scholarly journals Binary Linear Compression for Multi-label Classification

2017 ◽  
Author(s):  
Wen-Ji Zhou ◽  
Yang Yu ◽  
Min-Ling Zhang
Keyword(s):  
Dimensional Space ◽  
Classification Problem ◽  
Complex Model ◽  
Linear Mapping ◽  
Regression Problem ◽  
Low Dimensional ◽  
The Relationship ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Linear Compression

In multi-label classification tasks, labels are commonly related with each other. It has been well recognized that utilizing label relationship is essential to multi-label learning. One way to utilizing label relationship is to map labels to a lower-dimensional space of uncorrelated labels, where the relationship could be encoded in the mapping. Previous linear mapping methods commonly result in regression subproblems in the lower-dimensional label space. In this paper, we disclose that mappings to a low-dimensional multi-label regression problem can be worse than mapping to a classification problem, since regression requires more complex model than classification. We then propose the binary linear compression (BILC) method that results in a binary label space, leading to classification subproblems. Experiments on several multi-label datasets show that, employing classification in the embedded space results in much simpler models than regression, leading to smaller structure risk. The proposed methods are also shown to be superior to some state-of-the-art approaches.

Methods for Binary Multidimensional Scaling

2002 ◽  
Vol 14 (5) ◽  
pp. 1195-1232 ◽  
Author(s):  
Douglas L. T. Rohde
Keyword(s):  
Neural Networks ◽  
Multidimensional Scaling ◽  
Dimensional Space ◽  
Discrete Space ◽  
High Dimensional ◽  
Continuous Space ◽  
Low Dimensional ◽  
Set Of Points ◽  
Lower Dimensional Space ◽  
Lower Dimensional

Multidimensional scaling (MDS) is the process of transforming a set of points in a high-dimensional space to a lower-dimensional one while preserving the relative distances between pairs of points. Although effective methods have been developed for solving a variety of MDS problems, they mainly depend on the vectors in the lower-dimensional space having real-valued components. For some applications, the training of neural networks in particular, it is preferable or necessary to obtain vectors in a discrete, binary space. Unfortunately, MDS into a low-dimensional discrete space appears to be a significantly harder problem than MDS into a continuous space. This article introduces and analyzes several methods for performing approximately optimized binary MDS.

scholarly journals Optimization of the multidimensional signal interpolator in a lower dimensional space

2019 ◽  
Vol 43 (4) ◽  
pp. 653-660 ◽  
Author(s):  
M.V. Gashnikov
Keyword(s):  
Experimental Study ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Multidimensional Signals ◽  
Multidimensional Signal ◽  
Signal Sample ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Selection Of

Adaptive multidimensional signal interpolators are developed. These interpolators take into account the presence and direction of boundaries of flat signal regions in each local neighborhood based on the automatic selection of the interpolating function for each signal sample. The selection of the interpolating function is performed by a parameterized rule, which is optimized in a parametric lower dimensional space. The dimension reduction is performed using rank filtering of local differences in the neighborhood of each signal sample. The interpolating functions of adaptive interpolators are written for the multidimensional, three-dimensional and two-dimensional cases. The use of adaptive interpolators in the problem of compression of multidimensional signals is also considered. Results of an experimental study of adaptive interpolators for real multidimensional signals of various types are presented.

scholarly journals GENETIC ALGORITHMS FOR MULTIDIMENSIONAL SCALING / GENETINIŲ ALGORITMŲ TAIKYMAS DAUGIAMATĖMS SKALĖMS

2015 ◽  
Vol 7 (3) ◽  
pp. 275-279 ◽  
Author(s):  
Agnė Dzidolikaitė
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Multidimensional Scaling ◽  
Optimization Problem ◽  
Dimensional Space ◽  
Local Solution ◽  
Multidimensional Data ◽  
Global Optimization Problem ◽  
Lower Dimensional Space ◽  
Lower Dimensional

