Looking for the best AI photo editor? An AI photo editor is software that uses machine learning to help you get more done — it can save you hours every week by automating repetitive work. Most options offer a generous free tier, with paid plans unlocking higher limits, faster processing, and team features. Whether you are a beginner or a pro, the right AI photo editor slots into your workflow and pays for itself fast. This guide breaks down the top picks, their pros and cons, and who each one is best for.
Voice user interface
A voice user interface (VUI) enables spoken human interaction with computers, using speech recognition to understand spoken commands and answer questions, and typically text to speech to play a reply. A voice command device is a device controlled with a voice user interface. Voice user interfaces have been added to automobiles, home automation systems, computer operating systems, home appliances like washing machines and microwave ovens, and television remote controls. They are the primary way of interacting with virtual assistants on smartphones and smart speakers. Older automated attendants (which route phone calls to the correct extension) and interactive voice response systems (which conduct more complicated transactions over the phone) can respond to the pressing of keypad buttons via DTMF tones, but those with a full voice user interface allow callers to speak requests and responses without having to press any buttons. Newer voice command devices are speaker-independent, so they can respond to multiple voices, regardless of accent or dialectal influences. They are also capable of responding to several commands at once, separating vocal messages, and providing appropriate feedback, accurately imitating a natural conversation. == Overview == A VUI is the interface to any speech application. Only a short time ago, controlling a machine by simply talking to it was only possible in science fiction. Until recently, this area was considered to be artificial intelligence. However, advances in technologies like text-to-speech, speech-to-text, natural language processing, and cloud services contributed to the mass adoption of these types of interfaces. VUIs have become more commonplace, and people are taking advantage of the value that these hands-free, eyes-free interfaces provide in many situations. VUIs rely on the ability to process input reliably, inconsistent performance often leads to decreased user engagement and negative feedback. Designing a good VUI requires interdisciplinary talents of computer science, linguistics and human factors such as psychology. Even with advanced development tools, constructing an effective VUI requires understanding of both the tasks to be performed, as well as the target audience that will use the final system. The closer the VUI matches the user's mental model of the task, the easier it will be to use with little or no training, resulting in both higher efficiency and higher user satisfaction. A VUI designed for the general public should emphasize ease of use and provide a lot of help and guidance for first-time callers. In contrast, a VUI designed for a small group of power users (including field service workers), should focus more on productivity and less on help and guidance. Such applications should streamline the call flows, minimize prompts, eliminate unnecessary iterations and allow elaborate "mixed initiative dialogs", which enable callers to enter several pieces of information in a single utterance and in any order or combination. In short, speech applications have to be carefully crafted for the specific business process that is being automated. Not all business processes render themselves equally well for speech automation. In general, the more complex the inquiries and transactions are, the more challenging they will be to automate, and the more likely they will be to fail with the general public. In some scenarios, automation is simply not applicable, so live agent assistance is the only option. A legal advice hotline, for example, would be very difficult to automate. On the flip side, speech is perfect for handling quick and routine transactions, like changing the status of a work order, completing a time or expense entry, or transferring funds between accounts. == History == Early applications for VUI included voice-activated dialing of phones, either directly or through a (typically Bluetooth) headset or vehicle audio system. In 2007, a CNN business article reported that voice command was over a billion dollar industry and that companies like Google and Apple were trying to create speech recognition features. In the years since the article was published, the world has witnessed a variety of voice command devices. Additionally, Google has created a speech recognition engine called Pico TTS and Apple released Siri. Voice command devices are becoming more widely available, and innovative ways for using the human voice are always being created. For example, Business Week suggests that the future remote controller is going to be the human voice. Currently Xbox Live allows