The Data Management Association (DAMA), formerly known as the Data Administration Management Association, is a global not-for-profit organization which aims to advance concepts and practices about information management and data management. It describes itself as vendor-independent, all-volunteer organization, and has a membership consisting of technical and business professionals. Its international branch is called DAMA International (or DAMA-I), and DAMA also has various continental and national branches around the world. == History == The Data Management Association International was founded in 1980 in Los Angeles. Other early chapters were: San Francisco, Portland, Seattle, Minneapolis, New York, and Washington D.C. == Data Management Body of Knowledge == DAMA has published the Data Management Body of Knowledge (DMBOK), which contains suggestions on best practices and suggestions of a common vernacular for enterprise data management. The first edition (DAMA-DMBOK) was published on 2009 November 1, the second edition (DAMA-DMBOK2) was published on 2017 July 1., and the Revised second edition (DAMA-DMBOK2 rev.2) was published on 2019 March 19. DMBOK has been described by the authors as being an "equivalent" to the Project Management Body of Knowledge (PMBOK) and Business Analysis Body of Knowledge (BABOK). It encompasses topics such as data architecture, security, quality, modelling, governance, big data, data science, and more. DMBOK also includes the DAMA Data Wheel, an infographic which represents core data management practices. The center of the infographic is data governance, and the surrounding segments each represent a different aspect of data management: Data architecture Data modeling and design Data storage and operations Data security Data integration and interoperability Document management Content management Master data management Reference data and master data Data warehousing Metadata management Data quality Business intelligence Data science == Professional Accreditation == DAMA also provides a professional data management certification for individuals known as a Certified Data Management Professional (CDMP), which is based on the DMBOK as a study reference. There are four levels of certification based on career experience and exam results. The highest level, Fellow, requires 25 years of experience and nomination by DAMA members. It is an example of one of many competing certifications for data management professionals.
Network eavesdropping
Network eavesdropping, also known as eavesdropping attack, sniffing attack, or snooping attack, is a method that retrieves user information through the internet. This attack happens on electronic devices like computers and smartphones. This network attack typically happens under the usage of unsecured networks, such as public wifi connections or shared electronic devices. Eavesdropping attacks through the network is considered one of the most urgent threats in industries that rely on collecting and storing data. Internet users use eavesdropping via the Internet to improve information security. A typical network eavesdropper may be called a Black-hat hacker and is considered a low-level hacker as it is simple to network eavesdrop successfully. The threat of network eavesdroppers is a growing concern. Research and discussions are brought up in the public's eye, for instance, types of eavesdropping, open-source tools, and commercial tools to prevent eavesdropping. Models against network eavesdropping attempts are built and developed as privacy is increasingly valued. Sections on cases of successful network eavesdropping attempts and its laws and policies in the National Security Agency are mentioned. Some laws include the Electronic Communications Privacy Act and the Foreign Intelligence Surveillance Act. == Types of attacks == Types of network eavesdropping include intervening in the process of decryption of messages on communication systems, attempting to access documents stored in a network system, and listening on electronic devices. Types include electronic performance monitoring and control systems, keystroke logging, man-in-the-middle attacks, observing exit nodes on a network, and Skype & Type. === Electronic performance monitoring and control systems (EPMCSs) === Electronic performance monitoring and control systems are used by employees or companies and organizations to collect, store, analyze, and report actions or performances of employers when they are working. The beginning of this system is used to increase the efficiency of workers, but instances of unintentional eavesdropping can occur, for example, when employees' casual phone calls or conversations would be recorded. === Keystroke logging === Keystroke logging is a program that can oversee the writing process of the user. It can be used to analyze the user's typing activities, as keystroke logging provides detailed information on activities like typing speed, pausing, deletion of texts, and more behaviors. By monitoring the activities and sounds of the keyboard strikes, the message typed by the user can be translated. Although keystroke logging systems do not explain reasons for pauses or deletion of texts, it allows attackers to analyze text information. Keystroke logging can also be used with eye-tracking devices which monitor the movements of the user's eyes to determine patterns of the user's typing actions which can be used to explain the reasons for pauses or deletion of texts. === Man-in-the-middle attack (MitM) === A Man-in-the-middle attack is an active eavesdropping method that intrudes on the network system. It can retrieve and alter the information sent between two parties without anyone noticing. The attacker hijacks the communication systems and gains control over the transport of data, but cannot insert voice messages that sound or act like the actual users. Attackers also create independent communications through the system with the users acting as if the conversation between users is private. The "man-in-the-middle" can also be referred to as lurkers in a social context. A lurker is a person who rarely or never posts anything online, but the person stays online and observes other users' actions. Lurking can be valuable as it lets people gain knowledge from other users. However, like eavesdropping, lurking into other users' private information violates privacy and social norms. === Observing exit nodes === Distributed networks including communication networks are usually designed so that nodes can enter and exit the network freely. However, this poses a danger in which attacks can easily access the