustering generally fall into two categories: Agglomerative: This is a "bottom-up" approach: Each observation starts in its own cluster, and pairs of clusters are merged as one moves up the hierarchy. Divisive: This is a "top-down" approach: All observations start in one cluster, and splits are performed recursively as one moves down the hierarchy.