such features and Jobs hinted at such a feature on the new Apple TV. == Voice command software products on computing devices == Both Apple Mac and Windows PC provide built in speech recognition features for their latest operating systems. === Microsoft Windows === Two Microsoft operating systems, Windows 7 and Windows Vista, provide speech recognition capabilities. Microsoft integrated voice commands into their operating systems to provide a mechanism for people who want to limit their use of the mouse and keyboard, but still want to maintain or increase their overall productivity. ==== Windows Vista ==== With Windows Vista voice control, a user may dictate documents and emails in mainstream applications, start and switch between applications, control the operating system, format documents, save documents, edit files, efficiently correct errors, and fill out forms on the Web. The speech recognition software learns automatically every time a user uses it, and speech recognition is available in English (U.S.), English (U.K.), German (Germany), French (France), Spanish (Spain), Japanese, Chinese (Traditional), and Chinese (Simplified). In addition, the software comes with an interactive tutorial, which can be used to train both the user and the speech recognition engine. ==== Windows 7 ==== In addition to all the features provided in Windows Vista, Windows 7 provides a wizard for setting up the microphone and a tutorial on how to use the feature. ==== Mac OS X ==== All Mac OS X computers come pre-installed with the speech recognition software. The software is user-independent, and it allows for a user to, "navigate menus and enter keyboard shortcuts; speak checkbox names, radio button names, list items, and button names; and open, close, control, and switch among applications." However, the Apple website recommends a user buy a commercial product called Dictate. === Commercial products === If a user is not satisfied with the built in speech recognition software or a user does not have a built speech recognition software for their OS, then a user may experiment with a commercial product such as Braina Pro or DragonNaturallySpeaking for Windows PCs, and Dictate, the name of the same software for Mac OS. == Voice command mobile devices == Any mobile device running Android OS, Microsoft Windows Phone, iOS 9 or later, or Blackberry OS provides voice command capabilities. In addition to the built-in speech recognition software for each mobile phone's operating system, a user may download third party voice command applications from each operating system's application store: Apple App store, Google Play, Windows Phone Marketplace (initially Windows Marketplace for Mobile), or BlackBerry App World. === Android OS === Google has developed an open source operating system called Android, which allows a user to perform voice commands such as: send text messages, listen to music, get directions, call businesses, call contacts, send email, view a map, go to websites, write a note, and search Google. The speech recognition software is available for all devices since Android 2.2 "Froyo", but the settings must be set to English. Google allows for the user to change the language, and the user is prompted when he or she first uses the speech recognition feature if he or she would like their voice data to be attached to their Google account. If a user decides to opt into this service, it allows Google to train the software to the user's voice. Google introduced the Google Assistant with Android 7.0 "Nougat". It is much more advanced than the older version. Amazon.com has the Echo that uses Amazon's custom version of Android to provide a voice interface. === Microsoft Windows === Windows Phone is Microsoft's mobile device's operating system. On Windows Phone 7.5, the speech app is user independent and can be used to: call someone from your contact list, call any phone number, redial the last number, send a text message, call your voice mail, open an application, read appointments, query phone status, and search the web. In addition, speech can also be used during a phone call, and the following actions are possible during a phone call: press a number, turn the speaker phone on, or call someone, which puts the current call on hold. Windows 10 introduces Cortana, a voice control system that replaces the formerly used voice control on Windows
Hyperion Data Center
