An improved optimization algorithm and a Bayes factor termination criterion for sequential projection pursuit

Sequential projection pursuit (SPP) is proposed to detect inhomogeneities (clusters) in high-dimensional analytical data. Such inhomogeneities indicate that there are groups of objects (samples) with different chemical characteristics. The method is compared with principal component analysis (PCA). PCA is generally applied to visually explore structure in high-dimensional data, but is not specifically used to find clustering tendency. Projection pursuit (PP) is specifically designed to find inhomogeneities, but the original method is computationally very intensive. SPP combines the advantages of both methods and overcomes most of their weak points. In this method, latent variables are obtained sequentially according to their importance measured by the entropy index. This involves an optimization step, which is achieved by using a genetic algorithm. The performance of the method is demonstrated and evaluated, first on simulated data sets, and then on near-infrared and gas chromatography data sets. It is shown that SPP indeed reveals more easily information about inhomogeneities than PCA.

Exploratory chemometric analysis of the classification of pharmaceutical substances based on chromatographic data

Principal Component Analysis (PCA) is a common exploratory tool used to evaluate large complex data sets. The resulting lower-dimensional representations are often valuable for pattern visualization, clustering, or classification of the data. However, PCA cannot be applied directly to many -omics data sets generated by newer technologies such as label-free mass spectrometry due to large numbers of non-random missing values. Here we present a sequential projection pursuit PCA (sppPCA) method for defining principal components in the presence of missing data. Our results demonstrate that this approach generates robust and informative low-dimensional data representations compared to commonly used imputation approaches.

This paper carries on research surrounding the influences produced by dimensionality reduction on machine learning classification effect. Firstly, paper constructs the analysis architecture of data dimension reduction classification, combines the two different unsupervised dimension reduction methods, locally linear embedding (LLE) and principal component analysis (PCA) with the five machine learning classification methods: Gradient Boosting Decision Tree (GBDT), Random Forest, Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Logistic Regression. And then uses the handwritten digital identification dataset to analyze the classification performance of these five classification methods on different dimension datasets by different dimensionality reduction methods. The analysis shows that using the appropriate dimensionality reduction method for dimensionality reduction classification can effectively improve the classification accuracy; the dimensionality reduction classification effect of non-linear dimensionality reduction method is generally better than the linear dimensionality reduction method; different machine learning classification algorithms have significant differences in the sensitivity of dimensions.

Telecom Companies logs customer’s actions which generate a huge amount of data that can bring important findings related to customer’s behavior and needs. The main characteristics of such data are the large number of features and the high sparsity that impose challenges to the analytics steps. This paper aims to explore dimensionality reduction on a real telecom dataset and evaluate customers’ clustering in reduced and latent space, compared to original space in order to achieve better quality clustering results. The original dataset contains 220 features that belonging to 100,000 customers. However, dimensionality reduction is an important data preprocessing step in the data mining process specially with the presence of curse of dimensionality. In particular, the aim of data reduction techniques is to filter out irrelevant features and noisy data samples. To reduce the high dimensional data, we projected it down to a subspace using well known Principal Component Analysis (PCA) decomposition and a novel approach based on Autoencoder Neural Network, performing in this way dimensionality reduction of original data. Then K-Means Clustering is applied on both-original and reduced data set. Different internal measures were performed to evaluate clustering for different numbers of dimensions and then we evaluated how the reduction method impacts the clustering task.