system and may cause serious consequences, for example, leakage of the user's phone number or credit card number. In many anonymous network pathways, the last node before exiting the network may contain actual information sent by users. Tor exit nodes are an example. Tor is an anonymous communication system that allows users to hide their IP addresses. It also has layers of encryption that protect information sent between users from eavesdropping attempts trying to observe the network traffic. However, Tor exit nodes are used to eavesdrop at the end of the network traffic. The last node in the network path flowing through the traffic, for instance, Tor exit nodes, can acquire original information or messages that were transmitted between different users. === Skype & Type (S&T) === Skype & Type (S&T) is a new keyboard acoustic eavesdropping attack that takes advantage of Voice-over IP (VoIP). S&T is practical and can be used in many applications in the real world, as it does not require attackers to be close to the victim and it can work with only some leaked keystrokes instead of every keystroke. With some knowledge of the victim's typing patterns, attackers can gain a 91.7% accuracy typed by the victim. Different recording devices including laptop microphones, smartphones, and headset microphones can be used for attackers to eavesdrop on the victim's style and speed of typing. It is especially dangerous when attackers know what language the victim is typing in. == Tools to prevent eavesdropping attacks == Computer programs where the source code of the system is shared with the public for free or for commercial use can be used to prevent network eavesdropping. They are often modified to cater to different network systems, and the tools are specific in what task it performs. In this case, Advanced Encryption Standard-256, Bro, Chaosreader, CommView, Firewalls, Security Agencies, Snort, Tcptrace, and Wireshark are tools that address network security and network eavesdropping. === Advanced encryption standard-256 (AES-256) === It is a cipher block chaining (CBC) mode for ciphered messages and hash-based message codes. The AES-256 contains 256 keys for identifying the actual user, and it represents the standard used for securing many layers on the internet. AES-256 is used by Zoom Phone apps that help encrypt chat messages sent by Zoom users. If this feature is used in the app, users will only see encrypted chats when they use the app, and notifications of an encrypted chat will be sent with no content involved. === Bro === Bro is a system that detects network attackers and abnormal traffic on the internet. It emerged at the University of California, Berkeley that detects invading network systems. The system does not apply to the detection of eavesdropping by default, but can be modified to an offline analyzing tool for eavesdropping attacks. Bro runs under Digital Unix, FreeBSD, IRIX, SunOS, and Solaris operating systems, with the implementation of approximately 22,000 lines of C++ and 1,900 lines of Bro. It is still in the process of development for real-world applications. === Chaosreader === Chaosreader is a simplified version of many open-source eavesdropping tools. It creates HTML pages on the content of when a network intrusion is detected. No actions are taken when an attack occurs and only information such as time, network location on which system or wall the user is trying to attack will be recorded. === CommView === CommView is specific to Windows systems which limits real-world applications because of its specific system usage. It captures network traffic and eavesdropping attempts by using packet analyzing and decoding. === Firewalls === Firewall technology filters network traffic and blocks malicious users from attacking the network system. It prevents users from intruding into private networks. Having a firewall in the entrance to a network system requires user authentications before allowing actions performed by users. There are different types of firewall technologies that can be applied to different types of networks. === Security agencies === A Secure Node Identification Agent is a mobile agent used to distinguish secure neighbor nodes and informs the Node Monitoring System (NMOA). The NMOA stays within nodes and monitors the energy exerted, and receives information about nodes including node ID, location, signal strength, hop counts, and more. It detects nodes nearby that are moving out of range by comparing signal strengths. The NMOA signals the Secure Node Identification Agent (SNIA) and updates each other on neighboring node information. The Node BlackBoard is a knowledge base that reads and updates the agents, acting as the brain of the security system. The Node Key Management agent is created when an encryption key is inserted to th
Relational data mining
Relational data mining is the data mining technique for relational databases. Unlike traditional data mining algorithms, which look for patterns in a single table (propositional patterns), relational data mining algorithms look for patterns among multiple tables (relational patterns). For most types of propositional patterns, there are corresponding relational patterns. For example, there are relational classification rules (relational classification), relational regression tree, and relational association rules. There are several approaches to relational data mining: Inductive Logic Programming (ILP) Statistical Relational Learning (SRL) Graph Mining Propositionalization Multi-view learning == Algorithms == Multi-Relation Association Rules: Multi-Relation Association Rules (MRAR) is a new class of association rules which in contrast to primitive, simple and even multi-relational association rules (that are usually extracted from multi-relational databases), each rule item consists of one entity but several relations. These relations indicate indirect relationship between the entities. Consider the following MRAR where the first item consists of three relations live in, nearby and humid: “Those who live in a place which is near by a city with humid climate type and also are younger than 20 -> their health condition is good”. Such association rules are extractable from RDBMS data or semantic web data. == Software == Safarii: a Data Mining environment for analysing large relational databases based on a multi-relational data mining engine. Dataconda: a software, free for research and teaching purposes, that helps mining relational databases without the use of SQL. == Datasets == Relational dataset repository: a collection of publicly available relational datasets.
