Matrix factorization

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Non-negative matrix factorization for medical imaging

Non-negative matrix factorization for medical imaging

Abstract. A non-negative matrix factorization approach to dimension- ality reduction is proposed to aid classification of images. The original images can be stored as lower-dimensional columns of a matrix that hold degrees of belonging to feature components, so they can be used in the training phase of the classification at lower runtime and without loss in ac- curacy. The extracted features can be visually examined and images recon- structed with limited error. The proof of concept is performed on a bench- mark of handwritten digits, followed by the application to histopathologi- cal colorectal cancer slides. Results are encouraging, though dealing with real-world medical data raises a number of issues.
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6 Lee mas

Técnicas híbridas en sistemas de recomendación para optimizar el modelo non negative matrix factorization

Técnicas híbridas en sistemas de recomendación para optimizar el modelo non negative matrix factorization

Los factores latentes son un enfoque alternativo para tratar de explicar los votos que caracterizan a los usuarios e ´ıtems. Seg´un la cantidad de factores a inferir estos exponen en el caso de los ´ıtems diferentes dimensiones explicables, por ejemplo si las recomendaciones son pel´ıculas, los factores pueden definir el g´enero (acci´on, romance, ficci´on, etc.), el p´ublico al que est´a dirigido (todo p´ublico, mayores de 12 a˜nos, adultos, etc.); los factores tambi´en pueden definir dimensio- nes inexplicables. Para el caso de los usuarios, los factores indican cuanto le agrada a un usuario el ´ıtem en cada una de sus dimensiones. La implementaci´on m´as utilizada de factores latentes es el modelo Matrix Factorization, que en resumen lo que realiza es caracterizar los usuarios e ´ıtems en factores inferidos a partir de los patrones de votos. Estos m´etodos han cobrado re- levancia en los ´ultimos a˜nos porque combinan una buena escalabilidad con una buena calidad de predicciones, adem´as ofrecen mucha flexibilidad para modelar varias situaciones de la vida real.
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A Framework for Semantic Analysis of Histopathological Images Using Nonnegative Matrix Factorization

A Framework for Semantic Analysis of Histopathological Images Using Nonnegative Matrix Factorization

Abstract—This paper presents a novel and general framework for histopathology image analysis using nonnegative matrix factorization. The proposed method uses a collection-based image representation called Bag of Features (BOF) to represents the visual information of a histopathology image collection. Con- vex Nonnegative Matrix Factorization (CNMF) is applied to a training set of images to find a compact representation in a latent topic space. The latent representation has two important characteristics: first, CNMF is able to find representative clusters of images in the collection, second, clusters are represented by convex linear combinations of images in the training set. This latent representation is exploited in different ways by the proposed framework: concept labels can be assigned to clusters using the labels of the constituting images, representative images and visual words can be identified for each cluster, and new unlabeled images can be labeled by mapping them to the latent space. The proposed annotation model has an interesting property, it is easily interpretable since it is possible to trace those visual words present in the image which contribute the most to a given annotation. This implies that annotations in an image may be explained by identifying the regions that contributed to them. An exploratory experimentation was performed in a histopathology dataset used to diagnose a type of skin cancer called basal cell carcinoma. The preliminary results show that the combination of BOF and NMF is an interesting alternative for biomedical image collection analysis with a high level of interpretability.
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Towards reliability in collaborative filtering recommender systems

