Silhouette (clustering)

Silhouette is a method of interpretation and validation of consistency within clusters of data. The technique provides a succinct graphical representation of how well each object has been classified. It was proposed by Belgian statistician Peter Rousseeuw in 1987. The silhouette value is a measure of how similar an object is to its own cluster (cohesion) compared to other clusters (separation). The silhouette value ranges from −1 to +1, where a high value indicates that the object is well matched to its own cluster and poorly matched to neighboring clusters. If most objects have a high value, then the clustering configuration is appropriate. If many points have a low or negative value, then the clustering configuration may have too many or too few clusters. A clustering with an average silhouette width of over 0.7 is considered to be "strong", a value over 0.5 "reasonable", and over 0.25 "weak". However, with an increasing dimensionality of the data, it becomes difficult to achieve such high values because of the curse of dimensionality, as the distances become more similar. The silhouette score is specialized for measuring cluster quality when the clusters are convex-shaped, and may not perform well if the data clusters have irregular shapes or are of varying sizes. The silhouette value can be calculated with any distance metric, such as Euclidean distance or Manhattan distance. == Definition == Assume the data have been clustered via any technique, such as k-medoids or k-means, into k {\displaystyle k} clusters. For data point i ∈ C i {\displaystyle i\in C_{i}} (data point i {\displaystyle i} in the cluster C i {\displaystyle C_{i}} ), calculate a ( i ) {\displaystyle a(i)} , the average distance that i {\displaystyle i} is from all other points in that cluster: a ( i ) = 1 | C i | − 1 ∑ j ∈ C i , i ≠ j d ( i , j ) {\displaystyle a(i)={\frac {1}{|C_{i}|-1}}\sum _{j\in C_{i},i\neq j}d(i,j)} where | C i | {\displaystyle |C_{i}|} is the number of points belonging to cluster C i {\displaystyle C_{i}} , and d ( i , j ) {\displaystyle d(i,j)} is the distance between data points i {\displaystyle i} and j {\displaystyle j} in the cluster C i {\displaystyle C_{i}} (we divide by | C i | − 1 {\displaystyle |C_{i}|-1} because the distance d ( i , i ) {\displaystyle d(i,i)} is not included in the sum). a ( i ) {\displaystyle a(i)} can be interpreted as a measure of how well i {\displaystyle i} is assigned to its cluster (the smaller the value, the better the assignment). We then define the mean dissimilarity of point i {\displaystyle i} to some cluster C j {\displaystyle C_{j}} as the mean of the distance from i {\displaystyle i} to all points in C j {\displaystyle C_{j}} (where C j ≠ C i {\displaystyle C_{j}\neq C_{i}} ). For each data point i ∈ C i {\displaystyle i\in C_{i}} , we now define b ( i ) {\displaystyle b(i)} as the average distance between i {\displaystyle i} and the points in the closest cluster (hence: "min") that i {\displaystyle i} does not belong to: b ( i ) = min j ≠ i 1 | C j | ∑ l ∈ C j d ( i , l ) {\displaystyle b(i)=\min _{j\neq i}{\frac {1}{|C_{j}|}}\sum _{l\in C_{j}}d(i,l)} The cluster with the smallest mean dissimilarity is said to be the "neighboring cluster" of i {\displaystyle i} because it is the next best fit cluster for point i {\displaystyle i} . We now define a silhouette (value) of one data point i {\displaystyle i} s ( i ) = b ( i ) − a ( i ) max { a ( i ) , b ( i ) } {\displaystyle s(i)={\frac {b(i)-a(i)}{\max\{a(i),b(i)\}}}} , if | C i | > 1 {\displaystyle |C_{i}|>1} and s ( i ) = 0 {\displaystyle s(i)=0} , if | C i | = 1 {\displaystyle |C_{i}|=1} , which can also be written as s ( i ) = { 1 − a ( i ) b ( i ) , if a ( i ) < b ( i ) 0 , if a ( i ) = b ( i ) b ( i ) a ( i ) − 1 , if a ( i ) > b ( i ) {\displaystyle s(i)={\begin{cases}1-{\frac {a(i)}{b(i)}},&{\mbox{ if }}a(i)b(i)\\\end{cases}}} From the above definition, s ( i ) {\displaystyle s(i)} is bounded to the interval [ − 1 , 1 ] {\displaystyle [-1,1]} , i.e. − 1 ≤ s ( i ) ≤ 1. {\displaystyle -1\leq s(i)\leq 1.