Sparse multi-view image clustering with complete similarity information

BackgroundMulti-dimensional scaling (MDS) is aimed to represent high dimensional data in a low dimensional space with preservation of the similarities between data points. This reduction in dimensionality is crucial for analyzing and revealing the genuine structure hidden in the data. For noisy data, dimension reduction can effectively reduce the effect of noise on the embedded structure. For large data set, dimension reduction can effectively reduce information retrieval complexity. Thus, MDS techniques are used in many applications of data mining and gene network research. However, although there have been a number of studies that applied MDS techniques to genomics research, the number of analyzed data points was restricted by the high computational complexity of MDS. In general, a non-metric MDS method is faster than a metric MDS, but it does not preserve the true relationships. The computational complexity of most metric MDS methods is over O(N2), so that it is difficult to process a data set of a large number of genes N, such as in the case of whole genome microarray data.ResultsWe developed a new rapid metric MDS method with a low computational complexity, making metric MDS applicable for large data sets. Computer simulation showed that the new method of split-and-combine MDS (SC-MDS) is fast, accurate and efficient. Our empirical studies using microarray data on the yeast cell cycle showed that the performance of K-means in the reduced dimensional space is similar to or slightly better than that of K-means in the original space, but about three times faster to obtain the clustering results. Our clustering results using SC-MDS are more stable than those in the original space. Hence, the proposed SC-MDS is useful for analyzing whole genome data.ConclusionOur new method reduces the computational complexity from O(N3) to O(N) when the dimension of the feature space is far less than the number of genes N, and it successfully reconstructs the low dimensional representation as does the classical MDS. Its performance depends on the grouping method and the minimal number of the intersection points between groups. Feasible methods for grouping methods are suggested; each group must contain both neighboring and far apart data points. Our method can represent high dimensional large data set in a low dimensional space not only efficiently but also effectively.

Dimensionality reduction via preserving local information

Dimensionality reduction methods compute a mapping from a high-dimensional space to a space with lower dimensions while preserving important information. The idea of hybridizing dimensionality reduction with evolution strategies is that the search in a space that employs a larger dimensionality than the original solution space may be easier. We propose a dimensionality reduction evolution strategy (DRES) based on a self-adaptive (μ, λ)-ES that generates points in a space with a dimensionality higher than the original solution space. After the population has been generated, it is mapped to the solution space with dimensionality reduction (DR) methods, the solutions are evaluated and the best w.r.t. the fitness in the original space are inherited to the next generation. We employ principal component analysis (PCA) as DR method and show a performance tweak on a small set of benchmark problems.

For the clustering of subspaces and multi-manifolds in low-dimensional space, this paper adopts Spectral Multi-Manifold Clustering (SMMC) to achieve mixed-manifold clustering. From the perspective of similarity matrix, we effectively use natural local geometric structure information in the manifold sampling points to assist in constructing a more appropriate similarity matrix and then find the correct manifold clustering. This paper establishes a sparse subspace clustering (SSC) model for linear problems to perform cluster analysis, then creates a spectral multi-manifold clustering (SMMC) model for nonlinear problems to perform mixed manifold clustering analysis. Such model effectively separates two straight lines that do not intersect at the origin but perpendicular to each other into two categories; separates a plane and two straight lines into three categories; separates two disjoint quadratic curves into two categories; separates two intersecting spirals into two categories.

Dimensionality reduction is vital in many fields, and alignment-based methods for nonlinear dimensionality reduction have become popular recently because they can map the high-dimensional data into a low-dimensional subspace with the property of local isometry. However, the relationships between patches in original high-dimensional space cannot be ensured to be fully preserved during the alignment process. In this paper, we propose a novel method for nonlinear dimensionality reduction called local coordinates alignment with global preservation. We first introduce a reasonable definition of topology-preserving landmarks (TPLs), which not only contribute to preserving the global structure of datasets and constructing a collection of overlapping linear patches, but they also ensure that the right landmark is allocated to the new test point. Then, an existing method for dimensionality reduction that has good performance in preserving the global structure is used to derive the low-dimensional coordinates of TPLs. Local coordinates of each patch are derived using tangent space of the manifold at the corresponding landmark, and then these local coordinates are aligned into a global coordinate space with the set of landmarks in low-dimensional space as reference points. The proposed alignment method, called landmarks-based alignment, can produce a closed-form solution without any constraints, while most previous alignment-based methods impose the unit covariance constraint, which will result in the deficiency of global metrics and undesired rescaling of the manifold. Experiments on both synthetic and real-world datasets demonstrate the effectiveness of the proposed algorithm.