Towards reliability in collaborative filtering recommender systems

ability in certain tasks encourages many researchers to apply these promising tech- niques to constantly update the state-of-the-art frontier. Comparing to other families of model based CF techniques, neural network based ones can more easily capture the intrinsic non-linear and non-trivial user-item interactions, and obtain different levels of abstraction by means of complex representations achieved by hierarchical network structure. Recently a survey (Zhang, Yao, and Sun, 2017) gives a deep sys- tematic insight review on RS techniques that integrate different shadow or deep neu- ral network models, and a two-dimension scheme for classification of deep learning based RS is also provided as shown in Figure 2.4. The low dimensional represen- tation assumption still holds for this family of RS methods since the deep learning techniques are also recognized as the representation learning techniques. In gen- eral these methods based on neural network models need to achieve two objectives: representation learning and rating/ranking prediction, either jointly or sequentially. Different neural embedding techniques, such as word2vec (Mikolov et al., 2013), GloVe (Pennington, Socher, and Manning, 2014), doc2vec (Le and Mikolov, 2014) and StarSpace (Wu et al., 2018), are typically applied to learn the distributed repre- sentations (Rumelhart, Hinton, and Williams, 1986) of item descriptions in a shadow window to leverage the local contextual information of target item based on explicit ratings and side information like text descriptions. A series of publications such as Item2vec (Barkan and Koenigstein, 2016), Prod2Vec (Grbovic et al., 2015) and Meta- Prod2Vec (Vasile, Smirnova, and Conneau, 2016), are inspired by adopting embed- ding techniques developed from Skip-Gram with Negative Sampling (Mikolov et al., 2013) to recommendation field. As for the rating/ranking prediction task, both neural network models and previously introduced latent factor models like matrix factorization can be iteratively trained when the learned low dimensional represen- tations are fed into them. According to whether there are interactions between the representation learning and prediction components, the neural network based mod- els can be further categorized into loosely coupled methods and tightly coupled methods (Wang, Wang, and Yeung, 2015; Zhang, Yao, and Sun, 2017). As shown in Figure 2.5, loosely coupled methods sequentially conduct representation learning and prediction as a uni-direction work flow. On the contrary, tightly coupled methods alternatively and iteratively optimize the parameters of the neural network model for representa- tion learning and the parameters of the applied neural network or other latent factor model for the prediction task.
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Facial expression recognition using shape and texture information

Facial expression recognition using shape and texture information

The algorithm used was the DNMF algorithm, which is a extension of the Non-negative Matrix Factorization (NMF) algorithm. The NMF algorithm al- gorithm is an object decomposition algorithm that allows only additive com- binations of non negative components. DNMF was the result of an attempt to introduce discriminant information to the NMF decomposition. Both NMF and DNMF algorithms will be presented analytically below.

10 Lee mas

Matrix moment perturbations and the inverse Szegő matrix transformation

Matrix moment perturbations and the inverse Szegő matrix transformation

The term moment problem was used for the first time in T. J. Stieltjes’ clas- sic memoir [32] (published posthumously between 1894 and 1895) dedicated to the study of continued fractions. The moment problem is a question in classical analysis that has produced a rich theory in applied and pure mathematics. This problem is beautifully connected to the theory of orthogonal polynomials, spectral representation of operators, matrix factorization problems, probability, statistics, prediction of stochastic processes, polynomial optimization, inverse problems in financial mathematics and function theory, among many other areas. In the ma- trix case, M. Krein was the first to consider this problem in [21], and later on some density questions related to the matrix moment problem were addressed in [14, 15, 24, 25]. Recently, the theory of the matrix moment problem is used in [10] for the analysis of random matrix-valued measures. Since the matrix moment problem is closely related to the theory of matrix orthogonal polynomials, M. Krein was the first to consider these polynomials in [22]. Later, several researchers have made contributions to this theory until today. In the last 30 years, several known properties of orthogonal polynomials in the scalar case have been extended to the matrix case, such as algebraic aspects related to their zeros, recurrence relations, Favard type theorems, and Christoffel–Darboux formulas, among many others.
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A Lie Deprit perturbation algorithm for linear differential equations with periodic coefficients

A Lie Deprit perturbation algorithm for linear differential equations with periodic coefficients

Abstract. A perturbative procedure based on the Lie–Deprit algorithm of classical mechanics is proposed to compute analytic approximations to the fundamental matrix of linear differential equations with periodic coefficients. These approximations reproduce the structure assured by the Floquet theorem. Alternatively, the algorithm provides explicit approximations to the Lyapunov transformation reducing the original periodic problem to an autonomous sys- tem and also to its characteristic exponents. The procedure is computationally well adapted and converges for sufficiently small values of the perturbation pa- rameter. Moreover, when the system evolves in a Lie group, the approximations also belong to the same Lie group, thus preserving qualitative properties of the exact solution.
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18 Lee mas

Being in the Matrix

Being in the Matrix

omnipotent Frankenstein: An autopoietic daemon, invented and invited by the human race, which will not stop until a 'superhuman' being will stop it. It evokes the image of the brooms being stopped by the master sorcerer in Goethe’s poem The Sorcerer’s Apprentice. The Matrix’ agents, the Smiths, are like the mythical dragons which multiply their heads once the neck is cut by the hero’s sword. But not the human being made the consequent, consistent and systematic attempt to safe the planet – which he destroyed. Here is a twisted retribution: The Matrix, paralyses nature’s destroyer and abuses the human race as humans had abused nature before. For humans the Matrix is an evil God or a machine-Devil. For nature, machines – artificial creations like those which had previously destroyed it – now become the unlikely ally, since the human race is the terminal disease of the planet by both accounts. To take it one step further, perhaps the human race is even a sexually transmitted disease, since overpopulation and the accompanying destruction of nature were only possible by human procreation…. until the Matrix stops this procreation and replaces it by artificial but controlled and systematic fertilization. Consider the words of Agent Smith:
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The Matrix y el mito de la caverna

