Nonlinear Dimensionality Reduction via Path-Based Isometric Mapping

Abstract

Nonlinear dimensionality reduction methods have demonstrated top-notch performance in many pattern recognition and image classification tasks. Despite their popularity, they suffer from highly expensive time and memory requirements, which render them inapplicable to large-scale datasets. To leverage such cases we propose a new method called "Path-Based Isomap". Similar to Isomap, we exploit geodesic paths to find the low-dimensional embedding. However, instead of preserving pairwise geodesic distances, the low-dimensional embedding is computed via a path-mapping algorithm. Due to the much fewer number of paths compared to number of data points, a significant improvement in time and memory complexity with a comparable performance is achieved. The method demonstrates state-of-the-art performance on well-known synthetic and real-world datasets, as well as in the presence of noise.

Soft Sensor Model Based on Improved Elman Neural Network with Variable Data Preprocessing and Its Application

“…Formulated the Criterion of Evaluating. After the variable selection and training, the prediction value of the soft sensor model based on improved Elman NN as in equation (18) needs be further evaluated. In this paper, the evaluation criterion, the Bayesian information criterion (BIC), is adopted as a measure between the complexity of the soft sensor model and the accuracy.…”

“…where y i is the prediction value by modified weight parameters as in equation (18). y is the actual value.…”

“…Step 4. Update the weight parameters by equation 17and obtain novel neural network by equation (18).…”

“…Sun et al [17] presented the principal component analysis (PCA) method to analyze the correlation of input variables, which is effective to reduce the dimensions of input variables from the chemical oxygen demand prediction model based on LS-SVM. Najafi et al [18] proposed a new method called "Path-Based Isomap" to find the low-dimensional embedding. The low-dimensional embedding is computed by exploiting geodesic path-mapping algorithm.…”

Novel Prediction Model for Steel Mechanical Properties with MSVR Based on MIC and Complex Network Clustering

“…Embedded methods integrate feature selection and training learners, which automatically select features during learner training [9]. Moreover, some dimension reduction methods such as principal component analysis (PCA), singular value decomposition (SVD), linear discriminant analysis (LDA), and ISOMAP algorithm can also be regarded as feature selection methods for special basic data [10][11][12][13]. However, such methods do not consider the correlation and redundancy between attributes before and after dimensionality reduction, and the results are lack of interpretability.…”