Zoho Office Suite is an online office suite developed by Zoho Corporation. == History == Zoho Office Suite was launched in 2005 with a web-based word processor. Additional products, such as those for spreadsheets and presentations, were incorporated later into the suite. The applications are distributed as software as a service (SaaS). == Products == Zoho uses an open API for its Writer, Sheet, Show, Creator, Meeting, and Planner products. It also has plugins into Microsoft Word and Excel, an OpenOffice.org plugin, and a plugin for Firefox. Zoho Office Suite is free for individuals but offers a plan for teams, which includes Zoho WorkDrive, Zoho Workplace and other Zoho apps. In October 2009, Zoho integrated some of their applications with the Google Apps online suite.
Teamwork (project management)
Teamwork.com is an Irish, privately owned, web-based software company headquartered in Cork, Ireland. Teamwork creates task management and team collaboration software. Founded in 2007, as of 2016 the company stated that its software was in use by over 370,000 organisations worldwide (including Disney, Spotify and HP), and that it had over 2.4m users. == History == Peter Coppinger and Dan Mackey founded a company, Digital Crew, in 2007. This company built websites, intranets and custom web-based solutions for clients in Cork, Ireland. Frustrated by whiteboards and software management tools, Coppinger wanted a software system that would help manage client projects and which would be easy to use and generic enough to be used by different types of companies. Originally 37signals Basecamp users themselves, Coppinger and Mackey were frustrated by the limited feature set, and by Basecamp's apparent inaction on their feedback. In October 2007, Coppinger and Mackey launched Teamwork Project Manager, nicknamed TeamworkPM. In March 2015, this was renamed as Teamwork Projects. In 2014, after two years of negotiations, TeamworkPM bought the domain name 'Teamwork.com' for US$675,000 (€500,000). At the time this was one of the most expensive domain name purchases by an Irish company, and involved the transfer of a domain name which had been dormant since it was first acquired by the original owner in 1999. In 2015, Teamwork.com was named by Gartner to be one of their "Cool Vendors" in the Program and Portfolio Management Category. This was followed by the launch of a new real-time messaging product, Teamwork Chat, in January 2015. In June 2015, the company announced a drive to recruit for 40 positions by the end of the year. This was followed by the announcement that the company was investing more than €1 million in a new office, and had leased office space in Park House, Blackpool. In June 2016, Teamwork.com undertook a further recruitment drive to entice developers to Cork. In July 2021, the company announced that it had raised an investment of $70 million (€59.1 million) from venture capital firm Bregal Milestone to fund further growth. == Products == Teamwork markets a number of cloud-based applications, including Teamwork, Teamwork Desk, Teamwork Spaces, Teamwork CRM and Teamwork Chat. Teamwork was launched on 4 October 2007, at which time it had time management, milestone management, file sharing, time tracking, and messaging features. Teamwork's platform reportedly integrates with martech software like HubSpot, as well as other productivity tools like Slack, G Suite, MS Teams, Zapier, Dropbox and QuickBooks. == Awards == In 2016, Teamwork was awarded Cork's Best SME in the Cork Chamber of Commerce "Company of the Year" awards. In 2016, Teamwork was named number 7 in Deloitte's Fast 50 tech companies hit €1.6bn turnover. In 2015, Teamwork was identified as a Gartner "Cool Vendor" in the Program and Portfolio Management Category.
