FlowVella (formerly Flowboard) is an interactive presentation platform that includes an iPad/iPhone app, a Mac app and web site for viewing presentations, built first for the iPad and web. FlowVella allows users to create, publish and share presentations through their cloud-based SaaS system. FlowVella allows embedding of text, images, PDFs, video and gallery objects in easy linkable screens, defining modern interactive presentations. FlowVella grew out of Treemo Labs. == History == FlowVella launched as 'Flowboard' on April 18, 2013 after being built for almost a year. FlowVella was incubated out of Treemo Labs, which had years of experience building native apps for iPhone, iPad and Android devices. FlowVella is an iPad app and Mac app where users create, view, publish and share interactive presentations. Presentations are viewable on flowvella.com through a web-based viewer on any device or through the FlowVella native iPad app or Mac app. On December 18, 2014, Flowboard rebranded as FlowVella after a trademark dispute. == Presentation format == FlowVella is an interactive presentation format where instead of single directional slides, presentations are made up of linkable screens with embeddable media and content objects. While 'Flows' can be exported to PDF, they all have a web address and are meant to be viewed via a web browser or the FlowVella native applications. == Revenue model == FlowVella uses the freemium model for its presentation apps. Free users can make 4 public presentations with limited number of screens/slides, but most features are available to try out the software. In 2016, FlowVella introduced a second paid plan called PRO which includes team sharing, tracking and newly introduced 'Kiosk Mode' that launched in March of 2017. == Features == FlowVella is a native iPad app and Mac app which has advantages over web based tools. All downloaded presentations can be viewed offline, without an Internet connection. This includes videos which are enabled by caching the video files into memory. For students, teachers, sales people and all users, this is extremely important because this prevents having a presentation fail because of lack of an Internet connection. Beyond the offline capabilities, there is a trend to build native applications versus HTML5 as noted by Facebook and LinkedIn both rebuilding their mobile apps as 100% native applications.
Common data model
A common data model (CDM) can refer to any standardised data model which allows for data and information exchange between different applications and data sources. Common data models aim to standardise logical infrastructure so that related applications can "operate on and share the same data", and can be seen as a way to "organize data from many sources that are in different formats into a standard structure". A common data model has been described as one of the components of a "strong information system". A standardised common data model has also been described as a typical component of a well designed agile application besides a common communication protocol. Providing a single common data model within an organisation is one of the typical tasks of a data warehouse. == Examples of common data models == === Border crossings === X-trans.eu was a cross-border pilot project between the Free State of Bavaria (Germany) and Upper Austria with the aim of developing a faster procedure for the application and approval of cross-border large-capacity transports. The portal was based on a common data model that contained all the information required for approval. === Climate data === The Climate Data Store Common Data Model is a common data model set up by the Copernicus Climate Change Service for harmonising essential climate variables from different sources and data providers. === General information technology === Within service-oriented architecture, S-RAMP is a specification released by HP, IBM, Software AG, TIBCO, and Red Hat which defines a common data model for SOA repositories as well as an interaction protocol to facilitate the use of common tooling and sharing of data. Content Management Interoperability Services (CMIS) is an open standard for inter-operation of different content management systems over the internet, and provides a common data model for typed files and folders used with version control. The NetCDF software libraries for array-oriented scientific data implements a common data model called the NetCDF Java common data model, which consists of three layers built on top of each other to add successively richer semantics. === Health === Within genomic and medical data, the Observational Medical Outcomes Partnership (OMOP) research program established under the U.S. National Institutes of Health has created a common data model for claims and electronic health records which can accommodate data from different sources around the world. PCORnet, which was developed by the Patient-Centered Outcomes Research Institute, is another common data model for health data including electronic health records and patient claims. The Sentinel Common Data Model was initially started as Mini-Sentinel in 2008. It is used by the Sentinel Initiative of the USA's Food and Drug Administration. The Generalized Data Model was first published in 2019. It was designed to be a stand-alone data model as well as to allow for further transformation into other data models (e.g., OMOP, PCORNet, Sentinel). It has a hierarchical structure to flexibly capture relationships among data elements. The JANUS clinical trial data repository also provides a common data model which is based on the SDTM standard to represent clinical data submitted to regulatory agencies, such as tabulation datasets, patient profiles, listings, etc. === Logistics === SX000i is a specification developed jointly by the Aerospace and Defence Industries Association of Europe (ASD) and the American Aerospace Industries Association (AIA) to provide information, guidance and instructions to ensure compatibility and the commonality. The associated SX002D specification contains a common data model. === Microsoft Common Data Model === The Microsoft Common Data Model is a collection of many standardised extensible data schemas with entities, attributes, semantic metadata, and relationships, which represent commonly used concepts and activities in various businesses areas. It is maintained by Microsoft and its partners, and is published on GitHub. Microsoft's Common Data Model is used amongst others in Microsoft Dataverse and with various Microsoft Power Platform and Microsoft Dynamics 365 services. === Rail transport === RailTopoModel is a common data model for the railway sector. === Other === There are many more examples of various common data models for different uses published by different sources.