} Note that a ( i ) {\displaystyle a(i)} is not clearly defined for clusters with size = 1, in which case we set s ( i ) = 0 {\displaystyle s(i)=0} . This choice is arbitrary, but neutral in the sense that it is at the midpoint of the bounds, -1 and 1. For s ( i ) {\displaystyle s(i)} to be close to 1 we require a ( i ) ≪ b ( i ) {\displaystyle a(i)\ll b(i)} . As a ( i ) {\displaystyle a(i)} is a measure of how dissimilar i {\displaystyle i} is to its own cluster, a small value means it is well matched. Furthermore, a large b ( i ) {\displaystyle b(i)} implies that i {\displaystyle i} is badly matched to its neighbouring cluster. Thus an s ( i ) {\displaystyle s(i)} close to 1 means that the data is appropriately clustered. If s ( i ) {\displaystyle s(i)} is close to -1, then by the same logic we see that i {\displaystyle i} would be more appropriate if it was clustered in its neighbouring cluster. An s ( i ) {\displaystyle s(i)} near zero means that the datum is on the border of two natural clusters. The mean s ( i ) {\displaystyle s(i)} over all points of a cluster is a measure of how tightly grouped all the points in the cluster are. Thus the mean s ( i ) {\displaystyle s(i)} over all data of the entire dataset is a measure of how appropriately the data have been clustered. If there are too many or too few clusters, as may occur when a poor choice of k {\displaystyle k} is used in the clustering algorithm (e.g., k-means), some of the clusters will typically display much narrower silhouettes than the rest. Thus silhouette plots and means may be used to determine the natural number of clusters within a dataset. One can also increase the likelihood of the silhouette being maximized at the correct number of clusters by re-scaling the data using feature weights that are cluster specific. Kaufman et al. introduced the term silhouette coefficient for the maximum value of the mean s ( i ) {\displaystyle s(i)} over all data of the entire dataset, i.e., S C = max k s ~ ( k ) , {\displaystyle SC=\max _{k}{\tilde {s}}\left(k\right),} where s ~ ( k ) {\displaystyle {\tilde {s}}\left(k\right)} represents the mean s ( i ) {\displaystyle s(i)} over all data of the entire dataset for a specific number of clusters k {\displaystyle k} . The silhouette coefficient describes the best possible clustering possible for a given number of clusters, as measured by the highest average silhouette score for all points in the dataset. == Simplified and medoid silhouette == Computing the silhouette coefficient needs all O ( N 2 ) {\displaystyle {\mathcal {O}}(N^{2})} pairwise distances, making this evaluation much more costly than clustering with k-means. For a clustering with centers μ C I {\displaystyle \mu _{C_{I}}} for each cluster C I {\displaystyle C_{I}} , we can use the following simplified Silhouette for each point i ∈ C I {\displaystyle i\in C_{I}} instead, which can be computed using only O ( N k ) {\displaystyle {\mathcal {O}}(Nk)} distances: a ′ ( i ) = d ( i , μ C I ) {\displaystyle a'(i)=d(i,\mu _{C_{I}})} and b ′ ( i ) = min C J ≠ C I d ( i , μ C J ) {\displaystyle b'(i)=\min _{C_{J}\neq C_{I}}d(i,\mu _{C_{J}})} , which has the additional benefit that a ′ ( i ) {\displaystyle a'(i)} is always defined, then define accordingly the simplified silhouette and simplified silhouette coefficient s ′ ( i ) = b ′ ( i ) − a ′ ( i ) max { a ′ ( i ) , b ′ ( i ) } {\displaystyle s'(i)={\frac {b'(i)-a'(i)}{\max\{a'(i),b'(i)\}}}} S C ′ = max k 1 N ∑ i s ′ ( i ) {\displaystyle SC'=\max _{k}{\frac {1}{N}}\sum _{i}s'\left(i\right)} . If the cluster centers are medoids (as in k-medoids clustering) instead of arithmetic means (as in k-means clustering), this is also called the medoid-based silhouette or medoid silhouette. If every object is assigned to the nearest medoid (as in k-medoids clustering), we know that a ′ ( i ) ≤ b ′ ( i ) {\displaystyle a'(i)\leq b'(i)} , and hence s ′ ( i ) = b ′ ( i ) − a ′ ( i ) b ′ ( i ) = 1 − a ′ ( i ) b ′ ( i ) {\displaystyle s'(i)={\frac {b'(i)-a'(i)}{b'(i)}}=1-{\frac {a'(i)}{b'(i)}}} . == Silhouette clustering == Instead of using the average silhouette to evaluate a clustering obtained from, e.g., k-medoids or k-means, we can try to directly find a solution that maximizes the Silhouette. We do not have a closed form solution to maximize this, but it will usually be best to assign points to the nearest cluster as done by these methods. Van der Laan et al. proposed to adapt the standard algorithm for k-medoids, PAM, for this purpose and call this algorithm PAMSIL: Choose initial medoids by using PAM Compute the average silhouette of this initial solution For each pair of a medoid m and a non-medoid x swap m and x compute the average silhouette of the resulting solution remember the best swap un-swap m and x for the next iteration Perform the best swap and return to