PurposeA set of routers that are connected over communication channels can from network-on-chip (NoC). High performance, scalability, modularity and the ability to parallel the structure of the communications are some of its advantages. Because of the growing number of cores of NoC, their arrangement has got more valuable. The mapping action is done based on assigning different functional units to different nodes on the NoC, and the way it is done contains a significant effect on implementation and network power utilization. The NoC mapping issue is one of the NP-hard problems. Therefore, for achieving optimal or near-optimal answers, meta-heuristic algorithms are the perfect choices. The purpose of this paper is to design a novel procedure for mapping process cores for reducing communication delays and cost parameters. A multi-objective particle swarm optimization algorithm standing on crowding distance (MOPSO-CD) has been used for this purpose.Design/methodology/approachIn the proposed approach, in which the two-dimensional mesh topology has been used as base construction, the mapping operation is divided into two stages as follows: allocating the tasks to suitable cores of intellectual property; and plotting the map of these cores in a specific tile on the platform of NoC.FindingsThe proposed method has dramatically improved the related problems and limitations of meta-heuristic algorithms. This algorithm performs better than the particle swarm optimization (PSO) and genetic algorithm in convergence to the Pareto, producing a proficiently divided collection of solving ways and the computational time. The results of the simulation also show that the delay parameter of the proposed method is 1.1 per cent better than the genetic algorithm and 0.5 per cent better than the PSO algorithm. Also, in the communication cost parameter, the proposed method has 2.7 per cent better action than a genetic algorithm and 0.16 per cent better action than the PSO algorithm.Originality/valueAs yet, the MOPSO-CD algorithm has not been used for solving the task mapping issue in the NoC.

Principal component analysis (PCA) is known to be a powerful linear technique for data set dimensionality reduction. This paper focuses on revealing the essence of PCA to interpret the data, which is to identify the internal structure of the random process from a large experimental data set. We give an explanation of the PCA procedure performed on a generated data set to demonstrate the exact meaning of the dimensionality reduction. Especially, a method is proposed to precisely determine the number of significant principal components for a random process. Then, the internal structure of the random process can be modeled by analyzing the relation between the PCA results and the original data set. This is vital in the efficient random process modeling, which is finally applied to an application in HRTF Modeling.

The solar home system (SHS) often experience a shading condition that caused by the objects near the PVs installment. The shading affect to the harvesting of power from generation side of the system. The system will experience lower output power because the characteristic of PVs have chance, such as the P-V curve. P-V curve changed by the rapid changing of irradiation level and temperature. In this curve, there is a point that produce highest rate of power harvesting, its called Maximum Power Point (MPP). The MPP Tracking is technique to track the MPP, so the system will run in optimal mode. In the other side, the partial shading to PV surface will cause more than one MPP, even though only one MPP that produce highest rate of output power. It is called global MPP, the other is local MPP. This article shows the genetic algorithm (GA) which is implemented in MPPT technique as a meta-heuristic search. The GA implemented in a DC/DC buck converter with the STM32 F4 microcontroller to run the algorithm and control the converter as real-time. The GA performance is compared to the PO’s by their system efficiency, power output, and tracking time. The experimental treatment done by a single tracking cycle and a single solar daily cycle in the roof of Herman Yohanes Building, Universitas Gadjah Mada. The test conducted for single solar daily cycle, shows that GA implementation on MPPT has 91% efficiency (in average) and PO implementation on MPPT has 89% efficiency (in average). In terms of output power, GA has an average output power + 10% higher than PO. While in terms of time tracking, GA has a mean time of + 61% longer than the PO

The purpose of this research is to solve the Unit Commitment Problem (UCP), which is a critical task in power system optimization. The UCP involves determining the optimal scheduling of power generating units over a specified time horizon to meet the electricity demand while minimizing costs and satisfying operational constraints. In this study, a Genetic Algorithm (GA) method is proposed to solve the UCP efficiently. GA is inspired by the process of natural selection and evolution and is often used to solve complex optimization problems where traditional methods may be inefficient. The algorithm proceeds through several steps, namely parameters initialization, generating population, modification, calculating fitness function, parent selection, crossover, and mutation. The implementation of GA to solve UCP using C++ includes four different scenarios: a system with 4 units, 5 units, 10 units, and 26 units. The results obtained from the implementation of the GA on the different data sets indicate that the more iterations and the bigger initial population, the smaller the solution in the form of the total cost incurred.