The Richland Parish Data Center, nicknamed "Hyperion", is a planned artificial intelligence data center by Meta Platforms under-construction along Highway La. 183 in Richland Parish, Louisiana, just outside of Holly Ridge. It is one of a number of "titan clusters" being built in preparation for the emergence of AI superintelligence. Modern technological researchers disagree as to whether or not superintelligence will ever exist, though Meta CEO Mark Zuckerberg has expressed belief that its creation is inevitable. Current plans allot for the investment of $27 billion, as the structure is built from 2025 to 2030. == History == Meta was considering potential locations for their flagship data center in early 2024. Before being announced later in December, the plan was completely secret; meetings held between involved organisations and even government officials could only refer to it by the codename "Project Sucre" to protect it from potential corporate espionage. The data center was first announced on 04 December 2024, though its full scale was yet to be revealed. At first, Meta would not even claim responsibility for it, channelling all of its investments through the secret shell subsidiary Laidley LLC. We set out looking for a place where we could expand into gigawatts pretty quickly, and really get moving within that community on a large plot of land very quickly. We looked at finding very, very large contiguous plots of land that had access to the infrastructure that we need, the energy that we needed, and could move very, very quickly for us. The Louisiana-based Entergy Corporation, aiming for the facility to be built in its own backyard, negotiated a deal with the government of Louisiana to provide Meta with enormous tax breaks if they agreed to build Hyperion there. The Louisiana legislature responded by passing Act 730, which provides significant tax rebates on the purchase or lease of equipment for building and operating data centers. Meta found the arrangement acceptable, and bought a plot of land from the government. The government also had to further amend its laws to allow Meta to do this, as pre-existing policy forbade purchasing land directly from the government instead of hosting a public auction. The plot of land, originally called Franklin Farms, was purchased from the Franklin family in 2006 by the government, intending for it to be developed into an automotive manufacturing plant. Greater attention was brought to Hyperion it when Zuckerberg posted about the project on 14 July 2025 on Threads. The project subsequently caught media attention for its large size, as Zuckerberg's post portrayed the structure superimposed over Manhattan (pictured). The construction site spans 2,250 acres (9.1 km2) with a planned floor area of 4,000,000 square feet (371612 m2), making it the third largest building in the world by floor area upon completion. Meta initially reported the construction cost to be over $10 billion, but in October 2025, it announced a partnership with Blue Owl Capital providing for at least $27 billion. == Operation == The facility is expected to consume up to 5 gigawatts (GW) of computational power, more electricity than is currently used by the entire State of Louisiana. As part of their deal made with Meta, Entergy plans to be able to produce at least 3.8 GW of electricity for the operation. == Response to the project == Louisiana Governor Jeff Landry thanked Meta for their decision to build Hyperion in Louisiana, stating that it would "create opportunities for Louisiana workers to fill high-paying jobs of the future." and calling it "A New Chapter" for the state. The Louisiana Economic Development (LED) state agency further praised the project, citing Meta's estimate that it would create 1,500 jobs. Additionally, Richland Parish Supervisor Joey Evans stated that he was excited about the project. As part of their agreement with Meta, Energy announced their plan to increase electricity production state-wide. They say that this will result in the cost of energy reducing, though Entergy filings revealed in June 2025 that the cost of electricity would rise and be passed onto consumers. Meta also pledged to match all of Hyperion's power consumption with 100% environmentally friendly electricity production. So far, Entergy has begun building three gas-powered combined-cycle power plants and a substation in response to the project. Delta Community College announced in response to Hyperion's construction that it would expand its construction and trade programs. In January 2025, Business Facilities Magazine selected Hyperion for its annual Deal of the Year Platinum Award for 2024. Much of the initial backlash following Hyperion's announcement centered around the fast-tracked approval of the project by the state government, and scepticism around Meta's various claims (environmental friendliness, 100% renewable energy, local economic stimulation, price reductions). The Sierra Club criticised Meta for gentrifying the surrounding area, and was highly sceptical of their promise to keep it environmentally friendly. Environmental activist group Earthjustice attempted to have a subpoena of Meta approved to determine if they were compliant with environmental protection laws, though they were unsuccessful. Many residents of Holy Ridge have been critical of the construction, complaining about the increased construction vehicle traffic and intense gentrification. Another point of contention is Meta's continued reliance on out-of-state contractors in the facility's construction in spite of their previous commitment to "hire as many local folk as [we] possibly can." In spite of Entergy's continual denial that the facility's construction will not adversely affect the power grid, numerous electrical outages have been reported since construction began.