Landweber iteration

The Landweber iteration or Landweber algorithm is an algorithm to solve ill-posed linear inverse problems, and it has been extended to solve non-linear problems that involve constraints. The method was first proposed in the 1950s by Louis Landweber, and it can be now viewed as a special case of many other more general methods. == Basic algorithm == The original Landweber algorithm attempts to recover a signal x from (noisy) measurements y. The linear version assumes that y = A x {\displaystyle y=Ax} for a linear operator A. When the problem is in finite dimensions, A is just a matrix. When A is nonsingular, then an explicit solution is x = A − 1 y {\displaystyle x=A^{-1}y} . However, if A is ill-conditioned, the explicit solution is a poor choice since it is sensitive to any noise in the data y. If A is singular, this explicit solution doesn't even exist. The Landweber algorithm is an attempt to regularize the problem, and is one of the alternatives to Tikhonov regularization. We may view the Landweber algorithm as solving: min x ‖ A x − y ‖ 2 2 / 2 {\displaystyle \min _{x}\|Ax-y\|_{2}^{2}/2} using an iterative method. The algorithm is given by the update x k + 1 = x k − ω A ∗ ( A x k − y ) . {\displaystyle x_{k+1}=x_{k}-\omega A^{}(Ax_{k}-y).} where the relaxation factor ω {\displaystyle \omega } satisfies 0 < ω < 2 / σ 1 2 {\displaystyle 0<\omega <2/\sigma _{1}^{2}} . Here σ 1 {\displaystyle \sigma _{1}} is the largest singular value of A {\displaystyle A} . If we write f ( x ) = ‖ A x − y ‖ 2 2 / 2 {\displaystyle f(x)=\|Ax-y\|_{2}^{2}/2} , then the update can be written in terms of the gradient x k + 1 = x k − ω ∇ f ( x k ) {\displaystyle x_{k+1}=x_{k}-\omega \nabla f(x_{k})} and hence the algorithm is a special case of gradient descent. For ill-posed problems, the iterative method needs to be stopped at a suitable iteration index, because it semi-converges. This means that the iterates approach a regularized solution during the first iterations, but become unstable in further iterations. The reciprocal of the iteration index 1 / k {\displaystyle 1/k} acts as a regularization parameter. A suitable parameter is found, when the mismatch ‖ A x k − y ‖ 2 2 {\displaystyle \|Ax_{k}-y\|_{2}^{2}} approaches the noise level. Using the Landweber iteration as a regularization algorithm has been discussed in the literature. == Nonlinear extension == In general, the updates generated by x k + 1 = x k − τ ∇ f ( x k ) {\displaystyle x_{k+1}=x_{k}-\tau \nabla f(x_{k})} will generate a sequence f ( x k ) {\displaystyle f(x_{k})} that converges to a minimizer of f whenever f is convex and the stepsize τ {\displaystyle \tau } is chosen such that 0 < τ < 2 / ( ‖ ∇ f ‖ 2 ) {\displaystyle 0<\tau <2/(\|\nabla f\|^{2})} where ‖ ⋅ ‖ {\displaystyle \|\cdot \|} is the spectral norm. Since this is special type of gradient descent, there currently is not much benefit to analyzing it on its own as the nonlinear Landweber, but such analysis was performed historically by many communities not aware of unifying frameworks. The nonlinear Landweber problem has been studied in many papers in many communities; see, for example. == Extension to constrained problems == If f is a convex function and C is a convex set, then the problem min x ∈ C f ( x ) {\displaystyle \min _{x\in C}f(x)} can be solved by the constrained, nonlinear Landweber iteration, given by: x k + 1 = P C ( x k − τ ∇ f ( x k ) ) {\displaystyle x_{k+1}={\mathcal {P}}_{C}(x_{k}-\tau \nabla f(x_{k}))} where P {\displaystyle {\mathcal {P}}} is the projection onto the set C. Convergence is guaranteed when 0 < τ < 2 / ( ‖ A ‖ 2 ) {\displaystyle 0<\tau <2/(\|A\|^{2})} . This is again a special case of projected gradient descent (which is a special case of the forward–backward algorithm) as discussed in. == Applications == Since the method has been around since the 1950s, it has been adopted and rediscovered by many scientific communities, especially those studying ill-posed problems. In X-ray computed tomography it is called simultaneous iterative reconstruction technique (SIRT). It has also been used in the computer vision community and the signal restoration community. It is also used in image processing, since many image problems, such as deconvolution, are ill-posed. Variants of this method have been used also in sparse approximation problems and compressed sensing settings.

