In machine learning, manifold regularization is a technique for using the shape of a dataset to constrain the functions that should be learned on that dataset. In many machine learning problems, the data to be learned do not cover the entire input space. For example, a facial recognition system may not need to classify any possible image, but only the subset of images that contain faces. The technique of manifold learning assumes that the relevant subset of data comes from a manifold, a mathematical structure with useful properties. The technique also assumes that the function to be learned is smooth: data with different labels are not likely to be close together, and so the labeling function should not change quickly in areas where there are likely to be many data points. Because of this assumption, a manifold regularization algorithm can use unlabeled data to inform where the learned function is allowed to change quickly and where it is not, using an extension of the technique of Tikhonov regularization. Manifold regularization algorithms can extend supervised learning algorithms in semi-supervised learning and transductive learning settings, where unlabeled data are available. The technique has been used for applications including medical imaging, geographical imaging, and object recognition. == Manifold regularizer == === Motivation === Manifold regularization is a type of regularization, a family of techniques that reduces overfitting and ensures that a problem is well-posed by penalizing complex solutions. In particular, manifold regularization extends the technique of Tikhonov regularization as applied to Reproducing kernel Hilbert spaces (RKHSs). Under standard Tikhonov regularization on RKHSs, a learning algorithm attempts to learn a function f {\displaystyle f} from among a hypothesis space of functions H {\displaystyle {\mathcal {H}}} . The hypothesis space is an RKHS, meaning that it is associated with a kernel K {\displaystyle K} , and so every candidate function f {\displaystyle f} has a norm ‖ f ‖ K {\displaystyle \left\|f\right\|_{K}} , which represents the complexity of the candidate function in the hypothesis space. When the algorithm considers a candidate function, it takes its norm into account in order to penalize complex functions. Formally, given a set of labeled training data ( x 1 , y 1 ) , … , ( x ℓ , y ℓ ) {\displaystyle (x_{1},y_{1}),\ldots ,(x_{\ell },y_{\ell })} with x i ∈ X , y i ∈ Y {\displaystyle x_{i}\in X,y_{i}\in Y} and a loss function V {\displaystyle V} , a learning algorithm using Tikhonov regularization will attempt to solve the expression arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ ‖ f ‖ K 2 {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma \left\|f\right\|_{K}^{2}} where γ {\displaystyle \gamma } is a hyperparameter that controls how much the algorithm will prefer simpler functions over functions that fit the data better. Manifold regularization adds a second regularization term, the intrinsic regularizer, to the ambient regularizer used in standard Tikhonov regularization. Under the manifold assumption in machine learning, the data in question do not come from the entire input space X {\displaystyle X} , but instead from a nonlinear manifold M ⊂ X {\displaystyle M\subset X} . The geometry of this manifold, the intrinsic space, is used to determine the regularization norm. === Laplacian norm === There are many possible choices for the intrinsic regularizer ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} . Many natural choices involve the gradient on the manifold ∇ M {\displaystyle \nabla _{M}} , which can provide a measure of how smooth a target function is. A smooth function should change slowly where the input data are dense; that is, the gradient ∇ M f ( x ) {\displaystyle \nabla _{M}f(x)} should be small where the marginal probability density P X ( x ) {\displaystyle {\mathcal {P}}_{X}(x)} , the probability density of a randomly drawn data point appearing at x {\displaystyle x} , is large. This gives one appropriate choice for the intrinsic regularizer: ‖ f ‖ I 2 = ∫ x ∈ M ‖ ∇ M f ( x ) ‖ 2 d P X ( x ) {\displaystyle \left\|f\right\|_{I}^{2}=\int _{x\in M}\left\|\nabla _{M}f(x)\right\|^{2}\,d{\mathcal {P}}_{X}(x)} In practice, this norm cannot be computed directly because the marginal distribution P X {\displaystyle {\mathcal {P}}_{X}} is unknown, but it can be estimated from the provided data. === Graph-based approach of the Laplacian norm === When the distances between input points are interpreted as a graph, then the Laplacian matrix of the graph can help to estimate the marginal distribution. Suppose that the input data include ℓ {\displaystyle \ell } labeled examples (pairs of an input x {\displaystyle x} and a label y {\displaystyle y} ) and u {\displaystyle u} unlabeled examples (inputs without associated labels). Define W {\displaystyle W} to be a matrix of edge weights for a graph, where W i j {\displaystyle W_{ij}} is a similarity built from distance measure between the data points x i {\displaystyle x_{i}} and x j {\displaystyle x_{j}} (so that more close implies higher W i j {\displaystyle W_{ij}} ). Define D {\displaystyle D} to be a diagonal matrix with D i i = ∑ j = 1 ℓ + u W i j {\displaystyle D_{ii}=\sum _{j=1}^{\ell +u}W_{ij}} and L {\displaystyle L} to be the Laplacian matrix D − W {\displaystyle D-W} . Then, as the number of data points ℓ + u {\displaystyle \ell +u} increases, L {\displaystyle L} converges to the Laplace–Beltrami operator Δ M {\displaystyle \Delta _{M}} , which is the divergence of the gradient ∇ M {\displaystyle \nabla _{M}} . Then, if f {\displaystyle \mathbf {f} } is a vector of the values of f {\displaystyle f} at the data, f = [ f ( x 1 ) , … , f ( x l + u ) ] T {\displaystyle \mathbf {f} =[f(x_{1}),\ldots ,f(x_{l+u})]^{\mathrm {T} }} , the intrinsic norm can be estimated: ‖ f ‖ I 2 = 1 ( ℓ + u ) 2 f T L f {\displaystyle \left\|f\right\|_{I}^{2}={\frac {1}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As the number of data points ℓ + u {\displaystyle \ell +u} increases, this empirical definition of ‖ f ‖ I 2 {\displaystyle \left\|f\right\|_{I}^{2}} converges to the definition when P X {\displaystyle {\mathcal {P}}_{X}} is known. === Solving the regularization problem with graph-based approach === Using the weights γ A {\displaystyle \gamma _{A}} and γ I {\displaystyle \gamma _{I}} for the ambient and intrinsic regularizers, the final expression to be solved becomes: arg min f ∈ H 1 ℓ ∑ i = 1 ℓ V ( f ( x i ) , y i ) + γ A ‖ f ‖ K 2 + γ I ( ℓ + u ) 2 f T L f {\displaystyle {\underset {f\in {\mathcal {H}}}{\arg \!\min }}{\frac {1}{\ell }}\sum _{i=1}^{\ell }V(f(x_{i}),y_{i})+\gamma _{A}\left\|f\right\|_{K}^{2}+{\frac {\gamma _{I}}{(\ell +u)^{2}}}\mathbf {f} ^{\mathrm {T} }L\mathbf {f} } As with other kernel methods, H {\displaystyle {\mathcal {H}}} may be an infinite-dimensional space, so if the regularization expression cannot be solved explicitly, it is impossible to search the entire space for a solution. Instead, a representer theorem shows that under certain conditions on the choice of the norm ‖ f ‖ I {\displaystyle \left\|f\right\|_{I}} , the optimal solution f ∗ {\displaystyle f^{}} must be a linear combination of the kernel centered at each of the input points: for some weights α i {\displaystyle \alpha _{i}} , f ∗ ( x ) = ∑ i = 1 ℓ + u α i K ( x i , x ) {\displaystyle f^{}(x)=\sum _{i=1}^{\ell +u}\alpha _{i}K(x_{i},x)} Using this result, it is possible to search for the optimal solution f ∗ {\displaystyle f^{}} by searching the finite-dimensional space defined by the possible choices of α i {\displaystyle \alpha _{i}} . === Functional approach of the Laplacian norm === The idea beyond the graph-Laplacian is to use neighbors to estimate the Laplacian. This method is akin to local averaging methods, that are known to scale poorly in high-dimensional problems. Indeed, the graph Laplacian is known to suffer from the curse of dimensionality. Luckily, it is possible to leverage expected smoothness of the function to estimate thanks to more advanced functional analysis. This method consists of estimating the Laplacian operator using derivatives of the kernel reading ∂ 1 , j K ( x i , x ) {\displaystyle \partial _{1,j}K(x_{i},x)} where ∂ 1 , j {\displaystyle \partial _{1,j}} denotes the partial derivatives according to the j-th coordinate of the first variable. This second approach to the Laplacian norm is to put in relation with meshfree methods, that contrast with the finite difference method in PDE. == Applications == Manifold regularization can extend a variety of algorithms that can be expressed using Tikhonov regularization, by choosing an appropriate loss function V {\displaystyle V} and hypothesis space H {\displaystyle {\mathcal {H}}} . Two commonly used examples are the families of support vector machines and regularized least squares algorithm
Shader lamps
Shader lamps is a computer graphic technique used to change the appearance of physical objects. The still or moving objects are illuminated, using one or more video projectors, by static or animated texture or video stream. The method was invented at University of North Carolina at Chapel Hill by Ramesh Raskar, Greg Welch, Kok-lim Low and Deepak Bandyopadhyay in 1999 [1] as a follow on to Spatial Augmented Reality [2] also invented at University of North Carolina at Chapel Hill in 1998 by Ramesh Raskar, Greg Welch and Henry Fuchs. A 3D graphic rendering software is typically used to compute the deformation caused by the non perpendicular, non-planar or even complex projection surface. Complex objects (or aggregation of multiple simple objects) create self shadows that must be compensated by using several projectors. The objects are typically replaced by neutral color ones, the projection giving all its visual properties, thus the name shader lamps. The technique can be used to create a sense of invisibility, by rendering transparency. The object is illuminated not by a replacement of its own visual properties, but by the corresponding visual surface placed behind the object as seen from an arbitrary viewing point.