AI Mode
AI Mode is a search feature used within Google Search. In March 2025, Google introduced an experimental "AI Mode" within its search platform, enabling users to input complex, multi-part queries and receive comprehensive, AI-generated responses. This feature uses Google's Gemini model, which enhances the system's reasoning capabilities and supports multimodal inputs, including text, images, and voice. Users need to be signed in to be able to use the image generation features. Initially, AI Mode was available to Google One AI Premium subscribers in the United States, who could access it through the Search Labs platform. This phased rollout allowed Google to gather user feedback and refine the feature before a broader release.
Human–AI interaction
Human–AI interaction is a developing field of research and a sub-field of human–computer interaction (HCI). HCI is a field of research that explores the interactions between humans and computer-based technology, focusing on design implementation, user experience, and psychological factors. With the proliferation of artificial intelligence (AI), there has developed a sub-section of HCI research dedicated specifically to artificial intelligence and how people interact with and are impacted by it. This is human–AI interaction, abbreviated either as HAX or HAII. == Introduction == Artificial intelligence (AI), in general, has fluid definitions and varied research applications, but in brief can be applied to mechanizing tasks that would require human intelligence to complete. AI are tools designed to replicate the human abilities of navigating uncertainty, active learning, and processing information in different contexts. Within the context of HCI and HAX research, artificial intelligence can be broken into two sub-fields, natural language processing (NLP) and computer vision (CV). AI technologies notably include machine-learning, deep-learning and neural networks, and large-language models (LLMs). As a new and rapidly developing technology, AI is changing how computers work and therefore changing how humans interact with computers. Unlike the traditional human-computer interaction, where a human directs a machine, human-AI interaction is characterized by a more collaborative relationship between the computer program (the AI) and the human user, as AI is perceived as an active agent rather than a tool. This changing dynamic creates new questions and necessitates new research methods that are not present in traditional HCI research. According to a scoping review on the state of the discipline, the HAX field comprises research on the "design, development, and evaluation of AI systems" and encompasses the themes of human-AI collaboration, human-AI competition, human-AI conflict, and human-AI symbiosis. == Design == Machine learning and artificial intelligence have been used for decades in targeted advertising and to recommend content in social media. Ethical Guidelines (Framework for ethical AI development) == User Experience (UX) == This section should handle research on how users interact with tools. What techniques do they use, do they develop habits, what types of programs and devices are they using to access these tools, what do they use these tools to do exactly. === Cognitive Frameworks in AI Tool Users === AI has been viewed with various expectations, attributions, and often misconceptions. Many people exclusively understand AI as the LLM chatbots they interact with, like ChatGPT or Claude, or other generative AI programs. [Insert section: discuss how people interact with these specific AI tools as a connection to the following paragraphs] Most fundamentally, humans have a mental model of understanding AI's reasoning and motivation for its decision recommendations, and building a holistic and precise mental model of AI helps people create prompts to receive more valuable responses from AI. However, these mental models are not whole because people can only gain more information about AI through their limited interaction with it; more interaction with AI builds a better mental model that a person may build to produce better prompt outcomes. Research on human-AI interaction has emphasized that users develop mental models of AI systems and revise those models through repeated use, feedback, and explanation, while design research has stressed the importance of communicating capabilities and limitations early and supporting trust calibration through explanation and correction. In a 2025 SSRN working paper, John DeVadoss proposed "Hypothetico-Deductive Interaction" (HDI), a framework that describes human-AI interaction as a mutual process of conjecture and refutation in which users test assumptions about an AI system's capabilities while the system infers and updates assumptions about user goals through its responses and clarifying questions. DeVadoss argued that this framing helps explain prompt iteration, weak capability awareness, and trust miscalibration, and suggested design responses such as clearer communication of uncertainty, easier correction, actionable explanations, and safer failure modes. == Research themes == === Human-AI collaboration === Human-AI collaboration occurs when the human and AI supervise the task on the same level and extent to achieve the same goal. Some collaboration occurs in the form of augmenting human capability. AI may help human ability in analysis and decision-making through providing and weighing a volume of information, and learning to defer to the human decision when it recognizes its unreliability. It is especially beneficial when the human can detect a task that AI can