Lobsang Monlam

Geshe Lobsang Monlam (Tibetan: དགེ་བཤེས་བློ་བཟང་སྨོན་ལམ, Wylie: dge bshes blo bzang smon lam), born in 1976 in Ngawa eastern Tibet, is a Tibetan Buddhist scholar and programmer who uses digital technologies to preserve the Tibetan language and culture. He is best known for developing Tibetan typefaces and for the multi-volume Great Monlam Tibetan Dictionary. In 2025, he received the Snow Lion Award for Human Rights from the International Campaign for Tibet. He is also working on developing a "Dalai Lama AI," a specialized language model. == Biography == Lobsang Monlam was born in 1976 in Ngawa, eastern Tibet, anciently Tibetan Amdo, where he became a monk at the age of 12.. At the age of 17, in 1993, Lobsang Monlam fled Tibet by crossing the Himalayas to reach southern India and discovered computer science in a monastery. In 1993, he was ordained monk in the Sera Mey College in Bylakuppe, Karnataka, India, where he obtained a Geshe title in 2013.. By the early 2000s, Lobsang Monlam had already learned to paint thangkas and to compose plans and drawings. He used this knowledge to design a new assembly hall for Sera Mey, which the monks needed. Thanks to his work, Lobsang Monlam received donations from patrons of the monastery, which he was able to use to buy his first computer. He bought his first laptop in 2002 and largely taught himself how to use the hardware and software with the help of manuals. As a Buddhist scholar, he combines meditation practice with his digital work. In 2012, he founded and directs the Monlam Tibetan Information Technology Research Center in Dharamsala, which specializes in Tibetan language and software projects. Since then, he is its director, researching Tibetan language-related software. In 2019, advised by the 14th Dalai Lama, he founded Monlam IT and Research (OPC) Private Limited. Since the 2000s, Monlam has been developing Tibetan typefaces; the first Monlam Tibetan font was created in 2005. Under his direction, the Monlam Great Tibetan Dictionary was created, comprising 223 printed volumes and over 300,000 entries; approximately 150 people worked on this project for over nine years. On May 27, 2022, the Dalai Lama inaugurated the Monlam Tibetan Dictionary, produced by the Monlam Tibetan Information Technology Research Center, at Namgyal Monastery in McLeod Ganj. According to Penpa Tsering, this is the world's largest dictionary, created with guidance from the Dalai Lama, based on proposals from Lobsang Monlam and his team under the direction of Samdhong Rinpoche, and other lamas from all schools of Tibetan Buddhism and Yungdrung Bön. On December 5, 2024, Lobsang Monlam testified at a hearing of the US Congressional-Executive Commission on China in Washington, chaired by Christopher Smith, on the difficulties of preserving the Tibetan language and culture in Tibet and the Tibetan diaspora, and on the interest of the Monlam Tibetan Informatics Research Center in developing technologies for the preservation of the Tibetan language. On December 12, 2024, the work was presented to the Library of Congress in Washington, D.C., and launched at an event. The free Monlam Great Tibetan Dictionary app is available in several languages; the German version was created in collaboration with the Tibet Institute Rikon and has been downloaded millions of times. In total, Monlam has created over 37 apps related to the Tibetan language and translation; In 2023, its center launched the Monlam artificial intelligence platform, equipped with modules for machine translation, optical character recognition, speech transcription and speech synthesis.. For their efforts, he and Sophie Richardson received the Snow Lion Award in 2025, which was presented by Richard Gere and came with a prize of €3,000. In 2019, he started a PhD at Bangalore University on Library Science. He obtained his doctorate on November 30, 2023. Currently, he spearheads Monlam AI. Lobsang Monlam is developing "Dalai Lama AI" to digitally preserve the teachings of the 14th Dalai Lama, now 90 years old, for future generations. Lobsang Monlam states, "If we succeed in preserving the Dalai Lama, we also preserve the movement."