Security and Privacy in Computer Systems
Security and Privacy in Computer Systems is a paper by Willis Ware that was first presented to the public at the 1967 Spring Joint Computer Conference. == Significance == Ware's presentation was the first public conference session about information security and privacy in respect of computer systems, especially networked or remotely-accessed ones. The IEEE Annals of the History of Computing said that Ware's 1967 Spring Joint Computer Conference session, together with 1970's Ware report, marked the start of the field of computer security.
Sherwood Applied Business Security Architecture
SABSA (Sherwood Applied Business Security Architecture) is a model and methodology for developing a risk-driven enterprise information security architecture and service management, to support critical business processes. It was developed independently from the Zachman Framework, but has a similar structure. The primary characteristic of the SABSA model is that everything must be derived from an analysis of the business requirements for security, especially those in which security has an enabling function through which new business opportunities can be developed and exploited. The process analyzes the business requirements at the outset, and creates a chain of traceability through the strategy and concept, design, implementation, and ongoing ‘manage and measure’ phases of the lifecycle to ensure that the business mandate is preserved. Framework tools created from practical experience further support the whole methodology. The model is layered, with the top layer being the business requirements definition stage. At each lower layer a new level of abstraction and detail is developed, going through the definition of the conceptual architecture, logical services architecture, physical infrastructure architecture and finally at the lowest layer, the selection of technologies and products (component architecture). The SABSA model itself is generic and can be the starting point for any organization, but by going through the process of analysis and decision-making implied by its structure, it becomes specific to the enterprise, and is finally highly customized to a unique business model. It becomes in reality the enterprise security architecture, and it is central to the success of a strategic program of information security management within the organization. SABSA is a particular example of a methodology that can be used both for IT (information technology) and OT (operational technology) environments. == SABSA matrix == Note: The above is the original SABSA Matrix, which is still valid today, but it has been expanded by a comprehensive service management matrix and updated in some detail and terminology areas. In the words of David Lynas, SABSA author, "The SABSA Matrix and the SABSA Service Management Matrix have not been updated since the late 90s. We have redesigned them to deliver the improvements your feedback has requested over the years. We have not fundamentally changed the structure or principles of the matrices (very few elements have changed position) but have focused on terminology update and consistency." The new versions can be downloaded (along with the 2009 revision of the SABSA White Paper and other important documents like the SABSA Certification Roadmap) at the SABSA Members' Web Site.
Colour banding
Colour banding is a subtle form of posterisation in digital images, caused by the colour of each pixel being rounded to the nearest of the digital colour levels. While posterisation is often done for artistic effect, colour banding is an undesired artefact. In 24-bit colour modes, 8 bits per channel is usually considered sufficient to render images in Rec. 709 or sRGB. However the eye can see the difference between the colour levels, especially when there is a sharp border between two large areas of adjacent colour levels. This will happen with gradual gradients (like sunsets, dawns or clear blue skies), and also when blurring an image a large amount. Colour banding is more noticeable with fewer bits per pixel (BPP) at 16–256 colours (4–8 BPP), where there are fewer shades with a larger difference between them. The appearance of colour banding is exaggerated by the Mach bands effect. Possible solutions include the introduction of dithering and increasing the number of bits per colour channel. Because the banding comes from limitations in the presentation of the image, blurring the image does not fix this unless the image BPP is higher than the original.
