In machine learning (ML), a learning curve (or training curve) is a graphical representation that shows how a model's performance on a training set (and usually a validation set) changes with the number of training iterations (epochs) or the amount of training data. Typically, the number of training epochs or training set size is plotted on the x-axis, and the value of the loss function (and possibly some other metric such as the cross-validation score) on the y-axis. Synonyms include error curve, experience curve, improvement curve and generalization curve. More abstractly, learning curves plot the difference between learning effort and predictive performance, where "learning effort" usually means the number of training samples, and "predictive performance" means accuracy on testing samples. Learning curves have many useful purposes in ML, including: choosing model parameters during design, adjusting optimization to improve convergence, and diagnosing problems such as overfitting (or underfitting). Learning curves can also be tools for determining how much a model benefits from adding more training data, and whether the model suffers more from a variance error or a bias error. If both the validation score and the training score converge to a certain value, then the model will no longer significantly benefit from more training data. == Formal definition == When creating a function to approximate the distribution of some data, it is necessary to define a loss function L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} to measure how good the model output is (e.g., accuracy for classification tasks or mean squared error for regression). We then define an optimization process which finds model parameters θ {\displaystyle \theta } such that L ( f θ ( X ) , Y ) {\displaystyle L(f_{\theta }(X),Y)} is minimized, referred to as θ ∗ {\displaystyle \theta ^{}} . === Training curve for amount of data === If the training data is { x 1 , x 2 , … , x n } , { y 1 , y 2 , … y n } {\displaystyle \{x_{1},x_{2},\dots ,x_{n}\},\{y_{1},y_{2},\dots y_{n}\}} and the validation data is { x 1 ′ , x 2 ′ , … x m ′ } , { y 1 ′ , y 2 ′ , … y m ′ } {\displaystyle \{x_{1}',x_{2}',\dots x_{m}'\},\{y_{1}',y_{2}',\dots y_{m}'\}} , a learning curve is the plot of the two curves i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ) , Y i ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}),Y_{i})} i ↦ L ( f θ ∗ ( X i , Y i ) ( X i ′ ) , Y i ′ ) {\displaystyle i\mapsto L(f_{\theta ^{}(X_{i},Y_{i})}(X_{i}'),Y_{i}')} where X i = { x 1 , x 2 , … x i } {\displaystyle X_{i}=\{x_{1},x_{2},\dots x_{i}\}} === Training curve for number of iterations === Many optimization algorithms are iterative, repeating the same step (such as backpropagation) until the process converges to an optimal value. Gradient descent is one such algorithm. If θ i ∗ {\displaystyle \theta _{i}^{}} is the approximation of the optimal θ {\displaystyle \theta } after i {\displaystyle i} steps, a learning curve is the plot of i ↦ L ( f θ i ∗ ( X , Y ) ( X ) , Y ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X),Y)} i ↦ L ( f θ i ∗ ( X , Y ) ( X ′ ) , Y ′ ) {\displaystyle i\mapsto L(f_{\theta _{i}^{}(X,Y)}(X'),Y')}
Oculus Quill
Quill is a painting and animation software for virtual reality. It runs on Microsoft Windows with Oculus Rift headsets. It is used to create 3D paintings and animated cartoons. Quill was released on November 29, 2016, on the Oculus Store. Theater Elsewhere(formerly Quill Theater), an application for viewing creations made in Quill, was later made available following the release of the Oculus Quest. In September 2021, Facebook, now known as Meta Platforms, and the owner of Oculus, sold Quill to its original creator, who continues to develop and support the app. == Development == Quill was originally developed by Oculus Story Studio as an internal tool for the creative needs of the studio's project Dear Angelica directed by Saschka Unseld along with its art-director Wesley Allsbrook. == Controls == The software works on Oculus Rift utilizing its 6DoF motion controllers. Users can paint in 3D space using their hands naturally, and animate those paintings with keyframes. They can also capture videos and photos of their creations. == Reception == Dear Angelica, a VR story fully painted in Quill, was nominated for an Emmy Award in 2017.