Logic Programming Associates

Logic Programming Associates (LPA) is a company specializing in logic programming and artificial intelligence software. LPA was founded in 1980 and is widely known for its range of Prolog compilers, the Flex expert system toolkit and most recently, VisiRule. LPA was established to exploit research at the Department of Computing and Control at Imperial College London into logic programming carried out under the supervision of Prof Robert Kowalski. == History of LPA Prolog == One of the first Prolog implementations made available by LPA was micro-PROLOG which ran on popular 8-bit home computers such as the Sinclair ZX Spectrum and Apple II. The 8-bit micro-PROLOG interpreter was soon followed by micro-PROLOG Professional one of the first Prolog implementations for the IBM PC running MS-DOS. micro-PROLOG Professional could access all of the 640K memory available under MS-DOS and therefore manage much larger programs In 1985, LPA released LPA MacProlog which ran on the MacPlus and Mac II computers which could access up to 4 Mb memory. MacProlog was later licensed to Quintus for re-distribution in the USA. In 1989, LPA started work on a new 32-bit Prolog compiler which could use DOS-extender technology to access up to 4GB memory. This became the basis for LPA Prolog for Windows, aka WIN-PROLOG, which was then released for Windows 3.0 in 1990. LPA's core Prolog product is LPA Prolog for Windows, a compiler and development system for the Microsoft Windows platform. The current LPA software range comprises an integrated AI toolset which covers various aspects of Artificial Intelligence including Logic Programming, Expert Systems, Knowledge-based Systems, Data Mining, Agents and Case-based reasoning etc. As well as continuing with Prolog compiler technology development, LPA has a track record of creating innovative associated tools and products to address specific challenges and opportunities. == Flex Expert System toolkit == In 1989, in response to the rise of interest in Expert Systems and the emergence of products such as Crystal, GoldWorks, NExpert, LPA developed the Flex expert system toolkit, which incorporated frame-based reasoning with inheritance, rule-based programming and data-driven procedures. Flex has its own English-like Knowledge Specification Language (KSL) which means that knowledge and rules are defined in an easy-to-read and understand way. LPA supported Flex on Windows, DOS and Macintosh PCs, as an add-on toolkit to its various LPA Prolog systems and eanbled LPA to enter the then quick vibrant Expert Systems rules-market. Flex was quickly established as the leading Prolog-based expert system toolkit and was licensed to other Prolog providors on other hardware platforms including Telecomputing Plc to supplement Top One on IBM and ICL mainframes. Other implementations included Quintec-Flex, Quintus Flex, Poplog Flex and BIM Flex which were all running on Unix and/or Vax/VMS platforms. POPLOG-Flex was used to build BRAND EVALUATOR - an expert system to assist brand specialists in evaluating the worth of branded products Quintec-Flex was used to build a hybrid system for the non-linear dynamic analysis/design of coupled shear walls Flex was adopted by the Open University as part of its course T396, "Artificial intelligence for technology" which was designed by Prof Adrian Hopgood. Some of the teaching material is now available on his AI tookit website. Flex was also used by David A Ferrucci and Selmer Bringsjord in their storytelling machine, BRUTUS. == PVG == In 1992, LPA helped set up the Prolog Vendors Group, a not-for-profit organization whose aim was to help promote Prolog by making people aware of its usage in industry. == Business Integrity Ltd and Contract Express == Between 1996 and 1998, based on work co-funded through a DTI Smart award, LPA developed ScaffoldIT, a tool for building dynamic documents and intelligent web sites. This technology, built using the LPA Prolog engine and associated ProWeb Server, was able to generate complex, personalised documents such as insurance policy schedules, legal contracts, and complex sales proposals, over the Web. In 1999/2000, LPA helped set up Business Integrity Ltd, as a Joint Venture with Tarlo-Lyons, to bring the above document assembly technology to market. This product eventually became Contract Express. Contract Express became very popular amongst large law firms and was sold worldwide for both internal and external use. Partners and GCs liked Contract Express because lawyers were able to quickly and accurately automate and update their legal templates in Word without requiring IT specialists to convert them into programs. As a result of the commercial success of Contract Express, BIL was acquired by Thomson Reuters in 2015. The very early days of BIL are described by Clive Spenser here. == VisiRule == In 2004, LPA launched VisiRule a graphical tool for developing knowledge-based and decision support systems. VisiRule was described in IEEE Potentials in 2007 (see Drawing on your knowledge with VisiRule): VisiRule has been used in various sectors, to build legal expert systems, machine diagnostic programs, medical and financial advice systems, etc. In 2013, VisiRule was incorporated into Ecosystem Management Decision Support (EMDS) where it has been used to provide enhanced decision support capabilities. EMDS integrates state-of-the-art geographic information system (GIS) as well as logic programming and decision modeling technologies on multiple platforms (Windows, Linux, Mac