be trusted to make few errors so that there is not a lot of excessive checking process required on the human's end. Some findings show signs of human-AI augmentation, or human–AI symbiosis, in which AI enhances human ability in a way that co-working on a task with AI produces better outcomes than a human working alone. For example: the quality and speed of customer service tasks increase when a human agent collaborates with AI, training on specific models allows AI to improve diagnoses in clinical settings, and AI with human-intervention can improve creativity of artwork while fully AI-generated haikus were rated negatively. Human-AI synergy, a concept in which human-AI collaboration would produce more optimal outcomes than either human or AI working alone could explain why AI does not always help with performance. Some AI features and development may accelerate human-AI synergy, while others may stagnate it. For example, when AI updates for better performance, it sometimes worsens the team performance with human and AI by reducing the compatibility with the new model and the mental model a user has developed on the previous version. Research has found that AI often supports human capabilities in the form of human-AI augmentation and not human-AI synergy, potentially because people rely too much on AI and stop thinking on their own. Prompting people to actively engage in analysis and think when to follow AI recommendations reduces their over-reliance, especially for individuals with higher need for cognition. === Human-AI competition === Robots and computers have substituted routine tasks historically completed by humans, but agentic AI has made it possible to also replace cognitive tasks including taking phone calls for appointments and driving a car. At the point of 2016, research has estimated that 45% of paid activities could be replaced by AI by 2030. Perceived autonomy of robots is known to increase people's negative attitude toward them, and worry about the technology taking over leads people to reject it. There has been a consistent tendency of algorithm aversion in which people prefer human advice over AI advice. However, people are not always able to tell apart tasks completed by AI or other humans. See AI takeover for more information. It is also notable that this sentiment is more prominent in the Western cultures as Westerners tend to show less positive views about AI compared to East Asians. == Research on the psychological impacts of AI == === Perception on others who use AI === As much as people perceive and make judgment about AI itself, they also form impressions of themselves and others who use AI. In the workplace, employees who disclose the use of AI in their tasks are more likely to receive feedback that they are not as hardworking as those who are in the same job who receive non-AI help to complete the same tasks. AI use disclosure diminishes the perceived legitimacy in the employee's task and decision making which ultimately leads observers to distrust people who use AI. Although these negative effects of AI use disclosure are weakened by the observers who use AI frequently themselves, the effect is still not attenuated by the observers' positive attitude towards AI. === Bias, AI, and human === Although AI provides a wide range of information and suggestions to its users, AI itself is not free of biases and stereotypes, and it does not always help people reduce their cognitive errors and biases. People are prone to such errors by failing to see other potential ideas and cases that are not listed by AI responses and committing to a decision suggested by AI that directly contradicts the correct information and directions that they are already aware of. Gender bias is also reflected as the female gendering of AI technologies which conceptualizes females as a helpful assistant. == Emotional connection with AI == Human-AI interaction has been theorized in the context of interpersonal relationships mainly in social psychology, communications and media studies, and as a technology interface through the lens of hu
DigitaltMuseum
DigitaltMuseum (lit. 'The Digital Museum') is a website database in Norwegian and Swedish for art, images and cultural history museums. The service was established in 2009 after a trial period. The database is developed and operated by KulturIT. KulturIT ANS was established by the Norwegian Museum of Cultural History and Maihaugen in consultation with the Norwegian Archive, Library and Museum Authority (ABM) in 2007. In 2015, the company underwent a corporate transformation and KulturIT AS was established on 12 February. The website has per 2025 around 2,548,022 images. Many of the images are in the public domain or under Creative Commons licenses and are being imported into Wikimedia Commons. The website's API was developed in 2012. == Institutions == As of 2025, there are 223 collaborating museums. == Mission == DigitaltMuseum aims to make the museums' collections accessible to all interested parties, regardless of time and place. The website aims to facilitate easy use of the collections through various methods including image searches, research, teaching and joint knowledge development. DigitaltMuseum contains collections from several hundred Norwegian and Swedish museums, totalling around five million objects. The website contains both historical images from the areas and themes covered by the museums, as well as images of artefacts from the collections. Parts of the collection have previously only been shown in the museums' exhibitions and books and have therefore rarely or never been shown to the public.