Mutual information has been actively investigated as a tool for analyzing neural networks' behavior, most notably the information bottleneck theory. However, esti-mating mutual information is a notoriously tricky task, especially for high-dimensional stochastic variables. Recently, mutual information neural estimation (MINE) was proposed as a non-parametric method to estimate mutual information for contin-uous variables without discretization. Unfortunately, MINE also produces signifi-cant errors for high-dimensional variables. Analyzing the activity of neural networks requires a dimensionality reduction mechanism, with the resulting low-dimensional representations retaining as much information as possible. We investigated different dimensionality reduction methods to determine their capabilities in estimating mutual information regarding the activity of trained neural networks. We combined MIME with principal component analysis (PCA), a convolutional neural network (CNN), and global average pooling (GAP). The experiments showed that introducing dimensionality reduction provides more stable results than the baseline method. In terms of stability, PCA-MINE and GAP-MINE performed better than CNN-MINE. They also require much less computation time than CNN. Another advantage of GAP-MINE is that it requires no hyperparameter optimization. However, the results suggested that GAP-MINE may underestimate mutual information.

BackgroundUnsupervised clustering and outlier detection are important in medical research to understand the distributional composition of a collective of patients. A number of clustering methods exist, also for high-dimensional data after dimension reduction. Clustering and outlier detection may, however, become less robust or contradictory if multiple high-dimensional data sets per patient exist. Such a scenario is given when the focus is on 3-D data of multiple organs per patient, and a high-dimensional feature matrix per organ is extracted.MethodsWe use principal component analysis (PCA), t-distributed stochastic neighbor embedding (t-SNE) and multiple co-inertia analysis (MCIA) combined with bagplots to study the distribution of multi-organ 3-D data taken by computed tomography scans. After point-set registration of multiple organs from two public data sets, multiple hundred shape features are extracted per organ. While PCA and t-SNE can only be applied to each organ individually, MCIA can project the data of all organs into the same low-dimensional space.ResultsMCIA is the only approach, here, with which data of all organs can be projected into the same low-dimensional space. We studied how frequently (i.e., by how many organs) a patient was classified to belong to the inner or outer 50% of the population, or as an outlier. Outliers could only be detected with MCIA and PCA. MCIA and t-SNE were more robust in judging the distributional location of a patient in contrast to PCA.ConclusionsMCIA is more appropriate and robust in judging the distributional location of a patient in the case of multiple high-dimensional data sets per patient. It is still recommendable to apply PCA or t-SNE in parallel to MCIA to study the location of individual organs.

Purpose:To predict metastasis-free survival (MFS) for patients with prostate adenocarcinoma (PCa) treated with androgen deprivation therapy (ADT) and external radiotherapy using clinical factors and radiomics extracted from primary tumor and node volumes in pre-treatment PSMA PET/CT scans.Materials/Methods:Our cohort includes 134 PCa patients (nodal involvement in 28 patients). Gross tumor volumes of primary tumor (GTVp) and nodes (GTVn) on CT and PET scans were segmented. A 5 mm expansion ring area outside primary tumor was defined. Z-score normalization was applied to radiomics features extracted from tumor and ring; dimension reduction was performed using Principal Components Analysis (PCA). For patients with only primary tumor, we took 3 principal components (PCs) from GTVp and one ring PC as representative radiomics components from CT and PET scans. For patients with nodes, we calculated weighted average (by volume) of radiomics from primary tumor and nodes, computed first 3 PCs and combined it with 1st PC from the ring. Radiomics PCs and clinical variables (age, Gleason score, initial prostate specific antigen value (i PSA), PSA_relapse) formed the predictors. Due to MFS data imbalance (metastasis-24, no metastasis-110), we performed 70:30 train-test split and applied imbalance correction to training data. Univariate Cox-regression was used to select top predictors (logistic regression p < 0.05). Multivariate Cox-regression was performed on imbalance-corrected training data and fit on testing data (using predictors selected from training). Model 2 was built using clinical variables and radiomic PCs from primary tumors (GTVp, ring). Model 3 was built using clinical variables only. Binary classification analysis for prediction of five-year MFS was also performed.Results:Results of time-to-event analysis (MFS) were: Cox-regression c-scores: model1: train- 0.77 [0.72, 0.78]; test- 0.69 [0.64, 0.70]; model2: train- 0.72 [0.66, 0.73]; test- 0.63 [0.58, 0.64]; model3: train- 0.62 [0.57, 0.63]; test- 0.54 [0.51, 0.56]. The results of 5 year MFS classification analysis were [sensitivity, specificity, AUC]: model 1: train- [83.6 %, 91.3 %, 0.88]; test- [76.3 %, 82.5 %, 0.81]; model 2: train- [77.4 %, 85.1 %, 0.84]; test- [71.5 %, 78.2 %, 0.76]; model 3: train- [69.3 %, 78.2 %, 0.76]; test- [64.7 %, 72.6 %, 0.68]. The two cohorts of patients classified by model 1 showed statistically significant differences in their actual survival curves, demonstrating the efficacy of the classification. Integration of node with primary tumor-radiomics provides the best prognostic performance in MFS prediction.Conclusion:This is one of the first studies to explore the prognostic value of pre-treatment PSMA-PET, a relatively recent advancement in the care of prostate adenocarcinoma patients. Results demonstrated the potential of using imaging biomarkers from PSMA-PET/CT images for prognosis prediction before the treatment, which provides clinicians valuable information for customizing the treatment paradigm to improve the outcomes for primary prostate cancer patients.