Information Harvesting
Information Harvesting (IH) was an early data mining product from the 1990s. It was invented by Ralphe Wiggins and produced by the Ryan Corp, later Information Harvesting Inc., of Cambridge, Massachusetts. Wiggins had a background in genetic algorithms and fuzzy logic. IH sought to infer rules from sets of data. It did this first by classifying various input variables into one of a number of bins, thereby putting some structure on the continuous variables in the input. IH then proceeds to generate rules, trading off generalization against memorization, that will infer the value of the prediction variable, possibly creating many levels of rules in the process. It included strategies for checking if overfitting took place and, if so, correcting for it. Because of its strategies for correcting for overfitting by considering more data, and refining the rules based on that data, IH might also be considered to be a form of machine learning. The advantage of IH, as compared with other data mining products of its time and even later, was that it provided a mechanism for finding multiple rules that would classify the data and determining, according to set criteria, the best rules to use.
Policy gradient method
Policy gradient methods are a class of reinforcement learning algorithms and a sub-class of policy optimization methods. Unlike value-based methods which learn a value function to derive a policy, policy optimization methods directly learn a policy function π {\displaystyle \pi } that selects actions without consulting a value function. For policy gradient to apply, the policy function π θ {\displaystyle \pi _{\theta }} is parameterized by a differentiable parameter θ {\displaystyle \theta } . == Overview == In policy-based RL, the actor is a parameterized policy function π θ {\displaystyle \pi _{\theta }} , where θ {\displaystyle \theta } are the parameters of the actor. The actor takes as argument the state of the environment s {\displaystyle s} and produces a probability distribution π θ ( ⋅ ∣ s ) {\displaystyle \pi _{\theta }(\cdot \mid s)} . If the action space is discrete, then ∑ a π θ ( a ∣ s ) = 1 {\displaystyle \sum _{a}\pi _{\theta }(a\mid s)=1} . If the action space is continuous, then ∫ a π θ ( a ∣ s ) d a = 1 {\displaystyle \int _{a}\pi _{\theta }(a\mid s)\mathrm {d} a=1} . The goal of policy optimization is to find some θ {\displaystyle \theta } that maximizes the expected episodic reward J ( θ ) {\displaystyle J(\theta )} : J ( θ ) = E π θ [ ∑ t = 0 T γ t R t | S 0 = s 0 ] {\displaystyle J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\gamma ^{t}R_{t}{\Big |}S_{0}=s_{0}\right]} where γ {\displaystyle \gamma } is the discount factor, R t {\displaystyle R_{t}} is the reward at step t {\displaystyle t} , s 0 {\displaystyle s_{0}} is the starting state, and T {\displaystyle T} is the time-horizon (which can be infinite). The policy gradient is defined as ∇ θ J ( θ ) {\displaystyle \nabla _{\theta }J(\theta )} . Different policy gradient methods stochastically estimate the policy gradient in different ways. The goal of any policy gradient method is to iteratively maximize J ( θ ) {\displaystyle J(\theta )} by gradient ascent. Since the key part of any policy gradient method is the stochastic estimation of the policy gradient, they are also studied under the title of "Monte Carlo gradient estimation". == REINFORCE == === Policy gradient === The REINFORCE algorithm, introduced by Ronald J. Williams in 1992, was the first policy gradient method. It is based on the identity for the policy gradient ∇ θ J ( θ ) = E π θ [ ∑ t = 0 T ∇ θ ln π θ ( A t ∣ S t ) ∑ t = 0 T ( γ t R t ) | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\nabla _{\theta }\ln \pi _{\theta }(A_{t}\mid S_{t})\;\sum _{t=0}^{T}(\gamma ^{t}R_{t}){\Big |}S_{0}=s_{0}\right]} which can be improved via the "causality trick" ∇ θ J ( θ ) = E π θ [ ∑ t = 0 T ∇ θ ln π θ ( A t ∣ S t ) ∑ τ = t T ( γ τ R τ ) | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\nabla _{\theta }\ln \pi _{\theta }(A_{t}\mid S_{t})\sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau }){\Big |}S_{0}=s_{0}\right]} Thus, we have an unbiased estimator of the policy gradient: ∇ θ J ( θ ) ≈ 1 N ∑ n = 1 N [ ∑ t = 0 T ∇ θ ln π θ ( A t , n ∣ S t , n ) ∑ τ = t T ( γ τ − t R τ , n ) ] {\displaystyle \nabla _{\theta }J(\theta )\approx {\frac {1}{N}}\sum _{n=1}^{N}\left[\sum _{t=0}^{T}\nabla _{\theta }\ln \pi _{\theta }(A_{t,n}\mid S_{t,n})\sum _{\tau =t}^{T}(\gamma ^{\tau -t}R_{\tau ,n})\right]} where the index n {\displaystyle n} ranges over N {\displaystyle N} rollout trajectories using the policy π θ {\displaystyle \pi _{\theta }} . The score function ∇ θ ln π θ ( A t ∣ S t ) {\displaystyle \nabla _{\theta }\ln \pi _{\theta }(A_{t}\mid S_{t})} can be interpreted as the direction in the parameter space that increases the probability of taking action A t {\displaystyle A_{t}} in state S t {\displaystyle S_{t}} . The policy gradient, then, is a weighted average of all possible directions to increase the probability of taking any action in any state, but weighted by reward signals, so that if taking a certain action in a certain state is associated with high reward, then that direction would be highly reinforced, and vice versa. === Algorithm === The REINFORCE algorithm is a loop: Rollout N {\displaystyle N} trajectories in the environment, using π θ t {\displaystyle \pi _{\theta _{t}}} as the policy function. Compute the policy gradient estimation: g i ← 1 N ∑ n = 1 N [ ∑ t = 0 T ∇ θ t ln π θ ( A t , n ∣ S t , n ) ∑ τ = t T ( γ τ R τ , n ) ] {\displaystyle g_{i}\leftarrow {\frac {1}{N}}\sum _{n=1}^{N}\left[\sum _{t=0}^{T}\nabla _{\theta _{t}}\ln \pi _{\theta }(A_{t,n}\mid S_{t,n})\sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau ,n})\right]} Update the policy by gradient ascent: θ i + 1 ← θ i + α i g i {\displaystyle \theta _{i+1}\leftarrow \theta _{i}+\alpha _{i}g_{i}} Here, α i {\displaystyle \alpha _{i}} is the learning rate at update step i {\displaystyle i} . == Variance reduction == REINFORCE is an on-policy algorithm, meaning that the trajectories used for the update must be sampled from the current policy π θ {\displaystyle \pi _{\theta }} . This can lead to high variance in the updates, as the returns R ( τ ) {\displaystyle R(\tau )} can vary significantly between trajectories. Many variants of REINFORCE have been introduced, under the title of variance reduction. === REINFORCE with baseline === A common way for reducing variance is the REINFORCE with baseline algorithm, based on the following identity: ∇ θ J ( θ ) = E π θ [ ∑ t = 0 T ∇ θ ln π θ ( A t | S t ) ( ∑ τ = t T ( γ τ R τ ) − b ( S t ) ) | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\nabla _{\theta }\ln \pi _{\theta }(A_{t}|S_{t})\left(\sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau })-b(S_{t})\right){\Big |}S_{0}=s_{0}\right]} for any function b : States → R {\displaystyle b:{\text{States}}\to \mathbb {R} } . This can be proven by applying the previous lemma. The algorithm uses the modified gradient estimator g i ← 1 N ∑ n = 1 N [ ∑ t = 0 T ∇ θ t ln π θ ( A t , n | S t , n ) ( ∑ τ = t T ( γ τ R τ , n ) − b i ( S t , n ) ) ] {\displaystyle g_{i}\leftarrow {\frac {1}{N}}\sum _{n=1}^{N}\left[\sum _{t=0}^{T}\nabla _{\theta _{t}}\ln \pi _{\theta }(A_{t,n}|S_{t,n})\left(\sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau ,n})-b_{i}(S_{t,n})\right)\right]} and the original REINFORCE algorithm is the special case where b i ≡ 0 {\displaystyle b_{i}\equiv 0} . === Actor-critic methods === If b i {\textstyle b_{i}} is chosen well, such that b i ( S t ) ≈ ∑ τ = t T ( γ τ R τ ) = γ t V π θ i ( S t ) {\textstyle b_{i}(S_{t})\approx \sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau })=\gamma ^{t}V^{\pi _{\theta _{i}}}(S_{t})} , this could significantly decrease variance in the gradient estimation. That is, the