The Matrix y el mito de la caverna

The Matrix (1999), the movie of the Wachowski brothers, is one of these lucky examples that can be used in class to treat of philosophical complex concepts. It is not only a magnificent movie of action, is also an extraordinary allegory of copious utility for the analysis of notions not simple at all to deal as those of "reality" and “representation”, notions of undoubted ethical, aesthetic, ontological and epistemological scope.

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The Matrix and Philosophy

The Matrix and Philosophy

The Matrix is unquestionably a mixed-genre film. Our argu- ment is that, by considering the particular elements that make up the mix, we can find the narrative roots of The Matrix’s more obviously philosophical themes. And The Matrix certainly has its fair share of philosophical thematics and allusions. It alludes to core issues from metaphysics and epistemology such as the nature of truth and belief, the distinction between appearance and reality, as well as the possibilities and limits of knowledge. What, for instance, counts as a justifiable true belief in a virtual world? The Matrix alludes to central themes from ethics and moral philosophy, such as the question whether our will is free or whether in fact we are deterministically controlled by forces outside ourselves. Philosophers will immediately note parallels between The Matrix and such canonical texts as Plato’s Republic, especially the Allegory of the Cave, and Descartes’s Meditations on First Philosophy, notably the Dream Hypothesis. And we should not forget the spiritual and religious allusions which run from Nietzsche’s Übermensch through Zen Buddhism to apocalyptic Christianity, nor what The Matrix has to tell us about technology and science. Arguably, any properly philo- sophical consideration of The Matrix needs to recognize what is going on at the level of genre in the film. When the film’s genre inheritance is acknowledged, it becomes easier to see the liter- ary roots of its dominant philosophical motifs, and also to understand why, whatever philosophical questions the film alludes to, it does not propose philosophical answers, only genre ones.
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Ansoffs Matrix Basic Concepts

Ansoffs Matrix Basic Concepts

The need for this information means that you may find yourself in strategy meetings; a familiarity with the underlying business analysis techniques and jargon can help you to make a valuable contribution by bringing your own area of expertise into the discussion. The Ansoff Matrix, created by the American planning expert Igor Ansoff, is a strategic planning tool that links an organization’s marketing strategy with its general strategic di- rection. It presents four alternative growth strategies in the form of a 2x2 table or matrix. One dimension of the matrix considers ‘products’ (existing and new) and the other di- mension considers ‘markets’ (existing and new).
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Matrix : cuando al comecocos no le quedan opciones

Matrix : cuando al comecocos no le quedan opciones

Además los Wachowski buscan técnicas de cámaras vanguardistas de las que van a obtener unas escenas como nunca antes se habían visto. “Una vez que empiezas a tratar con la realidad digital - dicen los hermanos- puedes realmente ampliar los límites de lo que podría ser humanamente posible. Así que si los personajes de Matrix pueden lograr que se baje información instantáneamente a sus cabezas, deberían, por ejemplo, poder ser tan buenos maestros de kung fu como Jakie Chan”.[3]

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Matrix estimation using matrix forgetting factor and instrumental variable for nonstationary sequences with time variant matrix gain

Matrix estimation using matrix forgetting factor and instrumental variable for nonstationary sequences with time variant matrix gain

In this paper, deal with the class of models with varaying parameters and subjected to random disturbances of the moving-average type. We suggested a general version of (Instrumental Variable Method) IVM with Matrix Forgetting Factor (MFF) in agreement to the dynamical properties of the real system. A recursive version of this procedure has a basic description. The main issue of this work is the combination of MFF with IVM for multimatrices. Observing that a Digital Filter can be implemented into embedded systems using micro controllers, DSP's, and others electronic technologies, considering a recursive structure.
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Matrix, sistemas autopoiéticos e inestabilidad