Apache Parquet
Apache Parquet is a free and open-source column-oriented data storage format in the Apache Hadoop ecosystem inspired by Google Dremel interactive ad-hoc query system for analysis of read-only nested data. It is similar to RCFile and ORC, the other columnar-storage file formats in Hadoop, and is compatible with most of the data processing frameworks around Hadoop. It provides data compression and encoding schemes with enhanced performance to handle complex data in bulk. == History == The open-source project to build Apache Parquet began as a joint effort between Twitter and Cloudera using the record shredding and assembly algorithm as described in Google's Dremel. Parquet was designed as an improvement on the Trevni columnar storage format created by Doug Cutting, the creator of Hadoop. The name 'parquet' (lit. 'small compartment') refers to a style of decorative flooring and was chosen to "evoke the bottom layer of a database with an interesting layout". The first version, Apache Parquet 1.0, was released in July 2013. Since April 27, 2015, Apache Parquet has been a top-level Apache Software Foundation (ASF)-sponsored project. == Features == Apache Parquet is implemented using the record-shredding and assembly algorithm, which accommodates the complex data structures that can be used to store data. The values in each column are stored in contiguous memory locations, providing the following benefits: Column-wise compression is efficient in storage space Encoding and compression techniques specific to the type of data in each column can be used Queries that fetch specific column values need not read the entire row, thus improving performance Apache Parquet is implemented using the Apache Thrift framework, which increases its flexibility; it can work with a number of programming languages like C++, Java, Python, PHP, etc. As of August 2015, Parquet supports the big-data-processing frameworks including Apache Hive, Apache Drill, Apache Impala, Apache Crunch, Apache Pig, Cascading, Presto and Apache Spark. It is one of the external data formats used by the pandas Python data manipulation and analysis library. == Compression and encoding == In Parquet, compression is performed column by column, which enables different encoding schemes to be used for text and integer data. This strategy also keeps the door open for newer and better encoding schemes to be implemented as they are invented. Parquet supports various compression formats: snappy, gzip, LZO, brotli, zstd, and LZ4. === Dictionary encoding === Parquet has an automatic dictionary encoding enabled dynamically for data with a small number of unique values (i.e. below 105) that enables significant compression and boosts processing speed. === Bit packing === Storage of integers is usually done with dedicated 32 or 64 bits per integer. For small integers, packing multiple integers into the same space makes storage more efficient. === Run-length encoding (RLE) === To optimize storage of multiple occurrences of the same value, run-length encoding is used, which is where a single value is stored once along with the number of occurrences. Parquet implements a hybrid of bit packing and RLE, in which the encoding switches based on which produces the best compression results. This strategy works well for certain types of integer data and combines well with dictionary encoding. == Cloud Storage and Data Lakes == Parquet is widely used as the underlying file format in modern cloud-based data lake architectures. Cloud storage systems such as Amazon S3, Azure Data Lake Storage, and Google Cloud Storage commonly store data in Parquet format due to its efficient columnar representation and retrieval capabilities. Data lakehouse frameworks—including Apache Iceberg, Delta Lake, and Apache Hudi —build an additional metadata layer on top of Parquet files to support features such as schema evolution, time-travel queries, and ACID-compliant transactions. In these architectures, Parquet files serve as the immutable storage layer while the table formats manage data versioning and transactional integrity. == Comparison == Apache Parquet is comparable to RCFile and Optimized Row Columnar (ORC) file formats — all three fall under the category of columnar data storage within the Hadoop ecosystem. They all have better compression and encoding with improved read performance at the cost of slower writes. In addition to these features, Apache Parquet supports limited schema evolution, i.e., the schema can be modified according to the changes in the data. It also provides the ability to add new columns and merge schemas that do not conflict. Apache Arrow is designed as an in-memory complement to on-disk columnar formats like Parquet and ORC. The Arrow and Parquet projects include libraries that allow for reading and writing between the two formats. == Implementations == Known implementations of Parquet include:
Shaded Picture System
The Shaded Picture System was a 3D raster computer display processor introduced by Evans & Sutherland in October 1973. The Shaded Picture System was the first general-purpose, commercially available raster computer graphics display processor capable of real-time, shaded 3D graphics. It could only display black and white graphics at a resolution of 256 by 256. It was extremely expensive, and very few units were ever sold. == History == The principles of shaded, hidden-line true 3D graphics were pioneered at the University of Utah in 1967. However, this algorithm was slow and would take several minutes to produce an image. In 1970, Gary Watkins developed a FORTRAN simulator of a faster algorithm that would theoretically generate shaded 3D images in real-time, "if implemented in suitable hardware". The simulator itself was still not capable of real-time shaded 3D image rendering. Evans & Sutherland developed a functional prototype of this "suitable hardware", which was later sold as the Shaded Picture System in 1973. About a year earlier in 1972, Evans & Sutherland sold the first and only CT1 to Case Western Reserve University. The CT1, or Continuous Tone 1, was a specialized image generator, not meant as a marketable or mass-produced product. At the time, the CT1, along with G.E./NASA's upgraded Electronic Scene Generator from 1971, would have been the only real-time raster graphics systems sold to customers comparable to the Shaded Picture System, although both the CT1 and Electronic Scene Generator were intentionally produced as one-off products and specialized for the needs of their customers. The Shaded Picture System, in contrast, was intentionally marketed.In early 1975, Evans & Sutherland demonstrated a random-access video frame buffer using relatively low-cost semiconductor memory, which was much more capable than the Shaded Picture System. When interfaced with a (non-shaded) E&S Picture System, the frame buffer had a resolution of 512 by 512 in grayscale and partial color capabilities. By the end of 1975, this frame buffer was commercially available.