The paper analyzes global optimization problem. In order to solve this problem multidimensional scaling algorithm is combined with genetic algorithm. Using multidimensional scaling we search for multidimensional data projections in a lower-dimensional space and try to keep dissimilarities of the set that we analyze. Using genetic algorithms we can get more than one local solution, but the whole population of optimal points. Different optimal points give different images. Looking at several multidimensional data images an expert can notice some qualities of given multidimensional data. In the paper genetic algorithm is applied for multidimensional scaling and glass data is visualized, and certain qualities are noticed. Analizuojamas globaliojo optimizavimo uždavinys. Jis apibrėžiamas kaip netiesinės tolydžiųjų kintamųjų tikslo funkcijos optimizavimas leistinojoje srityje. Optimizuojant taikomi įvairūs algoritmai. Paprastai taikant tikslius algoritmus randamas tikslus sprendinys, tačiau tai gali trukti labai ilgai. Dažnai norima gauti gerą sprendinį per priimtiną laiko tarpą. Tokiu atveju galimi kiti – euristiniai, algoritmai, kitaip dar vadinami euristikomis. Viena iš euristikų yra genetiniai algoritmai, kopijuojantys gyvojoje gamtoje vykstančią evoliuciją. Sudarant algoritmus naudojami evoliuciniai operatoriai: paveldimumas, mutacija, selekcija ir rekombinacija. Taikant genetinius algoritmus galima rasti pakankamai gerus sprendinius tų uždavinių, kuriems nėra tikslių algoritmų. Genetiniai algoritmai taip pat taikytini vizualizuojant duomenis daugiamačių skalių metodu. Taikant daugiamates skales ieškoma daugiamačių duomenų projekcijų mažesnio skaičiaus matmenų erdvėje siekiant išsaugoti analizuojamos aibės panašumus arba skirtingumus. Taikant genetinius algoritmus gaunamas ne vienas lokalusis sprendinys, o visa optimumų populiacija. Skirtingi optimumai atitinka skirtingus vaizdus. Matydamas kelis daugiamačių duomenų variantus, ekspertas gali įžvelgti daugiau daugiamačių duomenų savybių. Straipsnyje genetinis algoritmas pritaikytas daugiamatėms skalėms. Parodoma, kad daugiamačių skalių algoritmą galima kombinuoti su genetiniu algoritmu ir panaudoti daugiamačiams duomenims vizualizuoti.

scholarly journals Interface-targeted seismic velocity estimation using machine learning

2019 ◽  
Vol 218 (1) ◽  
pp. 45-56 ◽  
Author(s):  
C Nur Schuba ◽  
Jonathan P Schuba ◽  
Gary G Gray ◽  
Richard G Davy
Keyword(s):  
Neural Network ◽  
Regression Model ◽  
Dimensional Space ◽  
Seismic Profile ◽  
Velocity Estimation ◽  
Seismic Survey ◽  
Wide Angle ◽  
Seismic Velocities ◽  
Lower Dimensional Space ◽  
Lower Dimensional

SUMMARY We present a new approach to estimate 3-D seismic velocities along a target interface. This approach uses an artificial neural network trained with user-supplied geological and geophysical input features derived from both a 3-D seismic reflection volume and a 2-D wide-angle seismic profile that were acquired from the Galicia margin, offshore Spain. The S-reflector detachment fault was selected as the interface of interest. The neural network in the form of a multilayer perceptron was employed with an autoencoder and a regression layer. The autoencoder was trained using a set of input features from the 3-D reflection volume. This set of features included the reflection amplitude and instantaneous frequency at the interface of interest, time-thicknesses of overlying major layers and ratios of major layer time-thicknesses to the total time-depth of the interface. The regression model was trained to estimate the seismic velocities of the crystalline basement and mantle from these features. The ‘true’ velocities were obtained from an independent full-waveform inversion along a 2-D wide-angle seismic profile, contained within the 3-D data set. The autoencoder compressed the vector of inputs into a lower dimensional space, then the regression layer was trained in the lower dimensional space to estimate velocities above and below the targeted interface. This model was trained on 50 networks with different initializations. A total of 37 networks reached minimum achievable error of 2 per cent. The low standard deviation (<300  m s−1) between different networks and low errors on velocity estimations demonstrate that the input features were sufficient to capture variations in the velocity above and below the targeted S-reflector. This regression model was then applied to the 3-D reflection volume where velocities were predicted over an area of ∼400 km2. This approach provides an alternative way to obtain velocities across a 3-D seismic survey from a deep non-reflective lithology (e.g. upper mantle) , where conventional reflection velocity estimations can be unreliable.

scholarly journals Predictability and Information Theory. Part II: Imperfect Forecasts

2005 ◽  
Vol 62 (9) ◽  
pp. 3368-3381 ◽  
Author(s):  
Timothy DelSole
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Dimensional Space ◽  
Nonlinear Behavior ◽  
Potential Predictability ◽  
Low Dimensional ◽  
Lower Dimensional Space ◽  
True System ◽  
Normally Distributed