Kernel principal component analysis
In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space. == Background: Linear PCA == Recall that conventional PCA operates on zero-centered data; that is, 1 N ∑ i = 1 N x i = 0 {\displaystyle {\frac {1}{N}}\sum _{i=1}^{N}\mathbf {x} _{i}=\mathbf {0} } , where x i {\displaystyle \mathbf {x} _{i}} is one of the N {\displaystyle N} multivariate observations. It operates by diagonalizing the covariance matrix, C = 1 N ∑ i = 1 N x i x i ⊤ {\displaystyle C={\frac {1}{N}}\sum _{i=1}^{N}\mathbf {x} _{i}\mathbf {x} _{i}^{\top }} in other words, it gives an eigendecomposition of the covariance matrix: λ v = C v {\displaystyle \lambda \mathbf {v} =C\mathbf {v} } which can be rewritten as λ x i ⊤ v = x i ⊤ C v for i = 1 , … , N {\displaystyle \lambda \mathbf {x} _{i}^{\top }\mathbf {v} =\mathbf {x} _{i}^{\top }C\mathbf {v} \quad {\textrm {for}}~i=1,\ldots ,N} . (See also: Covariance matrix as a linear operator) == Introduction of the Kernel to PCA == To understand the utility of kernel PCA, particularly for clustering, observe that, while N points cannot, in general, be linearly separated in d < N {\displaystyle d In machine learning, weighted majority algorithm (WMA) is a meta learning algorithm used to construct a compound algorithm from a pool of prediction algorithms, which could be any type of learning algorithms, classifiers, or even real human experts. The algorithm assumes that we have no prior knowledge about the accuracy of the algorithms in the pool, but there are sufficient reasons to believe that one or more will perform well. Assume that the problem is a binary decision problem. To construct the compound algorithm, a positive weight is given to each of the algorithms in the pool. The compound algorithm then collects weighted votes from all the algorithms in the pool, and gives the prediction that has a higher vote. If the compound algorithm makes a mistake, the algorithms in the pool that contributed to the wrong predicting will be discounted by a certain ratio β where 0<β<1. It can be shown that the upper bounds on the number of mistakes made in a given sequence of predictions from a pool of algorithms A {\displaystyle \mathbf {A} } is O ( l o g | A | + m ) {\displaystyle \mathbf {O(log|A|+m)} } if one algorithm in x i {\displaystyle \mathbf {x} _{i}} makes at most m {\displaystyle \mathbf {m} } mistakes. There are many variations of the weighted majority algorithm to handle different situations, like shifting targets, infinite pools, or randomized predictions. The core mechanism remains similar, with the final performances of the compound algorithm bounded by a function of the performance of the specialist (best performing algorithm) in the pool. In computational geometry, the farthest-first traversal of a compact metric space is a sequence of points in the space, where the first point is selected arbitrarily and each successive point is as far as possible from the set of previously-selected points. The same concept can also be applied to a finite set of geometric points, by restricting the selected points to belong to the set or equivalently by considering the finite metric space generated by these points. For a finite metric space or finite set of geometric points, the resulting sequence forms a permutation of the points, also known as the greedy permutation. Every prefix of a farthest-first traversal provides a set of points that is widely spaced and close to all remaining points. More precisely, no other set of equally many points can be spaced more than twice as widely, and no other set of equally many points can be less than half as far to its farthest remaining point. In part because of these properties, farthest-point traversals have many applications, including the approximation of the traveling salesman problem and the metric k-center problem. They may be constructed in polynomial time, or (for low-dimensional Euclidean spaces) approximated in near-linear time. == Definition and properties == A farthest-first traversal is a sequence of points in a compact metric space, with each point appearing at most once. If the space is finite, each point appears exactly once, and the traversal is a permutation of all of the points in the space. The first point of the sequence may be any point in the space. Each point p after the first must have the maximum possible distance to the set of points earlier than p in the sequence, where the distance from a point to a set is defined as the minimum of the pairwise distances to points in the set. A given space may have many different farthest-first traversals, depending both on the choice of the first point in the sequence (which may be any point in the space) and on ties for the maximum distance among later choices. Farthest-point traversals may be characterized by the following properties. Fix a number k, and consider the prefix formed by the first k points of the farthest-first traversal of any metric space. Let r be the distance between the final point of the prefix and the other points in the prefix. Then this subset has the following two properties: All pairs of the selected points are at distance at