Complex spontaneous brain dynamics mirror the large number of interactions taking place among regions, supporting higher functions. Such complexity is manifested in the interregional dependencies among signals derived from different brain areas, as observed utilising neuroimaging techniques, like magnetoencephalography. The dynamics of this data produce numerous subsets of active regions at any moment as they evolve. Notably, converging evidence shows that these states can be understood in terms of transient coordinated events that spread across the brain over multiple spatial and temporal scales. Those can be used as a proxy of the 'effectiveness' of the dynamics, as they become stereotyped or disorganised in neurological diseases. However, given the high-dimensional nature of the data, representing them has been challenging thus far. Dimensionality reduction techniques are typically deployed to describe complex interdependencies and improve their interpretability. However, many dimensionality reduction techniques lose information about the sequence of configurations that took place. Here, we leverage a newly described algorithm, potential of heat-diffusion for affinity-based transition embedding (PHATE), specifically designed to preserve the dynamics of the system in the low-dimensional embedding space. We analysed source-reconstructed resting-state magnetoencephalography from 18 healthy subjects to represent the dynamics of the configuration in low-dimensional space. After reduction with PHATE, unsupervised clustering via K-means is applied to identify distinct clusters. The topography of the states is described, and the dynamics are represented as a transition matrix. All the results have been checked against null models, providing a parsimonious account of the large-scale, fast, aperiodic dynamics during resting-state. The study applies the PHATE algorithm to source-reconstructed magnetoencephalography (MEG) data, reducing dimensionality while preserving large-scale neural dynamics. Results reveal distinct configurations, or 'states', of brain activity, identified via unsupervised clustering. Their transitions are characterised by a transition matrix. This method offers a simplified yet rich view of complex brain interactions, opening new perspectives on large-scale brain dynamics in health and disease.

Most existing typical dimension reduction methods, for example Isomap algorithm, are hard to deal with the problem of violation of pairwise constraint. In this paper, a pairwise-constraint supervised Isomap algorithm (PC-SIsomap) is proposed, in which the supervised information is taken on the form of pairwise constraint introduced to geodesic distance. Mapping high-dimensional and non-linear data points to low-dimensional embedding space, PC-SIsomap can effectively take advantage of pairwise constraint information to realize dimensionality reduction. At the same time in order to solve the out-of-sample problem in manifold learning, BP neural network is employed to build a nonlinear mapping relation from the high-dimensional original data space to a low-dimensional feature space. Consequentially, support vector machine (SVM) classifiers are designed for realizing pattern classification in the low-dimensional feature space. Some experiments are executed in UCI datasets and dataset of gas safety monitoring system in coal mine, the results show that PC-SIsomap not only reduces the residual value, but also improves the classification accuracy.KeywordsManifold learningpairwise constraintsdimensionality reductionIsomapgeodesic distance

<p>Flood management is the act of determining the frequency, magnitude, and duration of flood episodes based on the elements of a river basin that may be monitored. Floods endanger human lives and inflict significant property damage. It is essential for creating suitable flood risk management plans, lowering flood dangers, and evacuating people from flood-prone locations. Hydrodynamic methods for managing floods may be replaced with deep learning. Existing methods, however, concentrate on employing CNNs or RNNs to capture either the spatial or temporal flood patterns. Despite several advancements in flood control technology, less focus has been placed on minimising the damage that these systems do to the environment in order to boost their dependability and effectiveness. When the data is skewed, CNNs might overfit. We demonstrate how automated regularisation and uncertainty quantification allows Bayesian-CNN to get beyond these drawbacks. We have created a unique method to make use of the uncertainties that the Bayesian-CNN provides, which greatly improves performance on a big portion of the test data (around a 6% increase in accuracy on 77% of test data). By projecting the data into a low-dimensional space using a nonlinear dimensionality reduction approach, we also provide an entirely novel rationale for the uncertainty. This dimensionality reduction makes it possible to visualize the test data for interpretation and displays the data's structure in a low-dimensional feature space. This paper discusses and makes use of uncertainties for flood control while demonstrating the benefits of Bayesian-CNN over state-of-the-art technology. As a consequence, the Bayesian-CNN obtains 95.7% F1-score, 99.3% F1-score, 98.5% precision, and 98.3% recall.</p>