EM algorithm and GMM model
In statistics, EM (expectation maximization) algorithm handles latent variables, while GMM is the Gaussian mixture model. == Background == In the picture below, are shown the red blood cell hemoglobin concentration and the red blood cell volume data of two groups of people, the Anemia group and the control group (i.e. the group of people without Anemia). As expected, people with Anemia have lower red blood cell volume and lower red blood cell hemoglobin concentration than those without Anemia. x {\displaystyle x} is a random vector such as x := ( red blood cell volume , red blood cell hemoglobin concentration ) {\displaystyle x:={\big (}{\text{red blood cell volume}},{\text{red blood cell hemoglobin concentration}}{\big )}} , and from medical studies it is known that x {\displaystyle x} are normally distributed in each group, i.e. x ∼ N ( μ , Σ ) {\displaystyle x\sim {\mathcal {N}}(\mu ,\Sigma )} . z {\displaystyle z} is denoted as the group where x {\displaystyle x} belongs, with z i = 0 {\displaystyle z_{i}=0} when x i {\displaystyle x_{i}} belongs to the Anemia group and z i = 1 {\displaystyle z_{i}=1} when x i {\displaystyle x_{i}} belongs to the control group. Also z ∼ Categorical ( k , ϕ ) {\displaystyle z\sim \operatorname {Categorical} (k,\phi )} where k = 2 {\displaystyle k=2} , ϕ j ≥ 0 , {\displaystyle \phi _{j}\geq 0,} and ∑ j = 1 k ϕ j = 1 {\displaystyle \sum _{j=1}^{k}\phi _{j}=1} . See Categorical distribution. The following procedure can be used to estimate ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } . A maximum likelihood estimation can be applied: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log ( p ( x ( i ) ; ϕ , μ , Σ ) ) = ∑ i = 1 m log ∑ z ( i ) = 1 k p ( x ( i ) ∣ z ( i ) ; μ , Σ ) p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log(p(x^{(i)};\phi ,\mu ,\Sigma ))=\sum _{i=1}^{m}\log \sum _{z^{(i)}=1}^{k}p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)p(z^{(i)};\phi )} As the z i {\displaystyle z_{i}} for each x i {\displaystyle x_{i}} are known, the log likelihood function can be simplified as below: ℓ ( ϕ , μ , Σ ) = ∑ i = 1 m log p ( x ( i ) ∣ z ( i ) ; μ , Σ ) + log p ( z ( i ) ; ϕ ) {\displaystyle \ell (\phi ,\mu ,\Sigma )=\sum _{i=1}^{m}\log p\left(x^{(i)}\mid z^{(i)};\mu ,\Sigma \right)+\log p\left(z^{(i)};\phi \right)} Now the likelihood function can be maximized by making partial derivative over μ , Σ , ϕ {\displaystyle \mu ,\Sigma ,\phi } , obtaining: ϕ j = 1 m ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \phi _{j}={\frac {1}{m}}\sum _{i=1}^{m}1\{z^{(i)}=j\}} μ j = ∑ i = 1 m 1 { z ( i ) = j } x ( i ) ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \mu _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}x^{(i)}}{\sum _{i=1}^{m}1\left\{z^{(i)}=j\right\}}}} Σ j = ∑ i = 1 m 1 { z ( i ) = j } ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m 1 { z ( i ) = j } {\displaystyle \Sigma _{j}={\frac {\sum _{i=1}^{m}1\{z^{(i)}=j\}(x^{(i)}-\mu _{j})(x^{(i)}-\mu _{j})^{T}}{\sum _{i=1}^{m}1\{z^{(i)}=j\}}}} If z i {\displaystyle z_{i}} is known, the estimation of the parameters results to be quite simple with maximum likelihood estimation. But if z i {\displaystyle z_{i}} is unknown it is much more complicated. Being z {\displaystyle