least r from each other, and All points of the metric space are at distance at most r from the subset. Conversely any sequence having these properties, for all choices of k, must be a farthest-first traversal. These are the two defining properties of a Delone set, so each prefix of the farthest-first traversal forms a Delone set. == Applications == Rosenkrantz, Stearns & Lewis (1977) used the farthest-first traversal to define the farthest-insertion heuristic for the travelling salesman problem. This heuristic finds approximate solutions to the travelling salesman problem by building up a tour on a subset of points, adding one point at a time to the tour in the ordering given by a farthest-first traversal. To add each point to the tour, one edge of the previous tour is broken and replaced by a pair of edges through the added point, in the cheapest possible way. Although Rosenkrantz et al. prove only a logarithmic approximation ratio for this method, they show that in practice it often works better than other insertion methods with better provable approximation ratios. Later, the same sequence of points was popularized by Gonzalez (1985), who used it as part of greedy approximation algorithms for two problems in clustering, in which the goal is to partition a set of points into k clusters. One of the two problems that Gonzalez solve in this way seeks to minimize the maximum diameter of a cluster, while the other, known as the metric k-center problem, seeks to minimize the maximum radius, the distance from a chosen central point of a cluster to the farthest point from it in the same cluster. For instance, the k-center problem can be used to model the placement of fire stations within a city, in order to ensure that every address within the city can be reached quickly by a fire truck. For both clustering problems, Gonzalez chooses a set of k cluster centers by selecting the first k points of a farthest-first traversal, and then creates clusters by assigning each input point to the nearest cluster center. If r is the distance from the set of k selected centers to the next point at position k + 1 in the traversal, then with this clustering every point is within distance r of its center and every cluster has diameter at most 2r. However, the subset of k centers together with the next point are all at distance at least r from each other, and any k-clustering would put some two of these points into a single cluster, with one of them at distance at least r/2 from its center and with diameter at least r. Thus, Gonzalez's heuristic gives an approximation ratio of 2 for both clustering problems. Gonzalez's heuristic was independently rediscovered for the metric k-center problem by Dyer & Frieze (1985), who applied it more generally to weighted k-center problems. Another paper on the k-center problem from the same time, Hochbaum & Shmoys (1985), achieves the same approximation ratio of 2, but its techniques are different. Nevertheless, Gonzalez's heuristic, and the name "farthest-first traversal", are often incorrectly attributed to Hochbaum and Shmoys. For both the min-max diameter clustering problem and the metric k-center problem, these approximations are optimal: the existence of a polynomial-time heuristic with any constant approximation ratio less than 2 would imply that P = NP. As well as for clustering, the farthest-first traversal can also be used in another type of facility location problem, the max-min facility dispersion problem, in which the goal is to choose the locations of k different facilities so that they are as far apart from each other as possible. More precisely, the goal in this problem is to choose k points from a given metric space or a given set of candidate points, in such a way as to maximize the minimum pairwise distance between the selected points. Again, this can be approximated by choosing the first k points of a farthest-first traversal. If r denotes the distance of the kth point from all previous points, then every point of the metric space or the candidate set is within distance r of the first k − 1 points. By the pigeonhole principle, some two points of the optimal solution (whatever it is) must both be within distance r of the same point among these first k − 1 chosen points, and (by the triangle inequality) within distance 2r of each other. Therefore, the heuristic solution given by the farthest-first traversal is within a factor of two of optimal. Other applications of the farthest-first traversal include color quantization (clustering the colors in an image to a smaller set of representative colors), progressive scanning of images (choosing an order to display the pixels of an image so that prefixes of the ordering produce good lower-resolution versions of the whole image rather than filling in the image from top to bottom), point selection in the probabilistic roadmap method for motion planning, simplification of point clouds, generating masks for halftone images, hierarchical clustering, finding the similarities between polygon meshes of similar surfaces, choosing diverse and high-value observation targets for underwater robot exploration, fault detection in sensor