OS X) to provide decision support for a substantial portion of the adaptive management process of ecosystem management. EMDS is actively used, extended, supported and maintained by Mountain View Business Group (for an in-depth reprise of EMDS see the article in Frontiers in Environmental Science). In 2023, VisiRule was listed as one of the 5 best decision support software for large enterprises in 2024. == Customers == For many years, LPA has worked closely with Valdis Krebs, an American-Latvian researcher, author, and consultant in the field of social and organizational network analysis. Valdis is the founder and chief scientist of Orgnet, and the creator of the popular Inflow software package. LPA Prolog and Flex were used to create Allergenius, an expert system for the interpretation of allergen microarray results. Rules representing the knowledge base (KB) were derived from the literature and specialized databases. The input data included the patient's ID and disease(s), the results of either a skin prick test or specific IgE assays and ISAC results. The output was a medical report.

Six Little Dragons

Six Little Dragons (Chinese: 杭州六小龙), or Six Little Dragons of Hangzhou, are an informal grouping of the tech startups Game Science, DeepSeek, Unitree Robotics, DEEP Robotics, BrainCo and Manycore Tech. All six were established in Hangzhou, They are active in artificial intelligence, robotics, gaming, and brain-computer interface technology. Hangzhou is referred to as the China’s “e-commerce capital” (电商之都). The nickname "Six Little Dragons" originated from the Chinese internet. == Background == === Chinese government investments (2002 — 2010s) === From 2002 to 2007, under Xi Jinping's leadership as party secretary of Zhejiang, provincial spending on technology research grew over four times to 28 billion RMB. The province launched "Digital Zhejiang" (数字浙江) to advance modernization and the "Eight Eight Strategy" (八八战略), focusing on eight advantages and actions to boost industrial development, including specialized industries. In 2010, Hangzhou's government started "Project Eagle" (雏鹰计划) to aid science and technology startups. The project works with incubators and accelerators to find promising tech companies and offers public funding and other help, especially for startups by graduates and returning students. Unitree received support in the initial phase, along with government subsidies from Binjiang District. === AI-startups and further investments (2025 — present) === In January 2025, the Chinese government created the "Hangzhou AI Industry Chain High-Quality Development Action Plan" which focuses on computing power, LLM technologies, and AI applications. The plan was made to certify over 2,000 new high-tech enterprises, initiate over 300 major tech projects, and invest more than 300 billion RMB (US$40 billion) annually. The Chinese government also renewed "Project Eagle" and to allocate 15% of industrial policy funds for future industries. Hangzhou aimed to become a center for tech startups, highlighting the "six little dragons of Hangzhou," a nickname popularized in early 2025. This group includes DeepSeek, Game Science, Unitree Robotics, Manycore Tech, BrainCo, and DEEP Robotics, companies in gaming, robotics, and software development. Earlier in 2025, DeepSeek, one of the six dragons, launched an AI system at a much lower cost than those from Silicon Valley. Since then, DeepSeek and Alibaba have produced top-performing open source AI models. Game Science launched the successful video game Black Myth: Wukong in 2024, while Unitree gained attention for their dancing robots in the 2025 annual spring gala broadcast by Chinese state media. The group was acknowledged by Chinese authorities in Hangzhou in a New Years message for local businesses in January 2025. Hangzhou’s universities were given credit for the development of Chinese technological industry. Zhejiang University alumni founded three of the "Six Little Dragons". By September 2024, the university produced 102 executives in Chinese AI start-ups, ranking third among China's top institutions. On February 20, 2025, Alibaba's Eddie Wu stated that the company would focus on artificial generative intelligence and plans significant investment in AI. The company also sought to boost foreign investment to China's "Six Little Dragons" following Alibaba's founder Jack Ma attended General Secretary of the Chinese Communist Party Xi Jinping's business symposium with corporate leaders and entrepreneurs that same month. == Challenges == China's net foreign direct investment (FDI) fell by US$168 billion in 2024, marking the largest capital flight since 1990. Foreign investment peaked at US$344 billion in 2021 but has since declined according to the State Administration of Foreign Exchange. In 2024, foreign investors put in only US$4.5 billion while Chinese firms invested US$173 billion abroad. According to interviews conducted by The New York Times, some start-up company founders believe that Chinese government's support for Hangzhou's technological sector has deterred foreign investors. Tensions with the United States led many international companies to adopt a China Plus One strategy, while Chinese firms build factories overseas to avoid potential Trump tariffs. China also faced US restrictions on its access of advanced chips, forcing Chinese tech companies to stockpile Nvidia chips while Chinese producers like Huawei and Semiconductor Manufacturing International Corporation (SMIC) were competing to produce their own.