z} a latent variable (i.e. not observed), with unlabeled scenario, the expectation maximization algorithm is needed to estimate z {\displaystyle z} as well as other parameters. Generally, this problem is set as a GMM since the data in each group is normally distributed. In machine learning, the latent variable z {\displaystyle z} is considered as a latent pattern lying under the data, which the observer is not able to see very directly. x i {\displaystyle x_{i}} is the known data, while ϕ , μ , Σ {\displaystyle \phi ,\mu ,\Sigma } are the parameter of the model. With the EM algorithm, some underlying pattern z {\displaystyle z} in the data x i {\displaystyle x_{i}} can be found, along with the estimation of the parameters. The wide application of this circumstance in machine learning is what makes EM algorithm so important. == EM algorithm in GMM == The EM algorithm consists of two steps: the E-step and the M-step. Firstly, the model parameters and the z ( i ) {\displaystyle z^{(i)}} can be randomly initialized. In the E-step, the algorithm tries to guess the value of z ( i ) {\displaystyle z^{(i)}} based on the parameters, while in the M-step, the algorithm updates the value of the model parameters based on the guess of z ( i ) {\displaystyle z^{(i)}} of the E-step. These two steps are repeated until convergence is reached. The algorithm in GMM is: Repeat until convergence: 1. (E-step) For each i , j {\displaystyle i,j} , set w j ( i ) := p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) {\displaystyle w_{j}^{(i)}:=p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)} 2. (M-step) Update the parameters ϕ j := 1 m ∑ i = 1 m w j ( i ) {\displaystyle \phi _{j}:={\frac {1}{m}}\sum _{i=1}^{m}w_{j}^{(i)}} μ j := ∑ i = 1 m w j ( i ) x ( i ) ∑ i = 1 m w j ( i ) {\displaystyle \mu _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}x^{(i)}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} Σ j := ∑ i = 1 m w j ( i ) ( x ( i ) − μ j ) ( x ( i ) − μ j ) T ∑ i = 1 m w j ( i ) {\displaystyle \Sigma _{j}:={\frac {\sum _{i=1}^{m}w_{j}^{(i)}\left(x^{(i)}-\mu _{j}\right)\left(x^{(i)}-\mu _{j}\right)^{T}}{\sum _{i=1}^{m}w_{j}^{(i)}}}} With Bayes' rule, the following result is obtained by the E-step: p ( z ( i ) = j | x ( i ) ; ϕ , μ , Σ ) = p ( x ( i ) | z ( i ) = j ; μ , Σ ) p ( z ( i ) = j ; ϕ ) ∑ l = 1 k p ( x ( i ) | z ( i ) = l ; μ , Σ ) p ( z ( i ) = l ; ϕ ) {\displaystyle p\left(z^{(i)}=j|x^{(i)};\phi ,\mu ,\Sigma \right)={\frac {p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)p\left(z^{(i)}=j;\phi \right)}{\sum _{l=1}^{k}p\left(x^{(i)}|z^{(i)}=l;\mu ,\Sigma \right)p\left(z^{(i)}=l;\phi \right)}}} According to GMM setting, these following formulas are obtained: p ( x ( i ) | z ( i ) = j ; μ , Σ ) = 1 ( 2 π ) n / 2 | Σ j | 1 / 2 exp ( − 1 2 ( x ( i ) − μ j ) T Σ j − 1 ( x ( i ) − μ j ) ) {\displaystyle p\left(x^{(i)}|z^{(i)}=j;\mu ,\Sigma \right)={\frac {1}{(2\pi )^{n/2}\left|\Sigma _{j}\right|^{1/2}}}\exp \left(-{\frac {1}{2}}\left(x^{(i)}-\mu _{j}\right)^{T}\Sigma _{j}^{-1}\left(x^{(i)}-\mu _{j}\right)\right)} p ( z ( i ) = j ; ϕ ) = ϕ j {\displaystyle p\left(z^{(i)}=j;\phi \right)=\phi _{j}} In this way, a switch between the E-step and the M-step is possible, according to the randomly initialized parameters.