baseline should be as close to the value function V π θ i ( S t ) {\displaystyle V^{\pi _{\theta _{i}}}(S_{t})} as possible, approaching the ideal of: ∇ θ J ( θ ) = E π θ [ ∑ t = 0 T ∇ θ ln π θ ( A t | S t ) ( ∑ τ = t T ( γ τ R τ ) − γ t V π θ ( S t ) ) | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=\mathbb {E} _{\pi _{\theta }}\left[\sum _{t=0}^{T}\nabla _{\theta }\ln \pi _{\theta }(A_{t}|S_{t})\left(\sum _{\tau =t}^{T}(\gamma ^{\tau }R_{\tau })-\gamma ^{t}V^{\pi _{\theta }}(S_{t})\right){\Big |}S_{0}=s_{0}\right]} Note that, as the policy π θ t {\displaystyle \pi _{\theta _{t}}} updates, the value function V π θ i ( S t ) {\displaystyle V^{\pi _{\theta _{i}}}(S_{t})} updates as well, so the baseline should also be updated. One common approach is to train a separate function that estimates the value function, and use that as the baseline. This is one of the actor-critic methods, where the policy function is the actor and the value function is the critic. The Q-function Q π {\displaystyle Q^{\pi }} can also be used as the critic, since ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ t ≤ T γ t ∇ θ ln π θ ( A t | S t ) ⋅ Q π θ ( S t , A t ) | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=E_{\pi _{\theta }}\left[\sum _{0\leq t\leq T}\gamma ^{t}\nabla _{\theta }\ln \pi _{\theta }(A_{t}|S_{t})\cdot Q^{\pi _{\theta }}(S_{t},A_{t}){\Big |}S_{0}=s_{0}\right]} by a similar argument using the tower law. Subtracting the value function as a baseline, we find that the advantage function A π ( S , A ) = Q π ( S , A ) − V π ( S ) {\displaystyle A^{\pi }(S,A)=Q^{\pi }(S,A)-V^{\pi }(S)} can be used as the critic as well: ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ t ≤ T γ t ∇ θ ln π θ ( A t | S t ) ⋅ A π θ ( S t , A t ) | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=E_{\pi _{\theta }}\left[\sum _{0\leq t\leq T}\gamma ^{t}\nabla _{\theta }\ln \pi _{\theta }(A_{t}|S_{t})\cdot A^{\pi _{\theta }}(S_{t},A_{t}){\Big |}S_{0}=s_{0}\right]} In summary, there are many unbiased estimators for ∇ θ J θ {\textstyle \nabla _{\theta }J_{\theta }} , all in the form of: ∇ θ J ( θ ) = E π θ [ ∑ 0 ≤ t ≤ T ∇ θ ln π θ ( A t | S t ) ⋅ Ψ t | S 0 = s 0 ] {\displaystyle \nabla _{\theta }J(\theta )=E_{\pi _{\theta }}\left[\su
Premature convergence
Premature convergence is an unwanted effect in evolutionary algorithms (EA), a metaheuristic that mimics the basic principles of biological evolution as a computer algorithm for solving an optimization problem. The effect means that the population of an EA has converged too early, resulting in being suboptimal. In this context, the parental solutions, through the aid of genetic operators, are not able to generate offspring that are superior to, or outperform, their parents. Premature convergence is a common problem found in evolutionary algorithms, as it leads to a loss, or convergence of, a large number of alleles, subsequently making it very difficult to search for a specific gene in which the alleles were present. An allele is considered lost if, in a population, a gene is present, where all individuals are sharing the same value for that particular gene. An allele is, as defined by De Jong, considered to be a converged allele, when 95% of a population share the same value for a certain gene. == Strategies for preventing premature convergence == Strategies to regain genetic variation can be: a mating strategy called incest prevention, uniform crossover, mimicking sexual selection, favored replacement of similar individuals (preselection or crowding), segmentation of individuals of similar fitness (fitness sharing), increasing population size niche and specie The genetic variation can also be regained by mutation though this process is highly random. A general strategy to reduce the risk of premature convergence is to use structured populations instead of the commonly used panmictic ones. == Identification of the occurrence of premature convergence == It is hard to determine when premature convergence has occurred, and it is equally hard to predict its presence in the future. One measure is to use the difference between the average and maximum fitness values, as used by Patnaik & Srinivas, to then vary the crossover and mutation probabilities. Population diversity is another measure which has been extensively used in studies to measure premature convergence. However, although it has been widely accepted that a decrease in the population diversity directly leads to premature convergence, there have been little studies done on the analysis of population diversity. In other words, by using the term population diversity, the argument for a study in preventing premature convergence lacks robustness, unless specified what their definition of population diversity is. There are models to counter the effect and risk of premature convergence that do not compromise core GA parameters like population size, mutation rate, and other core mechanisms. These models were inspired by biological ecology, where genetic interactions are limited by external mechanisms such as spatial topologies or speciation. These ecological models, such as the Eco-GA, adopt diffusion-based strategies to improve the robustness of GA runs and increase the likelihood of reaching near-global optima. == Causes for premature convergence == There are a number of presumed or hypothesized causes for the occurrence of premature convergence. === Self-adaptive mutations === Rechenberg introduced the idea of self-adaptation of mutation distributions in evolution strategies. According to Rechenberg, the control parameters for these mutation distributions evolved internally through self-adaptation, rather than predetermination. He called it the 1/5-success rule of evolution strategies (1 + 1)-ES: The step size control parameter would be increased by some factor if the relative frequency of positive mutations through a determined period of time is larger than 1/5, vice versa if it is smaller than 1/5. Self-adaptive mutations may very well be one of the causes for premature convergence. Accurately locating of optima can be enhanced by self-adaptive mutation, as well as accelerating the search for this optima. This has been widely recognized, though the mechanism's underpinnings of this have been poorly studied, as it is often unclear whether the optima is found locally or globally. Self-adaptive methods can cause global convergence to global optimum, provided that the selection methods used are using elitism, as well as that the rule of self-adaptation doesn't interfere with the mutation distribution, which has the property of ensuring a positive minimum probability when hitting a random subset. This is for non-convex objective functions with sets that include bounded lower levels of non-zero measurements. A study by Rudolph suggests that self-adaption mechanisms among elitist evolution strategies do resemble the 1/5-success rule, and could very well get caught by a local optimum that include a positive probability. === Panmictic populations === Most EAs use unstructured or panmictic populations where basically every individual in the population is eligible for mate selection based on fitness. Thus, The genetic information of an only slightly better individual can spread in a population within a few generations, provided that no better other offspring is produced during this time. Especially in comparatively small populations, this can quickly lead to a loss of genotypic diversity and thus to premature convergence. A well-known countermeasure is to switch to alternative population models which introduce substructures into the population that preserve genotypic diversity over a longer period of time and thus counteract the tendency towards premature convergence. This has been shown for various EAs such as genetic algorithms, the evolution strategy, other EAs or memetic algorithms.