Comparison of vector graphics editors

A number of vector graphics editors exist for various platforms. Potential users of these editors will make comparisons based on factors such as the availability for the user's platform, the software license, the feature set, the merits of the user interface (UI) and the focus of the program. Some programs are more suitable for artistic work while others are better for technical drawings. Another important factor is the application's support of various vector and bitmap image formats for import and export. The tables in this article compare general and technical information for a number of vector graphics editors. See the article on each editor for further information. This article is neither all-inclusive nor necessarily up-to-date. == Some editors in detail == Adobe Fireworks (formerly Macromedia Fireworks) is a vector editor with bitmap editing capabilities with its main purpose being the creation of graphics for Web and screen. Fireworks supports RGB color scheme and has no CMYK support. This means it is mostly used for screen design. The native Fireworks file format is editable PNG (FWPNG or PNG). Adobe Fireworks has a competitive price, but its features can seem limited in comparison with other products. It is easier to learn than other products and can produce complex vector artwork. The Fireworks editable PNG file format is not supported by other Adobe products. Fireworks can manage the PSD and AI file formats which enables it to be integrated with other Adobe apps. Fireworks can also open FWPNG/PNG, PSD, AI, EPS, JPG, GIF, BMP, TIFF file formats, and save/export to FWPNG/PNG, PSD, AI (v.8), FXG (v.2.0), JPG, GIF, PDF, SWF and some others. Some support for exporting to SVG is available via a free Export extension. On May 6, 2013, Adobe announced that Fireworks would be phased out. Adobe Flash (formerly a Macromedia product) has straightforward vector editing tools that make it easier for designers and illustrators to use. The most important of these tools are vector lines and fills with bitmap-like selectable areas, simple modification of curves via the "selection" or the control points/handles through "direct selection" tools. Flash uses Actionscript for OOP, and has full XML functionality through E4X support. Adobe FreeHand (formerly Macromedia Freehand and Aldus Freehand) is mainly used by professional graphic designers. The functionality of FreeHand includes the flexibility of the application in the wide design environment, catering to the output needs of both traditional image reproduction methods and to contemporary print and digital media with its page-layout capabilities and text attribute controls. Specific functions of FreeHand include a superior image-tracing operation for vector editing, page layout features within multiple-page documents, and embedding custom print-settings (such as variable halftone-screen specifications within a single graphic, etc.) to each document independent of auxiliary printer-drivers. User-operation is considered to be more suited for designers with an artistic background compared to designers with a technical background. When being marketed, FreeHand lacked the promotional backing, development and PR support in comparison to other similar products. FreeHand was transferred to the classic print group after Macromedia was purchased by Adobe in 2005. On May 16, 2007, Adobe announced that no further updates to Freehand would be developed but continues to sell FreeHand MX as a Macromedia product. FreeHand continues to run on Mac OS X Snow Leopard (using an Adobe fix) and on Windows 7. For macOS, Affinity Designer is able to open version 10 & MX Freehand files. Adobe Illustrator is a commonly used editor because of Adobe's market dominance, but is more expensive than other similar products. It is primarily developed consistently in line with other Adobe products and is best integrated with Adobe's Creative Suite packages. The ai file format is proprietary, but some vector editors can open and save in that format. Illustrator imports over two dozen formats, including PSD, PDF and SVG, and exports AI, PDF, SVG, SVGZ, GIF, JPG, PNG, WBMP, and SWF. However, the user must be aware of unchecking the "Preserve Illustrator Editing Capabilities" option if generating interoperable SVG files is desired. Affinity Designer by Serif Europe (the successor to their previous product, DrawPlus) is non-subscription-based software that is often described as an alternative to Adobe Illustrator. The application can open Portable Document Format (PDF), Adobe Photoshop, and Adobe Illustrator files, as well as export to those formats and to the Scalable Vector Graphics (SVG) and Encapsulated PostScript (EPS) formats. It also supports import from some Adobe Freehand files (specifically versions 10 & MX). Apache OpenOffice Draw is the vector graphics editor of the Apache OpenOffice open source office suite. It supports many import and export file formats and is available for multiple desktop