Effective accelerationism
Effective accelerationism (e/acc) is a 21st-century ideological movement that advocates for an explicitly pro-technology stance. Its proponents believe that unrestricted technological progress, especially driven by artificial intelligence, is a solution to universal human problems, such as poverty, war, and climate change. They perceive themselves as a counterweight to more cautious views on technological innovation and often label their opponents derogatorily as "doomers" or "decels" (short for decelerationists). The movement carries utopian undertones and advocates for faster AI progress to ensure human survival and propagate consciousness throughout the universe. Although effective accelerationism has been described as a fringe movement and as cult-like, it has gained mainstream visibility in 2023. A number of high-profile Silicon Valley figures, including investors Marc Andreessen and Garry Tan, explicitly endorsed it by adding "e/acc" to their public social media profiles. == Etymology and central beliefs == Effective accelerationism, a portmanteau of "effective altruism" and "accelerationism", is a fundamentally techno-optimist movement. According to Guillaume Verdon, one of the movement's founders, its aim is for human civilization to "clim[b] the Kardashev gradient", meaning its purpose is for human civilization to rise to next levels on the Kardashev scale by maximizing energy usage. To achieve this goal, effective accelerationism wants to accelerate technological progress. It is strongly focused on artificial general intelligence (AGI), because it sees AGI as fundamental for climbing the Kardashev scale. The movement therefore advocates for unrestricted development and deployment of artificial intelligence. Regulation of artificial intelligence and government intervention in markets more generally is met with opposition. Many of its proponents have libertarian views and think that AGI will be most aligned if many AGIs compete against each other on the marketplace. The founders of the movement see it as rooted in Jeremy England's theory on the origin of life, which is focused on entropy and thermodynamics. According to them, the universe aims to increase entropy, and life is a way of increasing it. By spreading life throughout the universe and making life use up ever increasing amounts of energy, the universe's purpose would thus be fulfilled. == History == === Intellectual origins === While Nick Land is seen as the intellectual originator of contemporary accelerationism in general, the precise origins of effective accelerationism remain unclear. The earliest known reference to the movement can be traced back to a May 2022 newsletter published by four pseudonymous authors known by their X (formerly Twitter) usernames @BasedBeffJezos, @bayeslord, @zestular and @creatine_cycle. Effective accelerationism is an extension of the TESCREAL movement, being etymologically derived from Effective Altruism and heavily rooted in the older Silicon Valley subcultures of transhumanism and extropianism (which similarly emphasized the value of progress and resisted efforts to restrain the development of technology), alongside elements of singularitarianism, cosmism, and longtermism. It is also often considered to have emerged at least in part from the work of the Cybernetic Culture Research Unit (of which Nick Land was a leading member, alongside writers such as Mark Fisher and Sadie Plant). It is sometimes compared and contrasted with the work of philosopher Benjamin Bratton on planetary computation. === Disclosure of the identity of BasedBeffJezos === Forbes disclosed in December 2023 that the @BasedBeffJezos persona is maintained by Guillaume Verdon, a Canadian former Google quantum computing engineer and theoretical physicist. The revelation was supported by a voice analysis conducted by the National Center for Media Forensics of the University of Colorado Denver, which further confirmed the match between Jezos and Verdon. The magazine justified its decision to disclose Verdon's identity on the grounds of it being "in the public interest". On 29 December 2023 Guillaume Verdon was interviewed by Lex Fridman on the Lex Fridman Podcast and introduced as the "creator of the effective accelerationism movement". === Second Trump presidency === Following Donald Trump's victory in the 2024 U.S. presidential election, several prominent tech industry figures expressed support for positions aligned with effective accelerationism, particularly regarding deregulation and technological advancement. The potential appointment of Elon Musk to government roles focused on auditing federal programs drew support from venture capitalists who anticipated reduced regulatory oversight of the technology sector. Notable tech figures publicly connected these developments to the movement's principles. Aaron Levie, CEO of Box, expressed support for "removing unnecessary red tape and over-regulation", while Mark Pincus, early Facebook investor and Zynga founder, explicitly referenced "effective accelerationism" in his post-election commentary. Venture capitalists viewed the incoming administration as an opportunity to ease regulations that had affected technology mergers and acquisitions during the previous years. == Relation to other movements == === Traditional accelerationism === Traditional accelerationism, as developed