Floyd–Steinberg dithering
Floyd–Steinberg dithering is an image dithering algorithm first published in 1976 by Robert W. Floyd and Louis Steinberg. It is commonly used by image manipulation software, for example, when converting an image from a Truecolor 24-bit PNG format into a GIF format, which is restricted to a maximum of 256 colors. == Implementation == The algorithm achieves dithering using error diffusion, meaning it pushes (adds) the residual quantization error of a pixel onto its neighboring pixels, to be quantized after. It spreads the debt out according to the distribution (shown as a map of the neighboring pixels): [ ∗ 7 16 … … 3 16 5 16 1 16 … ] {\displaystyle {\begin{bmatrix}&&&{\frac {\displaystyle 7}{\displaystyle 16}}&\ldots \\\ldots &{\frac {\displaystyle 3}{\displaystyle 16}}&{\frac {\displaystyle 5}{\displaystyle 16}}&{\frac {\displaystyle 1}{\displaystyle 16}}&\ldots \\\end{bmatrix}}} The pixel indicated with a star () indicates the pixel currently being scanned, and the blank pixels are the previously scanned pixels. The specific values (7/16, 3/16, 5/16, 1/16) were originally found by trial-and-error, "guided by the desire to have a region of desired density 0.5 come out as a checkerboard pattern". The algorithm scans the image from left to right, top to bottom, quantizing pixel values one by one. Each time, the quantization error is transferred to the neighboring pixels, while not affecting the pixels that already have been quantized. Hence, if a number of pixels have been rounded downwards, it becomes more likely that the next pixel is rounded upwards, such that on average, the quantization error is close to zero. The diffusion coefficients have the property that if the original pixel values are exactly halfway in between the nearest available colors, the dithered result is a checkerboard pattern. For example, 50% grey data could be dithered as a black-and-white checkerboard pattern. For optimal dithering, the counting of quantization errors should be in sufficient accuracy to prevent rounding errors from affecting the result. For correct results, all values should be linearized first, rather than operating directly on sRGB values as is common for images stored on computers. In some implementations, the horizontal direction of scan alternates between lines; this is called "serpentine scanning" or boustrophedon transform dithering. The algorithm described above is in the following pseudocode. This works for any approximately linear encoding of pixel values, such as 8-bit integers, 16-bit integers or real numbers in the range [0, 1]. for each y from top to bottom do for each x from left to right do oldpixel := pixels[x][y] newpixel := find_closest_palette_color(oldpixel) pixels[x][y] := newpixel quant_error := oldpixel - newpixel pixels[x + 1][y ] := pixels[x + 1][y ] + quant_error × 7 / 16 pixels[x - 1][y + 1] := pixels[x - 1][y + 1] + quant_error × 3 / 16 pixels[x ][y + 1] := pixels[x ][y + 1] + quant_error × 5 / 16 pixels[x + 1][y + 1] := pixels[x + 1][y + 1] + quant_error × 1 / 16 When converting grayscale pixel values from a high to a low bit depth (e.g. 8-bit grayscale to 1-bit black-and-white), find_closest_palette_color() may perform just a simple rounding, for example: find_closest_palette_color(oldpixel) = round(oldpixel / 255) The pseudocode can result in pixel values exceeding the valid values (such as greater than 255 in 8-bit grayscale images). Such values should ideally be handled by the find_closest_palette_color() function, rather than clipping the intermediate values, since a subsequent error may bring the value back into range. However, if fixed-width integers are used, wrapping of intermediate values would cause inversion of black and white, and so should be avoided. The find_closest_palette_color() implementation is nontrivial for a palette that is not evenly distributed, however small inaccuracies in selecting the correct palette color have minimal visual impact due to error being propagated to future pixels. A nearest neighbor search in 3D is frequently used.
IRows
iRows was a web-based spreadsheet in beta with a GUI similar to the traditional desktop-based spreadsheet applications, such as Microsoft Excel and OpenOffice.org. It was shut down on December 31, 2006, after it was announced that its two founders had been hired by Google. iRows used Ajax and XML. It was described as an example of a Web 2.0 system. iRows supported conventional spreadsheet features functions, value formatting and charts and added web oriented spreadsheet capabilities like collaboration (multiple people using a shared spreadsheet, sending a spreadsheet as a link instead of an attachment and ability to publish spreadsheets on other web pages (e.g. blogs).