H (company)
H Company, also known simply as H, is a French artificial intelligence startup which develops "action-oriented" artificial intelligence agents for enterprise automation and productivity. In May 2024, H Company closed a record-setting $220 million seed round, at the time the largest AI raise in Europe. In 2026, H Company released Holo 3, the latest generation of its computer-use AI models. The update marked a major advance in agentic AI, enabling agents to navigate any user interface, interpret screens, and complete complex, multi-step tasks across enterprise systems—much like a human user. This breakthrough positioned H Company at the frontier of computer-use autonomy, accelerating the integration of AI in enterprise workflows. == History == H Company was founded in 2023 in Paris by Laurent Sifre, Charles Kantor, and three DeepMind veterans: Daan Wiestra, Karl Tuyls, Julien Perollat. In May 2024, the firm secured what was then the largest European AI seed round, totaling $220 million led by US investors including Eric Schmidt (former Google CEO), Amazon, and backed by Accel, Bpifrance, UiPath, Eurazeo, Xavier Niel, Yuri Milner, Bernard Arnault, Samsung and others. In August 2024, three cofounders (Wiestra, Tuyls, Perollat) left the company over operational disagreements. In November 2024, H launched Runner H, its first agentic-API platform, which combined a large language model (LLM) and a reduced, 2-billion parameter vision-language model (VLM). In May 2025, H Company acquired Mithril Security, and in June 2025 the company widened its offering for agentic models. In June 2025, Gautier Cloix (formerly CEO Palantir France) replaced Charles Kantor as CEO of H Company, aiming to pivot the company towards a "forward deployed engineers" model. In July 2025, H Company introduced Surfer-H-CLI, an open-source, web-native Chrome agent designed for browser-based automation—able to search, scroll, click, and type on behalf of users and controllable via any visual language model (VLM). When paired with its June 2025 open-sourced 3B-parameter Holo-1 model, Surfer-H-CLI achieved 92.2% WebVoyager benchmark accuracy. == Activity == H Company creates enterprise AI models and agents (agentic AI) to automate and optimize complex workflows. H Company specifically designs AI agents called computer use capable of autonomously interfacing with any software (local or cloud-based) to detect and automate repetitive operations. H Company is based in Paris, France, with international offices in London and New York. H Company raised $220 million since its inception. Gautier Cloix is president and CEO of the company. H Company client include the French national lottery FDJ United. In March 2026, H Company released Holo3, a family of artificial intelligence models designed to operate digital systems by interacting directly with user interfaces. Holo3 enables agents ("virtual humanoids") to understand what is displayed in front-end environments—such as web pages, desktop applications, and other graphical user interfaces—and perform actions such as clicking, typing, and navigating across them to complete multi-step tasks. On the OSWorld-Verified benchmark, Holo3 reportedly achieved about 78.9%, surpassing the scores of OpenAI’s GPT‑5.4 and Anthropic’s Claude Opus 4.6 on this specific test, at roughly one-tenth of the inference cost of these proprietary systems. The release has been presented as a significant step toward automating routine digital workflows, allowing organizations to offload repetitive on-screen work, such as data entry and reconciliation across multiple tools, to AI-based agents.
