scholarly journals Predicting future dynamics from short-term time series using an Anticipated Learning Machine

2020 ◽  
Vol 7 (6) ◽  
pp. 1079-1091 ◽  
Author(s):  
Chuan Chen ◽  
Rui Li ◽  
Lin Shu ◽  
Zhiyu He ◽  
Jining Wang ◽  
...  
Keyword(s):  
Machine Learning ◽  
Time Series ◽  
High Dimensional Data ◽  
Small Sample ◽  
High Dimensional ◽  
Target Variable ◽  
Short Term ◽  
Linear Dynamical Systems ◽  
Non Linear ◽  
Learning Machine

Abstract Predicting time series has significant practical applications over different disciplines. Here, we propose an Anticipated Learning Machine (ALM) to achieve precise future-state predictions based on short-term but high-dimensional data. From non-linear dynamical systems theory, we show that ALM can transform recent correlation/spatial information of high-dimensional variables into future dynamical/temporal information of any target variable, thereby overcoming the small-sample problem and achieving multistep-ahead predictions. Since the training samples generated from high-dimensional data also include information of the unknown future values of the target variable, it is called anticipated learning. Extensive experiments on real-world data demonstrate significantly superior performances of ALM over all of the existing 12 methods. In contrast to traditional statistics-based machine learning, ALM is based on non-linear dynamics, thus opening a new way for dynamics-based machine learning.

Predicting Time Series from Short-Term High-Dimensional Data

2014 ◽  
Vol 24 (12) ◽  
pp. 1430033 ◽  
Author(s):  
Huanfei Ma ◽  
Tianshou Zhou ◽  
Kazuyuki Aihara ◽  
Luonan Chen
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
High Dimensional Data ◽  
Series Data ◽  
High Dimensional ◽  
Short Term ◽  
Low Dimensional ◽  
Low Dimensional Dynamics ◽  
Term Data

The prediction of future values of time series is a challenging task in many fields. In particular, making prediction based on short-term data is believed to be difficult. Here, we propose a method to predict systems' low-dimensional dynamics from high-dimensional but short-term data. Intuitively, it can be considered as a transformation from the inter-variable information of the observed high-dimensional data into the corresponding low-dimensional but long-term data, thereby equivalent to prediction of time series data. Technically, this method can be viewed as an inverse implementation of delayed embedding reconstruction. Both methods and algorithms are developed. To demonstrate the effectiveness of the theoretical result, benchmark examples and real-world problems from various fields are studied.

scholarly journals Randomly distributed embedding making short-term high-dimensional data predictable

2018 ◽  
Vol 115 (43) ◽  
pp. E9994-E10002 ◽  
Author(s):  
Huanfei Ma ◽  
Siyang Leng ◽  
Kazuyuki Aihara ◽  
Wei Lin ◽  
Luonan Chen
Keyword(s):  
Real World ◽  
Nonlinear Dynamical Systems ◽  
High Dimensional Data ◽  
High Dimensional ◽  
World Systems ◽  
Target Variable ◽  
Short Term ◽  
Future State ◽  
State Prediction ◽  
Low Dimensional

Future state prediction for nonlinear dynamical systems is a challenging task, particularly when only a few time series samples for high-dimensional variables are available from real-world systems. In this work, we propose a model-free framework, named randomly distributed embedding (RDE), to achieve accurate future state prediction based on short-term high-dimensional data. Specifically, from the observed data of high-dimensional variables, the RDE framework randomly generates a sufficient number of low-dimensional “nondelay embeddings” and maps each of them to a “delay embedding,” which is constructed from the data of a to be predicted target variable. Any of these mappings can perform as a low-dimensional weak predictor for future state prediction, and all of such mappings generate a distribution of predicted future states. This distribution actually patches all pieces of association information from various embeddings unbiasedly or biasedly into the whole dynamics of the target variable, which after operated by appropriate estimation strategies, creates a stronger predictor for achieving prediction in a more reliable and robust form. Through applying the RDE framework to data from both representative models and real-world systems, we reveal that a high-dimension feature is no longer an obstacle but a source of information crucial to accurate prediction for short-term data, even under noise deterioration.

scholarly journals Data Quality Measures and Efficient Evaluation Algorithms for Large-Scale High-Dimensional Data

2021 ◽  
Vol 11 (2) ◽  
pp. 472
Author(s):  
Hyeongmin Cho ◽  
Sangkyun Lee
Keyword(s):  
Machine Learning ◽  
Data Quality ◽  
Large Scale ◽  
High Dimensional Data ◽  
Quality Measures ◽  
Training Data ◽  
Measure Data ◽  
High Dimensional ◽  
Small Scale ◽  
Class Separability