Matrix, sistemas autopoiéticos e inestabilidad

Entonces, Neo va a la Ciudad de las Máquinas donde habla con su interfase principal, una especie de metarrobot formado por otros robots pequeños llamado Deus Ex Machina (del latín, literalmente Dios surgido de la Máquina). Neo le dice que “el programa Smith está fuera de su control, pronto se esparcirá por esta ciudad como lo hizo en Matrix, usted no lo puede parar, pero yo sí”, y cuando Deus Ex Machina le pregunta qué quiere a cambio, Neo le contesta “Paz”, es decir, Neo le propone derrotar a Smith a cambio de que las máquinas no destruyan Zión. Inmediatamente, las máquinas de combate que estaban por llegar a la última línea defensiva de Zión se detienen. Deus Ex Machina conecta a Neo a la Matrix para que derrote a Smith, devolviendo la Matrix a su estabilidad habitual.
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Descartes in the Matrix: Addressing the Question “What Is Real?” from Non-Positivist Ground

Descartes in the Matrix: Addressing the Question “What Is Real?” from Non-Positivist Ground

Consider the leap of imagination entailed when President Kennedy proposed the bold initiative to send a man to the moon and return him safely within a few years time. In this bold imagining, what was previously the stuff of fantasy became increasingly possible as the object world was transformed to meet this challenge. Test pilots and other aviators became astronauts, physicists became ‘rocket scientists’ and soon what had been purely in the realm of the ‘mental’ was transformed and literally real-ized [v.] in the world of extended things. It is this power to take up and transform the given into a world that most characterizes our humanity. Empiricist epistemology ‘enframes’ (Heidegger 1954/1977) the world and delimits its disclosure to the terms deemed real within its view. In this view a thing is reduced to being defined by its most anonymous properties. In this re- ductionist vision, an empiricist epistemology reifies the given into the real and turns a blind eye to the transformative poetic power that is human existence. It describes a world like the matrix, anonymous and indifferent to the freedom of its inhabitants. It describes a world that lacks precisely the attributes of human dwelling and involvement that are essential to dif- ferentiating the human world from mere collection of things in space for Heidegger (1927/1962).
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An Algorithm by Blocks for SuperMatrix Band Cholesky Factorization

An Algorithm by Blocks for SuperMatrix Band Cholesky Factorization

One naturally thinks of matrices stored by blocks as matrices of matrices. As a result, if the API encapsulates information that describes a matrix in an object, as FLAME does, and allows an element in a matrix to itself be a matrix object, then algorithms over matrices stored by blocks can be represented in code at the same high level of abstraction. Multiple layers of this idea can be used if multiple hierarchical layers in the matrix are to be exposed. We call this extension to the FLAME API the FLASH API [15]. Examples of how simpler operations can be transformed from FLAME to FLASH implementations can be found in [7, 9].
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MATRIX Andy & Larry Wachowski

MATRIX Andy & Larry Wachowski

MORFEO: ¿Te gustaría saber lo que es? Matrix nos rodea. Está por todas partes, incluso ahora, en esta misma habitación. Puedes verla si miras por la ventana o al encender la televisión. Puedes sentirla, cuando vas a trabajar, cuando vas a la iglesia, cuando pagas tus impuestos. Es el mundo que ha sido puesto ante tus ojos para ocultarte la verdad.

10 Lee mas

Variadores industriales Matrix U1000

Variadores industriales Matrix U1000

Este proyecto incluye la venta del variador industrial Matrix U1000, este es un equipo todo en uno que cumple con los requerimientos del estándar IEEE519 en distorsión armónica, regeneración completa de energía, y alto factor real de potencia. Encontrará que las características de nuestro producto son inigualables y la mejor elección para su proyecto.

11 Lee mas

Factorization Approach to Superintegrable Systems: Formalism and Applications

Factorization Approach to Superintegrable Systems: Formalism and Applications

In this section we will consider another example of superintegrable system on the Euclidean plane, but using polar coordinates instead of Cartesian ones. This is the case of the well-known TTW system [32]. In what follows we will apply the factorization method to find the symmetries according to [1], although we will introduce some inessential changes in order to simplify the discussion.

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TítuloSparse Givens QR Factorization on a Multiprocessor

TítuloSparse Givens QR Factorization on a Multiprocessor

We present a parallel algorithm for the QR fac- torization with column pivoting of a sparse matrix by means of Givens rotations. Nonzero elements of the matrix M to be decomposed are stored in a one- dimensional doubly linked list data structure. We will discuss a strategy to reduce ll-in in order to gain me- mory savings and decrease the computation times. As an application of QR factorization, we will describe the least squares problem. This algorithm has been designed for a message passing multiprocessor and we have evaluated it on the Cray T3D supercomputer using the Harwell-Boeing sparse matrix collection.
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