Abstract This paper presents a framework for quantifying predictability based on the behavior of imperfect forecasts. The critical quantity in this framework is not the forecast distribution, as used in many other predictability studies, but the conditional distribution of the state given the forecasts, called the regression forecast distribution. The average predictability of the regression forecast distribution is given by a quantity called the mutual information. Standard inequalities in information theory show that this quantity is bounded above by the average predictability of the true system and by the average predictability of the forecast system. These bounds clarify the role of potential predictability, of which many incorrect statements can be found in the literature. Mutual information has further attractive properties: it is invariant with respect to nonlinear transformations of the data, cannot be improved by manipulating the forecast, and reduces to familiar measures of correlation skill when the forecast and verification are joint normally distributed. The concept of potential predictable components is shown to define a lower-dimensional space that captures the full predictability of the regression forecast without loss of generality. The predictability of stationary, Gaussian, Markov systems is examined in detail. Some simple numerical examples suggest that imperfect forecasts are not always useful for joint normally distributed systems since greater predictability often can be obtained directly from observations. Rather, the usefulness of imperfect forecasts appears to lie in the fact that they can identify potential predictable components and capture nonstationary and/or nonlinear behavior, which are difficult to capture by low-dimensional, empirical models estimated from short historical records.

scholarly journals TESTING THE RELATIONAL PERSPECTIVE MAP FOR VISUALIZATION OF MULTIDIMENSIONAL DATA

2006 ◽  
Vol 12 (4) ◽  
pp. 289-294 ◽  
Author(s):  
Rasa Karbauskaitė ◽  
Virginijus Marcinkevičius ◽  
Gintautas Dzemyda
Keyword(s):  
Dimensional Space ◽  
Multidimensional Data ◽  
Two Dimensional ◽  
Relational Perspective ◽  
Lower Dimensional Space ◽  
Lower Dimensional ◽  
Better Than ◽  
Closed Plane

This paper deals with a method, called the relational perspective map that visualizes multidimensional data onto two‐dimensional closed plane. It tries to preserve the distances between the multidimensional data in the lower‐dimensional space. But the most important feature of the relational perspective map is the ability to visualize data in a non‐overlapping manner so that it reveals small distances better than other known visualization methods. In this paper, the features of this method are explored experimentally and some disadvantages are noticed. We have proposed a modification of this method, which enables us to avoid them.

scholarly journals Deep Clustering with Self-supervision using Pairwise Data Similarities

2021 ◽  
Author(s):  
Mohammadreza Sadeghi ◽  
Narges Armanfard
Keyword(s):  
Dimensional Space ◽  
Second Phase ◽  
Similar Data ◽  
Number Of Clusters ◽  
Latent Space ◽  
Benchmark Datasets ◽  
Data Points ◽  
Complex Cluster ◽  
Lower Dimensional Space ◽  
Lower Dimensional

<div>Deep clustering incorporates embedding into clustering to find a lower-dimensional space appropriate for clustering. In this paper we propose a novel deep clustering framework with self-supervision using pairwise data similarities (DCSS). The proposed method consists of two successive phases. In the first phase we propose to form hypersphere-like groups of similar data points, i.e. one hypersphere per cluster, employing an autoencoder which is trained using cluster-specific losses. The hyper-spheres are formed in the autoencoder’s latent space. In the second phase, we propose to employ pairwise data similarities to create a K-dimensional space that is capable of accommodating more complex cluster distributions; hence, providing more accurate clustering performance. K is the number of clusters. The autoencoder’s latent space obtained in the first phase is used as the input of the second phase. Effectiveness of both phases are demonstrated on seven benchmark datasets through conducting a rigorous set of experiments.</div>

Deep context interaction network based on attention mechanism for click-through rate prediction

2021 ◽  
pp. 1-16
Author(s):  
Ling Yuan ◽  
Zhuwen Pan ◽  
Ping Sun ◽  
Yinzhen Wei ◽  
Haiping Yu
Keyword(s):  
Online Advertising ◽  
Dimensional Space ◽  
Interaction Network ◽  
High Order ◽  
Attention Mechanism ◽  
Feature Interaction ◽  
Feature Interactions ◽  
Low Dimensional ◽  
Click Through Rate ◽  
The Relationship

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad, is a critical task in online advertising systems. The problem is very challenging since(1) an effective prediction relies on high-order combinatorial features, and(2)the relationship to auxiliary ads that may impact the CTR. In this paper, we propose Deep Context Interaction Network on Attention Mechanism(DCIN-Attention) to process feature interaction and context at the same time. The context includes other ads in the current search page, historically clicked and unclicked ads of the user. Specifically, we use the attention mechanism to learn the interactions between the target ad and each type of auxiliary ad. The residual network is used to model the feature interactions in the low-dimensional space, and with the multi-head self-attention neural network, high-order feature interactions can be modeled. Experimental results on Avito dataset show that DCIN outperform several existing methods for CTR prediction.

Sign in / Sign up

Export Citation Format

Share Document