Investigating comparisons on the coal and gangue in various scenarios using multidimensional image features

We propose using the kernel dimension reduction (KDR) to extract a low-dimensional feature space for humanoid locomotion tasks. Although humanoids have many degrees of freedom, task relevant feature spaces can be much smaller than the number of dimension of the original state space. We consider an application of the proposed approach to improve the locomotive performance of humanoid robots using an extracted low-dimensional state space. To improve the locomotive performance, we use a reinforcement learning (RL) framework. While RL is a useful non-linear optimizer, it is usually difficult to apply RL to real robotic systems - due to the large number of iterations required to acquire suitable policies. In this study, we use the extracted low-dimensional feature space for RL so that the learning system can improve task performance quickly. The kernel dimension reduction method allows us to extract the feature space even if the task relevant mapping is non-linear. This is an essential property to improve humanoid locomotive performance since stepping or walking dynamics involves highly nonlinear dynamics. We show that we can improve stepping and walking policies by using a RL method on an extracted feature space by using KDR.

In multi-label learning, each object belongs to multiple class labels simultaneously. In the data explosion age, the size of data is often huge, i.e., large number of instances, features and class labels. The high dimension of both the feature and label spaces has posed great challenges to multi-label learning problems, e.g., high time and memory costs. In this paper, we propose a new framework for multi-label learning with a large number of class labels and features, i.e., M ulti- L abel L earning via F eature and L abel S pace D imension R eduction, namely MLL-FLSDR. Specifically, both the feature space and label space are reduced to low dimensional spaces respectively, in which the local structure of data points is utilized to constrain the geometrical structure on both the learned low dimensional spaces and guarantee the qualities of them. Then, an effective multi-label classifier is constructed from the low dimensional feature space to the latent label space. Last, the final prediction for new test data examples can be obtained by recovering from their prediction results in the latent label space with an encoding matrix learned in the previous stage. Extensive comparison experiments with the state-of-the-art approaches manifest the effectiveness of the proposed method MLL-FLSDR.

Projective Approximation Based Gradient Descent Modification

Multidimensional scaling maps a set of n-dimensional objects into a lower-dimension space, usually the Euclidean plane, preserving the distances among objects in the original space. Most algorithms for multidimensional scaling have been designed to work on numerical data, but in soft sciences, it is common that objects are described using quantitative and qualitative attributes, even with some missing values. For this reason, in this paper we propose a genetic algorithm especially designed for multidimensional scaling over mixed and incomplete data. Some experiments using datasets from the UCI repository, and a comparison against a common algorithm for multidimensional scaling, shows the behavior of our proposal.KeywordsMultidimensional scalingMixed and incomplete dataGenetic algorithms

In this article, the beginnings of a new approach to the theory of aggregation are developed. The basic idea is that aggregation should involve two things: (a) data over which social preferences are defined should be mapped into a smaller-dimensional space, and (b) there should exist an ordering on that lower-dimensional space such that an improvement in this criterion implies an improvement for any of a class of social preference functions and of a class of individual preference relations defined over the original space. Results are developed which show that this conception of aggregation can yield meaningful results; particularly with respect to comparisons of ‘real national income’ in two situations, for a given economy.

complexity of deploying high-performance spatial structures in transactional DBMS environments has motivated researchers to experiment with the idea of reusing the effort invested in developing a traditional indexing scheme. To enable reuse, the design of a spatial access method must employ a form of object transformation that maps extended objects in the original space into points of a dual space. If these points are further transformed into one-dimensional keys, they can be indexed by any traditional scheme for exact-match retrieval, e.g. B + -trees. This paper investigates the performance of two generations of object transformation schemes in both low- and high-dimensional spaces. The first-generation object transformation provides relatively good performance in low-dimensional spaces. But, as the number of dimensions grows, its performance deteriorates quickly. The second generation scheme applies a query transformation that refines an idea, introduced in connection with the design of LSD-trees, of limiting the search space by taking into account properties of the actual data set. The refined second- generation scheme enables a rapid deployment of a spatial access method while achieving performance comparable to that of advanced monolithic schemes.