Locally Linear Embedding Orthogonal Projection to Latent Structure

Quality variables are measured much less frequently and usually with a significant time delay by comparison with the measurement of process variables. Monitoring process variables and their associated quality variables is essential undertaking as it can lead to potential hazards that may cause system shutdowns and thus possibly huge economic losses. Maximum correlation was extracted between quality variables and process variables by partial least squares analysis (PLS) (Kruger et al. 2001; Song et al. 2004; Li et al. 2010; Hu et al. 2013; Zhang et al. 2015).

Temporal Registration of Cardiac Multimodal Images Using Locally Linear Embedding Algorithm

Purpose: Multimodal Cardiac Image (MCI) registration is one of the evolving fields in the diagnostic methods of Cardiovascular Diseases (CVDs). Since the heart has nonlinear and dynamic behavior, Temporal Registration (TR) is the fundamental step for the spatial registration and fusion of MCIs to integrate the heart's anatomical and functional information into a single and more informative display. Therefore, in this study, a TR framework is proposed to align MCIs in the same cardiac phase. Materials and Methods: A manifold learning-based method is proposed for the TR of MCIs. The Euclidean distance among consecutive samples lying on the Locally Linear Embedding (LLE) of MCIs is computed. By considering cardiac volume pattern concepts from distance plots of LLEs, six cardiac phases (end-diastole, rapid-ejection, end-systole, rapid-filling, reduced-filling, and atrial-contraction) are temporally registered. Results: The validation of the proposed method proceeds by collecting the data of Computed Tomography Coronary Angiography (CTCA) and Transthoracic Echocardiography (TTE) from ten patients in four acquisition views. The Correlation Coefficient (CC) between the frame number resulted from the proposed method and manually selected by an expert is analyzed. Results show that the average CC between two resulted frame numbers is about 0.82±0.08 for six cardiac phases. Moreover, the maximum Mean Absolute Error (MAE) value of two slice extraction methods is about 0.17 for four acquisition views. Conclusion: By extracting the intrinsic parameters of MCIs, and finding the relationship among them in a lower-dimensional space, a fast, fully automatic, and user-independent framework for TR of MCIs is presented. The proposed method is more accurate compared to Electrocardiogram (ECG) signal labeling or time-series processing methods which can be helpful in different MCI fusion methods.

Selection of Machine Learning Models for Oil Price Forecasting: Based on the Dual Attributes of Oil

Since the commodity and financial attributes of crude oil will have a long-term or short-term impact on crude oil prices, we propose a de-dimension machine learning model approach to forecast the international crude oil prices. First, we use principal component analysis (PCA), multidimensional scale (MDS), and locally linear embedding (LLE) methods to reduce the dimensions of the data. Then, based on the recurrent neural network (RNN) and long-term and short-term memory (LSTM) models, we build eight models for predicting the future and spot prices of international crude oil. From the analysis and comparison of the prediction results, we find that reducing the dimension of the data can improve the accuracy of the model and the applicability of RNN and LSTM models. In addition, the LLE-RNN/LSTM models can most successfully capture the nonlinear characteristics of crude oil prices. When the moving window size is twenty, that is, when crude oil price data are lagging by almost a month, each model can minimize its error, and the LLE-RNN /LSTM models have the best robustness.

Dissimilarity space reinforced with manifold learning and latent space modeling for improved pattern classification

Dissimilarity representation plays a very important role in pattern recognition due to its ability to capture structural and relational information between samples. Dissimilarity space embedding is an approach in which each sample is represented as a vector based on its dissimilarity to some other samples called prototypes. However, lack of neighborhood-preserving, fixed and usually considerable prototype set for all training samples cause low classification accuracy and high computational complexity. To address these challenges, our proposed method creates dissimilarity space considering the neighbors of each data point on the manifold. For this purpose, Locally Linear Embedding (LLE) is used as an unsupervised manifold learning algorithm. The only goal of this step is to learn the global structure and the neighborhood of data on the manifold and mapping or dimension reduction is not performed. In order to create the dissimilarity space, each sample is compared only with its prototype set including its k-nearest neighbors on the manifold using the geodesic distance metric. Geodesic distance metric is used for the structure preserving and is computed using the weighted LLE neighborhood graph. Finally, Latent Space Model (LSM), is applied to reduce the dimensions of the Euclidean latent space so that the second challenge is resolved. To evaluate the resulted representation ad so called dissimilarity space, two common classifiers namely K Nearest Neighbor (KNN) and Support Vector Machine (SVM) are applied. Experiments on different datasets which included both Euclidean and non-Euclidean spaces, demonstrate that using the proposed approach, classifiers outperform the other basic dissimilarity spaces in both accuracy and runtime.

Local quasi-linear embedding based on kronecker product expansion of vectors

Locally Linear Embedding (LLE) is honored as the first algorithm of manifold learning. Generally speaking, the relation between a data and its nearest neighbors is nonlinear and LLE only extracts its linear part. Therefore, local nonlinear embedding is an important direction of improvement to LLE. However, any attempt in this direction may lead to a significant increase in computational complexity. In this paper, a novel algorithm called local quasi-linear embedding (LQLE) is proposed. In our LQLE, each high-dimensional data vector is first expanded by using Kronecker product. The expanded vector contains not only the components of the original vector, but also the polynomials of its components. Then, each expanded vector of high dimensional data is linearly approximated with the expanded vectors of its nearest neighbors. In this way, the proposed LQLE achieves a certain degree of local nonlinearity and learns the data dimensionality reduction results under the principle of keeping local nonlinearity unchanged. More importantly, LQLE does not increase computation complexity by only replacing the data vectors with their Kronecker product expansions in the original LLE program. Experimental results between our proposed methods and four comparison algorithms on various datasets demonstrate the well performance of the proposed methods.