The aim of data transformation is to transform the original feature space of data into another space with better properties. This is typically combined with dimensionality reduction, so that the dimensionality of the transformed space is smaller. A widely used method for data transformation and dimensionality reduction is Principal Component Analysis (PCA). PCA finds a subspace that explains most of the data variance. While the new PCA feature space has interesting properties, such as removing linear correlation, PCA is an unsupervised method. Therefore, there is no guarantee that the PCA feature space will be the most appropriate for supervised tasks, such as classification or regression. On the other hand, 3-layer Multi Layer Perceptrons (MLP), which are supervised methods, can also be understood as a data transformation carried out by the hidden layer, followed by a classification/regression operation performed by the output layer. Given that the hidden layer is obtained after a supervised training process, it can be considered that it is performing a supervised data transformation. And if the number of hidden neurons is smaller than the input, also dimensionality reduction. Despite this kind of transformation being widely available (any neural network package that allows access to the hidden layer weights can be used), no extensive experimentation on the quality of 3-layer MLP data transformation has been carried out. The aim of this article is to carry out this research for classification problems. Results show that, overall, this transformation offers better results than the PCA unsupervised transformation method.

&lt;span&gt;The curse of dimensionality and the empty space phenomenon emerged as a critical problem in text classification. One way of dealing with this problem is applying a feature selection technique before performing a classification model. This technique helps to reduce the time complexity and sometimes increase the classification accuracy. This study introduces a feature selection technique using K-Means clustering to overcome the weaknesses of traditional feature selection technique such as principal component analysis (PCA) that require a lot of time to transform all the inputs data. This proposed technique decides on features to retain based on the significance value of each feature in a cluster. This study found that k-means clustering helps to increase the efficiency of KNN model for a large data set while KNN model without feature selection technique is suitable for a small data set. A comparison between K-Means clustering and PCA as a feature selection technique shows that proposed technique is better than PCA especially in term of computation time. Hence, k-means clustering is found to be helpful in reducing the data dimensionality with less time complexity compared to PCA without affecting the accuracy of KNN model for a high frequency data.&lt;/span&gt;

A novel parameterization concept for structural truss topology optimization is presented in this article that enables the use of evolutionary algorithms in design of large-scale structures. The representational power of Boolean networks is used here to parameterize truss topology. A genetic algorithm then operates on parameters that govern the generation of truss topologies using this random network instead of operating directly on design variables. A genetic algorithm implementation is also presented that is congruent with the local rule application of the random network. The primary advantage of using a Boolean random network representation is that a relatively large number of ground structure nodes can be used, enabling successful exploration of a large-scale design space. In the classical binary representation of ground structures, the number of optimization variables increases quadratically with the number of nodes, restricting the maximum number of nodes that can be considered using a ground structure approach. The Boolean random network representation proposed here allows for the exploration of the entire topology space in a systematic way using only a linear number of variables. The number of nodes in the design domain, therefore, can be increased significantly. Truss member geometry and size optimization is performed here in a nested manner where an inner loop size optimization problem is solved for every candidate topology using sequential linear programming with move-limits. The Boolean random network and nested inner-loop optimization allows for the concurrent optimization of truss topology, geometry, and size. The effectiveness of this method is demonstrated using a planar truss design optimization benchmark problem.