Density-based clustering validation
Density-Based Clustering Validation (DBCV) is a metric designed to assess the quality of clustering solutions, particularly for density-based clustering algorithms like DBSCAN, Mean shift, and OPTICS. This metric is particularly suited for identifying concave and nested clusters, where traditional metrics such as the Silhouette coefficient, Davies–Bouldin index, or Calinski–Harabasz index often struggle to provide meaningful evaluations. Unlike traditional validation measures, which often rely on compact and well-separated clusters, DBCV index evaluates how well clusters are defined in terms of local density variations and structural coherence. This metric was introduced in 2014 by David Moulavi and colleagues in their work. It utilizes density connectivity principles to quantify clustering structures, making it especially effective at detecting arbitrarily shaped clusters in concave datasets, where traditional metrics may be less reliable. The DBCV index has been employed for clustering analysis in bioinformatics, ecology, techno-economy, and health informatics , as well as in numerous other fields. == Definition == DBCV index evaluates clustering structures by analyzing the relationships between data points within and across clusters. Given a dataset X = x 1 , x 2 , . . . , x n {\displaystyle X={x_{1},x_{2},...,x_{n}}} , a density-based algorithm partitions it into K clusters C 1 , C 2 , . . . , C K {\displaystyle {C_{1},C_{2},...,C_{K}}} . Each point x i {\displaystyle x_{i}} belongs to a specific cluster, denoted as C c l u s t e r ( x i ) {\displaystyle C_{cluster(x_{i})}} A key concept in DBCV index is the notion of density-connected paths. Two points within the same cluster are considered density-connected if there exists a sequence of intermediate points linking them, where each consecutive pair meets a predefined density criterion. The density-based distance between two points is determined by identifying the optimal path that minimizes the maximum local reachability distance along its trajectory. DBCV index extends the Silhouette coefficient by redefining cluster cohesion and separation using density-based distances: Within-cluster density distance measures how closely a point is related to other members of its cluster: a i = 1 | C c l u s t e r ( x i ) | − 1 ∑ x j ∈ C c l u s t e r ( x i ) , y ≠ x d d e n s i t y ( x j , x i ) {\displaystyle a_{i}={\frac {1}{|C_{cluster(x_{i})}|-1}}\sum _{x_{j}\in C_{cluster(x_{i})},y\neq x}d_{density}(x_{j},x_{i})} Nearest-cluster density distance quantifies how far a point is from the closest external cluster: b i = min C ≠ C cluster ( x i ) C ∈ { C 1 , … , C K } ( 1 | C | ∑ x j ∈ C d density ( x i , x j ) ) . {\displaystyle b_{i}=\min _{C\neq C_{{\text{cluster}}(x_{i})} \atop C\in \{C_{1},\dots ,C_{K}\}}\left({\frac {1}{|C|}}\sum _{x_{j}\in C}d_{\text{density}}(x_{i},x_{j})\right).} Using these measures, the DBCV index is computed as: D B C V = 1 n ∑ i = 1 n b i − a i max ( a i , b i ) {\displaystyle DBCV={\frac {1}{n}}\sum _{i=1}^{n}{\frac {b_{i}-a_{i}}{\max(a_{i},b_{i})}}} == Explanation == DBCV index values range between −1 and +1: +1: Strongly cohesive and well-separated clusters. 0: Ambiguous clustering structure. −1: Poorly formed clusters or incorrect assignments. By leveraging density-based distances instead of traditional Euclidean measures, DBCV index provides a more robust evaluation of clustering performance in datasets with irregular or non-spherical distributions.