by the British philosopher Nick Land, sees the acceleration of technological change as a way to bring about a fundamental transformation of current culture, society, and the political economy. This is done through capitalism, which Land views as "an autonomous force that’s reconfiguring society" that can overcome its limits if intensified. Land's work has also been characterized as concerning "the supposedly inevitable 'disintegration of the human species' when artificial intelligence improves sufficiently." While both concern ideas like a technocapital singularity and AGI progress, effective accelerationism focuses on using AGI for the greatest ethical good for conscious life and civilization (whether human or machine), as well as expanding civilization and maximizing energy usage in order to align with the "will of the universe". Land focuses on capitalist self-optimization as the driver of modernity, progress, and the eroding of existing social orders. Land has expressed support for effective accelerationism, while Thomas Murphy referred to the movement as "Nick Land diluted for LinkedIn". === Effective altruism === Effective accelerationism diverges from the principles of effective altruism, which prioritizes using evidence and reasoning to identify the most effective ways to altruistically improve the world. This divergence comes primarily from one of the causes effective altruists focus on – AI existential risk. Effective altruists (particularly longtermists) argue that AI companies should be cautious and strive to develop safe AI systems, as they fear that any misaligned AGI could eventually lead to human extinction. Proponents of effective accelerationism generally consider existential risks from AGI to be negligible, and claim that even if they were not, decentralized free markets would much better mitigate this risk than centralized governmental regulation. === Degrowth === Effective accelerationism stands in stark contrast with the degrowth movement, sometimes described by it as "decelerationism" or "decels". The degrowth movement advocates for reducing economic activity and consumption to address ecological and social issues. Effective accelerationism on the contrary embraces technological progress, energy consumption and the dynamics of capitalism, rather than advocating for a reduction in economic activity. == Reception == The "Techno-Optimist Manifesto", a 2023 essay by Marc Andreessen, has been described by the Financial Times and the German Süddeutsche Zeitung as espousing the views of effective accelerationism. Mother Jones also characterized it as expressing effective accelerationism and reported that Andressen cited Land's work. David Swan of The Sydney Morning Herald has criticized effective accelerationism due to its opposition to government and industry self-regulation. He argues that "innovations like AI needs thoughtful regulations and guardrails ... to avoid the myriad mistakes Silicon Valley has already made." During the 2023 Reagan National Defense Forum, U.S. Secretary of Commerce Gina Raimondo cautioned against embracing the "move fast and break things" mentality associated with "effective acceleration [sic]". She emphasized the need to exercise caution in dealing with AI, stating "that's too dangerous. You can't break things when you are talking about AI." In a similar vein, Ellen Huet argued on Bloomberg News that some of the ideas of the movement were "deeply unsettling", focusing especially on Guillaume Verdon's "post-humanism" and the view that "natural selection could lead AI to replace us as the dominant spe
StepFun
Shanghai Jieyue Xingchen Intelligent Technology Co., Ltd, known as StepFun, is an artificial intelligence (AI) company based in Shanghai, China. It has been dubbed one of China's "AI Tiger" companies by investors. == Background == StepFun was founded in April 2023 by former Microsoft employees. Investors include Tencent, Qiming Venture Partners and Shanghai State-owned Capital Investment. In July 2025 at the World Artificial Intelligence Conference, StepFun announced the "Model-Chip Ecosystem Innovation Alliance" which consisted of Chinese developers of large language models (LLMs) and AI chip manufacturers. This included companies such as Huawei, Biren Technology, Moore Threads and Enflame. Another second alliance named the "Shanghai General Chamber of Commerce AI Committee" was also established that included StepFun, SenseTime, MiniMax, MetaX and Iluvatar CoreX. On 25 February 2026, it was reported that StepFun was seeking an initial public offering on the Hong Kong Stock Exchange. StepFun focuses on multimodal models which are designed to understand multiple types of input data such as text, video and audio. == Products == In July 2024 at the World Artificial Intelligence Conference, StepFun officially launched Step-2, a trillion-parameter LLM, along with the Step-1.5V multimodal model and the Step-1X image generation model. In February 2025, StepFun and Geely jointly announced the open-sourcing of two multimodal large models to global developers. They were Step-Video-T2V and Step-Audio. In July 2025, StepFun released Step 3. The Model-Chip Ecosystem Innovation Alliance aimed to optimize Step 3 for domestic chips. In April 2025, Step-R1-V-Mini was released. It is a multimodal reasoning model designed for visual interpretation and image understanding. In February 2026, Step-3.5-Flash, a mixture-of-experts model with 196 billion parameters and 11 billion active parameters was released under the free and open-source Apache 2.0 license. It supports tool use and a 256k token context window. == Models ==