networks, modeling phylogenetic diversity, matching vehicles in a heterogenous fleet to customer delivery requests, uniform distribution of geodetic observatories on the Earth's surface or of other types of sensor network, generation of virtual point lights in the instant radiosity computer graphics rendering method, and geometric range searching data structures. == Algorithms == === Greedy exact algorithm === The farthest-first traversal of a finite point set may be computed by a greedy algorithm that maintains the distance of each point from the previously selected points, performing the following steps: Initialize the sequence of selected points to the empty sequence, and the distances of each point to the selected points to infinity. While not all points have been selected, repeat the following steps: Scan the list of not-yet-selected points to find a point p that has the maximum distance from the selected points. Remove p from the not-yet-selected points and add it to the end of the sequence of selected points. For each remaining not-yet-selected point q, replace the distance stored for q by the minimum of its old value and the distance from p to q. For a set of n points, this algorithm takes O(n2) steps and O(n2) distance computations. === Approximations === A faster approximation algorithm, given by Har-Peled & Mendel (2006), applie N-World is a 3D graphics package developed by Nichimen Graphics in the 1990s, for Silicon Graphics and Windows NT workstations. Intended primarily for video game content creation, it has polygon modeling tools, 2D and 3D paint, scripting, color reduction, and exporters for several popular game consoles. After its initial release on Windows NT, N-World was renamed Mirai. The winged edge 3D modeler in N-World inspired the development at Nichimen Graphics of Nendo, a standalone 3D modeler, which in turn inspired the open source modeler Wings 3D. == History == N-World originated with Symbolics, a computer manufacturer notable for producing Lisp-based systems in the 1980s. Among the software packages that were produced for Symbolics computers are S-Graphics, a 3D animation suite that includes modules for polygon modeling, dynamics, paint, and rendering — titled S-Geometry, S-Dynamics, S-Paint, and S-Render, respectively. In 1992, Japanese trading company Nichimen Corporation purchased the rights to S-Graphics, ported it to Silicon Graphics IRIX, and marketed it as N-World. N-World retains the Lisp-based underpinnings of its predecessor, but was targeted at interactive content producers, with features useful for game developers. It was priced at US$16,995 (equivalent to $34,100 in 2025) for the full suite, later reduced to $9,995 when ported to Windows NT in 1997. N-World was used to create graphics for many console games in the 1990s, specifically most of the Nintendo 64 games, like Super Mario 64 and Final Fantasy VII. It was superseded by Mirai in 1999. == Features == The N-World package, like its predecessor S-Graphics, is divided into several components: N-Geometry: 3D polygon-based modeling tools, including smoothing, "magnet" geometry editing, and instancing. N-Dynamics: Animation tools including scripting, curve-based animation, and skeletal animation. N-Render: Surfacing and rendering tools with ray tracing and materials output to various game console formats. N-Paint: 2D and 3D paint with mattes, effects, color reduction, and a visual VRAM editor for PlayStation. Game Tools: Utilities for game developers, including exporters for PlayStation, Nintendo 64, and Saturn consoles. == Credits == The following games were created using N-World. Rap Stars Online In machine learning, a nearest centroid classifier or nearest prototype classifier is a classification model that assigns to observations the label of the class of training samples whose mean (centroid) is closest to the observation. When applied to text classification using word vectors containing tfidf weights to represent documents, the nearest centroid classifier is known as the Rocchio classifier because of its similarity to the Rocchio algorithm for relevance feedback. An extended version of the nearest centroid classifier has found applications in the medical domain, specifically classification of tumors. == Algorithm == === Training === Given labeled training samples { ( x → 1 , y 1 ) , … , ( x → n , y n ) } {\displaystyle \textstyle \{({\vec {x}}_{1},y_{1}),\dots ,({\vec {x}}_{n},y_{n})\}} with class labels y i ∈ Y {\displaystyle y_{i}\in \mathbf {Y} } , compute the per-class centroids μ → ℓ = 1 | C ℓ | ∑ i ∈ C ℓ x → i {\displaystyle \textstyle {\vec {\mu }}_{\ell }={\frac {1}{|C_{\ell }|}}{\underset {i\in C_{\ell }}{\sum }}{\vec {x}}_{i}} where C ℓ {\displaystyle C_{\ell }} is the set of indices of samples belonging to class ℓ ∈ Y {\displaystyle \ell \in \mathbf {Y} } . === Prediction === The class assigned to an observation x → {\displaystyle {\vec {x}}} is y ^ = arg min ℓ ∈ Y ‖ μ → ℓ − x → ‖ {\displaystyle {\hat {y}}={\arg \min }_{\ell \in \mathbf {Y} }\|{\vec {\mu }}_{\ell }-{\vec {x}}\|} .Weighted majority algorithm (machine learning)
Farthest-first traversal
N-World
Nearest centroid classifier