operating systems. Boxy SVG is a chromium-based vector graphics editor for creating illustrations, as well as logos, icons, and other elements of graphic design. It is primarily focused on editing drawings in the SVG file format. The program is available as both a web app and a desktop application for Windows, macOS, ChromeOS, and Linux-based operating systems. Collabora Online Draw is the vector graphics editor of the Collabora Online open source office suite. It supports many import and export file formats and is accessible via any modern web browser, it also supports desktop editing features, Collabora Office is available for desktop and mobile operating systems, it is the enterprise ready version of LibreOffice. ConceptDraw PRO is a business diagramming tool and vector graphics editor available for both Windows and macOS. It supports multi-page documents, and includes an integrated presentation mode. ConceptDraw PRO supports imports and exports several formats, including Microsoft Visio and Microsoft PowerPoint. Corel Designer (originally Micrografx Designer) is one of the earliest vector-based graphics editors for the Microsoft Windows platform. The product is mainly used for the creation of engineering drawings and is shipped with extensive libraries for the needs of engineers. It is also flexible enough for most vector graphics design applications. CorelDRAW is an editor used in the graphic design, sign making and fashion design industries. CorelDRAW is capable of limited interoperation by reading file formats from Adobe Illustrator. CorelDRAW has over 50 import and export filters, on-screen and dialog box editing and the ability to create multi-page documents. It can also generate TrueType and Type 1 fonts, although refined typographic control is better suited to a more specific application. Some other features of CorelDRAW include the creation and execution of VBA macros, viewing of colour separations in print preview mode and integrated professional imposing options. Dia is a free and open-source diagramming and vector graphics editor available for Windows, Linux and other Unix-based computer operating systems. Dia has a modular design and several shape packages for flowcharting, network diagrams and circuit diagrams. Its design was inspired by Microsoft Visio, although it uses a Single Document Interface similar to other GNOME software (such as GIMP). DrawPlus, first built for the Windows platform in 1993, has matured into a full featured vector graphics editor for home and professional users. Also available as a feature-limited free 'starter edition': DrawPlus SE. DrawPlus developers, Serif Europe, have now ceased its development in order to focus on its successor, Affinity Designer. Edraw Max is a cross-platform diagram software and vector graphics editor available for Windows, Mac and Linux. It supports kinds of diagram types. It supports imports and exports SVG, PDF, HTML, Multiple page TIFF, Microsoft Visio and Microsoft PowerPoint. Embroidermodder is a free machine embroidery software tool that supports a variety of formats and allows the user to add custom modifications to their embroidery designs. Fatpaint is a free, light-weight, browser-based graphic design application with built-in vector drawing tools. It can be accessed through any browser with Flash 9 installed. Its integration with Zazzle makes it particularly suitable for people who want to create graphics for custom printed products such as T-shirts, mugs, iPhone cases, flyers and other promotional products. Figma is a collaborative web-based online vector graphics editor, used primarily for UX design and prototyping. GIMP, which works mainly with raster images, offers a limited set of features to create and record SVG files. It can also load and handle SVG files created with other software like Inkscape. Inkscape is a free and open-source vector editor with the primary native format being SVG. Inkscape is available for Linux, Windows, Mac OS X, and

NLWeb

Natural Language Web or NLWeb was introduced by Microsoft in 2025. It is an open Python project designed to simplify the creation of natural language interfaces for websites. It enables users to query website contents using natural language, similar to interacting with an AI assistant. Every instance functions as a Model Context Protocol (MCP) server allowing websites to make their content discoverable and accessible to AI agents and other participants. NLWeb leverages existing web standards like Schema.org and RSS to build conversational capabilities of processing user queries through language models, performing semantic searches against website content and generating natural responses. It is platform-agnostic, running on all major systems and connecting to any vector database. Content to be indexed by NLWeb works best when it is organized in an AI friendly way. This means short, interlinked and semantically annotated articles work best. Initial adopters of NLWeb include TripAdvisor, Shopify, Eventbrite, and Hearst.