Model-based clustering
In statistics, cluster analysis is the algorithmic grouping of objects into homogeneous groups based on numerical measurements. Model-based clustering based on a statistical model for the data, usually a mixture model. This has several advantages, including a principled statistical basis for clustering, and ways to choose the number of clusters, to choose the best clustering model, to assess the uncertainty of the clustering, and to identify outliers that do not belong to any group. == Model-based clustering == Suppose that for each of n {\displaystyle n} observations we have data on d {\displaystyle d} variables, denoted by y i = ( y i , 1 , … , y i , d ) {\displaystyle y_{i}=(y_{i,1},\ldots ,y_{i,d})} for observation i {\displaystyle i} . Then model-based clustering expresses the probability density function of y i {\displaystyle y_{i}} as a finite mixture, or weighted average of G {\displaystyle G} component probability density functions: p ( y i ) = ∑ g = 1 G τ g f g ( y i ∣ θ g ) , {\displaystyle p(y_{i})=\sum _{g=1}^{G}\tau _{g}f_{g}(y_{i}\mid \theta _{g}),} where f g {\displaystyle f_{g}} is a probability density function with parameter θ g {\displaystyle \theta _{g}} , τ g {\displaystyle \tau _{g}} is the corresponding mixture probability where ∑ g = 1 G τ g = 1 {\displaystyle \sum _{g=1}^{G}\tau _{g}=1} . Then in its simplest form, model-based clustering views each component of the mixture model as a cluster, estimates the model parameters, and assigns each observation to cluster corresponding to its most likely mixture component. === Gaussian mixture model === The most common model for continuous data is that f g {\displaystyle f_{g}} is a multivariate normal distribution with mean vector μ g {\displaystyle \mu _{g}} and covariance matrix Σ g {\displaystyle \Sigma _{g}} , so that θ g = ( μ g , Σ g ) {\displaystyle \theta _{g}=(\mu _{g},\Sigma _{g})} . This defines a Gaussian mixture model. The parameters of the model, τ g {\displaystyle \tau _{g}} and θ g {\displaystyle \theta _{g}} for g = 1 , … , G {\displaystyle g=1,\ldots ,G} , are typically estimated by maximum likelihood estimation using the expectation-maximization algorithm (EM); see also EM algorithm and GMM model. Bayesian inference is also often used for inference about finite mixture models. The Bayesian approach also allows for the case where the number of components, G {\displaystyle G} , is infinite, using a Dirichlet process prior, yielding a Dirichlet process mixture model for clustering. === Choosing the number of clusters === An advantage of model-based clustering is that it provides statistically principled ways to choose the number of clusters. Each different choice of the number of groups G {\displaystyle G} corresponds to a different mixture model. Then standard statistical model selection criteria such as the Bayesian information criterion (BIC) can be used to choose G {\displaystyle G} . The integrated completed likelihood (ICL) is a different criterion designed to choose the number of clusters rather than the number of mixture components in the model; these will often be different if highly non-Gaussian clusters are present. === Parsimonious Gaussian mixture model === For data with high dimension, d {\displaystyle d} , using a full covariance matrix for each mixture component requires estimation of many parameters, which can result in a loss of precision, generalizabity and interpretability. Thus it is common to use more parsimonious component covariance matrices exploiting their geometric interpretation. Gaussian clusters are ellipsoidal, with their volume, shape and orientation determined by the covariance matrix. Consider the eigendecomposition of a matrix Σ g = λ g D g A g D g T , {\displaystyle \Sigma _{g}=\lambda _{g}D_{g}A_{g}D_{g}^{T},} where D g {\displaystyle D_{g}} is the matrix of eigenvectors of Σ g {\displaystyle \Sigma _{g}} , A g = diag { A 1 , g , … , A d , g } {\displaystyle A_{g}={\mbox{diag}}\{A_{1,g},\ldots ,A_{d,g}\}} is a diagonal matrix whose elements are proportional to the eigenvalues of Σ g {\displaystyle \Sigma _{g}} in descending order, and λ g {\displaystyle \lambda _{g}} is the associated constant of proportionality. Then λ g {\displaystyle \lambda _{g}} controls the volume of the ellipsoid, A g {\displaystyle A_{g}} its shape, and D g {\displaystyle D_{g}} its orientation. Each of the volume, shape and orientation of the clusters can be constrained to be equal (E) or allowed to vary (V); the orientation can also be spherical, with identical eigenvalues (I). This yields 14 possible clustering models, shown in this table: It can be seen that many of these models are more parsimonious, with far fewer parameters than the unconstrained model that has 90 parameters when G = 4 {\displaystyle G=4} and d = 9 {\displaystyle d=9} . Several of these models correspond to well-known heuristic clustering methods. For example, k-means clustering is equivalent to estimation of the EII clustering model using the classification EM algorithm. The Bayesian information criterion (BIC) can be used to choose the best clustering model as well as the