Elasticity (computing)
In computing, elasticity is defined as "the degree to which a system is able to adapt to workload changes by provisioning and de-provisioning resources in an autonomic manner, such that at each point in time the available resources match the current demand as closely as possible". Elasticity is a defining characteristic that differentiates cloud computing from previously proposed distributed computing paradigms, such as grid computing. The dynamic adaptation of capacity, e.g., by altering the use of computing resources, to meet a varying workload is called "elastic computing". In the world of distributed systems, there are several definitions according to the authors; some consider the concepts of scalability a sub-part of elasticity, others as being distinct. == Purpose == Elasticity aims to match the amount of resources allocated to a service with the amount of resources it actually requires, avoiding over- or under-provisioning. Over-provisioning, i.e., allocating more resources than required, should be avoided as it may incur extra costs (monetary, energy, operational, etc.) for unused or underutilized resources. For example, if a website is over-provisioned with two cloud computing resources to handle current demand that only requires one resource, the costs of maintaining the second resource would effectively be wasted. Under-provisioning, i.e., allocating fewer resources than required, must be avoided; otherwise, the service cannot serve its users with a good service. For example, under-provisioning a website may make it seem slow or unreachable, because not enough resources have been allocated to meet current demand. == Example == Elasticity can be illustrated through an example of a service provider who wants to run a website on the cloud. At moment t 0 {\displaystyle t_{0}} , the website is unpopular and a single machine is sufficient to serve all users. At moment t 1 {\displaystyle t_{1}} , the website suddenly becomes popular, and a single machine is no longer sufficient to serve all users. Based on the number of web users simultaneously accessing the website and the resource requirements of the web server, ten machines are needed. An elastic system should immediately detect this condition and provision nine additional machines from the cloud to serve all users responsively. At time t 2 {\displaystyle t_{2}} , the website becomes unpopular again. The ten machines currently allocated to the website are mostly idle and a single machine would be sufficient to serve the few users who are accessing the website. An elastic system should immediately detect this condition and deprovision nine machines, releasing them to the cloud. == Problems == === Resource provisioning time === Resource provisioning takes time. A cloud virtual machine (VM) can be acquired at any time by the user; however, it may take up to several minutes for the acquired VM to be ready to use. The VM startup time is dependent on factors such as image size, VM type, data center location, number of VMs, etc. Cloud providers have different VM startup performance. This implies that any control mechanism designed for elastic applications must consider the time needed for the resource provisioning actions to take effect. === Monitoring elastic applications === Elastic applications can allocate and deallocate resources on demand for specific application components. This makes cloud resources volatile, and traditional monitoring tools which associate monitoring data with a particular resource, such as Ganglia or Nagios, are no longer suitable for monitoring the behavior of elastic applications. For example, during its lifetime, a data storage tier of an elastic application might add and remove data storage VMs due to cost and performance requirements, varying the number of used VMs. Thus, additional information is needed in monitoring elastic applications, such as associating the logical application structure over the underlying virtual infrastructure. This in turn generates other problems, such as data aggregation from multiple VMs towards extracting the behavior of the application component running on top of those VMs, as different metrics may need to be aggregated differently (e.g., CPU usage could be averaged, network transfer might be summed up). === Stakeholder requirements === When deploying applications in cloud infrastructures (IaaS/PaaS), stakeholder requirements need to be considered in order to ensure that elastic behavior meets stakeholder needs. Traditionally, the optimal trade-off between cost and quality or performance is considered; however, for real world cloud users, requirements regarding elastic behavior are more complex and target multiple dimensions of elasticity (e.g., SYBL). === Multiple levels of control === Cloud applications vary in type and complexity, with multiple levels of artifacts deployed in layers. Controlling such structures must take into consideration a variety of issues. For multi-level control, control systems need to consider the impact lower level control has upon higher level ones, and vice versa (e.g., controlling virtual machines, web containers, or web services in the same time), as well as conflicts that may appear between various control strategies from various levels. Elastic strategies on in cloud computing can take advantage of control-theoretic methods (e.g., predictive control has been experimented in cloud computing scenarios by showing considerable advantages with respect to reactive methods). One approach to multi-level elastic clouc control is rSYBL.
Voice search
Voice search, also called voice-enabled search, allows the user to use a voice to search the Internet, a website, or an app. In a broader definition, voice search includes open-domain keyword query on any information on the Internet, for example in Google Voice Search, Cortana, Siri and Amazon Echo. Voice search is often interactive, involving several rounds of interaction that allows a system to ask for clarification. Voice search is a type of dialog system. Voice search is not a replacement for typed search. Rather the search terms, experience and use cases can differ heavily depending on the input type. == Supported language == Language is the most essential factor for a system to understand, and provide the most accurate results of what the user searches. This covers across languages, dialects, and accents, as users want a voice assistant that both understands them and speaks to them understandably. While spoken and written languages differ, voice search should support natural spoken language instead of only transforming voice into text and doing a regular text search with the help speech recognition. For example, in typed search an eCommerce user can easily copy and paste an alphanumeric product code to search field, but when speaking the search terms can be very different, such as "show me the new Bluetooth headphones by Samsung". == How it works == The difference between text and voice search is not only the input type. The mechanism must include an automatic speech recognition (ASR) for input, but it can also include natural language understanding for natural spoken search queries such as "What's the population for the United States" It can include text-to-speech (TTS) or a regular display for output modalities. Users might sometimes be required to activate the search by using a wake word. Then, the search system will detect the language spoken by the user. It will then detect the keywords and context of the sentence. Lastly, the device will return results depending on its output. A device with a screen might display the results, while a device without a screen will speak them back to the searcher.
Free boundary condition
In image processing, the free boundary condition is the convention used when applying a convolution kernel to a digital image in which pixel locations that lie outside the image boundaries are interpreted as having a value of zero.[1] The question of what value to assign out-of-bounds pixels may arise, for instance, when applying a 3×3 kernel to the corner pixel in an image.