Machine learning has been proven to be effective in various application areas, such as object and speech recognition on mobile systems. Since a critical key to machine learning success is the availability of large training data, many datasets are being disclosed and published online. From a data consumer or manager point of view, measuring data quality is an important first step in the learning process. We need to determine which datasets to use, update, and maintain. However, not many practical ways to measure data quality are available today, especially when it comes to large-scale high-dimensional data, such as images and videos. This paper proposes two data quality measures that can compute class separability and in-class variability, the two important aspects of data quality, for a given dataset. Classical data quality measures tend to focus only on class separability; however, we suggest that in-class variability is another important data quality factor. We provide efficient algorithms to compute our quality measures based on random projections and bootstrapping with statistical benefits on large-scale high-dimensional data. In experiments, we show that our measures are compatible with classical measures on small-scale data and can be computed much more efficiently on large-scale high-dimensional datasets.

Attribute-based Explanation of Non-Linear Embeddings of High-Dimensional Data

2021 ◽  
pp. 1-1
Author(s):  
Jan-Tobias Sohns ◽  
Michaela Schmitt ◽  
Fabian Jirasek ◽  
Hans Hasse ◽  
Heike Leitte
Keyword(s):  
High Dimensional Data ◽  
High Dimensional ◽  
Non Linear

scholarly journals A Machine Learning Approach to Reveal the NeuroPhenotypes of Autisms

2019 ◽  
Vol 29 (07) ◽  
pp. 1850058 ◽  
Author(s):  
Juan M. Górriz ◽  
Javier Ramírez ◽  
F. Segovia ◽  
Francisco J. Martínez ◽  
Meng-Chuan Lai ◽  
...  
Keyword(s):  
Machine Learning ◽  
Brain Structure ◽  
Feature Space ◽  
Classification Problem ◽  
Small Sample ◽  
Biological Sex ◽  
Machine Learning Approach ◽  
Learning Machine ◽  
Small Sample Sizes ◽  
Low Dimensional

Although much research has been undertaken, the spatial patterns, developmental course, and sexual dimorphism of brain structure associated with autism remains enigmatic. One of the difficulties in investigating differences between the sexes in autism is the small sample sizes of available imaging datasets with mixed sex. Thus, the majority of the investigations have involved male samples, with females somewhat overlooked. This paper deploys machine learning on partial least squares feature extraction to reveal differences in regional brain structure between individuals with autism and typically developing participants. A four-class classification problem (sex and condition) is specified, with theoretical restrictions based on the evaluation of a novel upper bound in the resubstitution estimate. These conditions were imposed on the classifier complexity and feature space dimension to assure generalizable results from the training set to test samples. Accuracies above [Formula: see text] on gray and white matter tissues estimated from voxel-based morphometry (VBM) features are obtained in a sample of equal-sized high-functioning male and female adults with and without autism ([Formula: see text], [Formula: see text]/group). The proposed learning machine revealed how autism is modulated by biological sex using a low-dimensional feature space extracted from VBM. In addition, a spatial overlap analysis on reference maps partially corroborated predictions of the “extreme male brain” theory of autism, in sexual dimorphic areas.

scholarly journals Scalable hierarchical clustering by composition rank vector encoding and tree structure

2020 ◽  
Author(s):  
Xiao Lai ◽  
Pu Tian
Keyword(s):  
Machine Learning ◽  
Hierarchical Clustering ◽  
Clustering Algorithm ◽  
High Dimensional Data ◽  
Machine Learning Algorithms ◽  
Tree Structure ◽  
Supervised Machine Learning ◽  
High Dimensional ◽  
Rank Vector ◽  
Nonlinear Correlations

AbstractSupervised machine learning, especially deep learning based on a wide variety of neural network architectures, have contributed tremendously to fields such as marketing, computer vision and natural language processing. However, development of un-supervised machine learning algorithms has been a bottleneck of artificial intelligence. Clustering is a fundamental unsupervised task in many different subjects. Unfortunately, no present algorithm is satisfactory for clustering of high dimensional data with strong nonlinear correlations. In this work, we propose a simple and highly efficient hierarchical clustering algorithm based on encoding by composition rank vectors and tree structure, and demonstrate its utility with clustering of protein structural domains. No record comparison, which is an expensive and essential common step to all present clustering algorithms, is involved. Consequently, it achieves linear time and space computational complexity hierarchical clustering, thus applicable to arbitrarily large datasets. The key factor in this algorithm is definition of composition, which is dependent upon physical nature of target data and therefore need to be constructed case by case. Nonetheless, the algorithm is general and applicable to any high dimensional data with strong nonlinear correlations. We hope this algorithm to inspire a rich research field of encoding based clustering well beyond composition rank vector trees.

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