number of clusters. It can also be used as the basis for a method to choose the variables in the clustering model, eliminating variables that are not useful for clustering. Different Gaussian model-based clustering methods have been developed with an eye to handling high-dimensional data. These include the pgmm method, which is based on the mixture of factor analyzers model, and the HDclassif method, based on the idea of subspace clustering. The mixture-of-experts framework extends model-based clustering to include covariates. == Example == We illustrate the method with a dateset consisting of three measurements (glucose, insulin, sspg) on 145 subjects for the purpose of diagnosing diabetes and the type of diabetes present. The subjects were clinically classified into three groups: normal, chemical diabetes and overt diabetes, but we use this information only for evaluating clustering methods, not for classifying subjects. The BIC plot shows the BIC values for each combination of the number of clusters, G {\displaystyle G} , and the clustering model from the Table. Each curve corresponds to a different clustering model. The BIC favors 3 groups, which corresponds to the clinical assessment. It also favors the unconstrained covariance model, VVV. This fits the data well, because the normal patients have low values of both sspg and insulin, while the distributions of the chemical and overt diabetes groups are elongated, but in different directions. Thus the volumes, shapes and orientations of the three groups are clearly different, and so the unconstrained model is appropriate, as selected by the model-based clustering method. The classification plot shows the classification of the subjects by model-based clustering. The classification was quite accurate, with a 12% error rate as defined by the clinical classification. Other well-known clustering methods performed worse with higher error rates, such as single-linkage clustering with 46%, average link clustering with 30%, complete-linkage clustering also with 30%, and k-means clustering with 28%. == Outliers in clustering == An outlier in clustering is a data point that does not belong to any of the clusters. One way of modeling outliers in model-based clustering is to include an additional mixture component that is very dispersed, with for example a uniform distribution. Another approach is to replace the multivariate normal densities by t {\displaystyle t} -distributions, with the idea that the long tails of the t {\displaystyle t} -distribution would ensure robustness to outliers. However, this is not breakdown-robust. A third approach is the "tclust" or data trimming approach which excludes observations identified as outliers when estimating the model parameters. == Non-Gaussian clusters and merging == Sometimes one or more clusters deviate strongly from the Gaussian assumption. If a Gaussian mixture is fitted to such data, a strongly non-Gaussian cluster will often be represented by several mixture components rather than a single one. In that case, cluster merging can be used to find a better clustering. A different approach is to use mixtures of complex component densities to represent non-Gaussian clusters. == Non-continuous data == === Categorical data === Clustering multivariate categorical data is most often done using the latent class model. This assumes that the data arise from a finite mixture model, where within each cluster the variables are independent. === Mixed data === These arise when variables are of different types, such as continuous, categorical or ordinal data. A latent class model for mixed data assumes local independence between the variable. The location model relaxes the local independence assumption. The clustMD approach assumes that the observed variables are manifestations of underlying continuous Gaussian latent
Layer (deep learning)
A layer in a deep learning model is a structure or network topology in the model's architecture, which takes information from the previous layers and then passes it to the next layer. == Layer types == The first type of layer is the Dense layer, also called the fully-connected layer, and is used for abstract representations of input data. In this layer, neurons connect to every neuron in the preceding layer. In multilayer perceptron networks, these layers are stacked together. The Convolutional layer is typically used for image analysis tasks. In this layer, the network detects edges, textures, and patterns. The outputs from this layer are then fed into a fully-connected layer for further processing. See also: CNN model. The Pooling layer is used to reduce the size of data input. The Recurrent layer is used for text processing with a memory function. Similar to the Convolutional layer, the output of recurrent layers are usually fed into a fully-connected layer for further processing. See also: RNN model. The Normalization layer adjusts the output data from previous layers to achieve a regular distribution. This results in improved scalability and model training. A Hidden layer is any of the layers in a Neural Network that aren't the input or output layers. == Differences with layers of the neocortex == There is an intrinsic difference between deep learning layering and neocortical layering: deep learning layering depends on network topology, while neocortical layering depends on intra-layers homogeneity.