Abstract: The functional time series (FTS) **models** are used for analyzing, modeling and forecasting age-specific mortality rates. However, the application of these **models** in presence of two or more groups within similar populations needs some modification. In these cases, it is desirable for the disaggregated forecasts to be coherent with the overall forecast. The 'coherent' forecasts are the non-divergent forecasts of sub-groups within a population. Reference [1] first proposed a coherent functional model based on product and ratios of mortality rates. In this paper, we relate some of the functional time series **models** to the **common** **principal** components (CPC) and partial **common** **principal** components (PCPC) **models** introduced by [2] and provide the methods to estimate these **models**. We call them **common** functional **principal** **component** (CFPC) **models** and use them for coherent mortality forecasting. Here, we propose a sequential procedure based on Johansen methodology to estimate the model parameters. We use vector approach and make use of error correction **models** to forecast the specific time series coefficient for each sub-group.

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We present two sets of experiments. In the first, we benchmark against the KHA with a conventional gain decay schedule (9), which we denote KHA/t, in a number of different settings: Performing ker- nel PCA and spectral clustering on the well-known USPS data set (LeCun et al., 1989), replicating image denoising and face image super-resolution experiments of Kim et al. (2005), and denoising human motion capture data. For Kim et al.’s (2005) experiments we also compare to their original KHA with the constant gain η t = η 0 they employed. A **common** feature of all these data sets is

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Abstract. Some pioneer WIFI signal based human activity recognition systems have been proposed. The **common** characteristic is to use the information of CSI(Channel State Information). Experimental results show that the extracted features of the PCA method are more obvious than that of the traditional denoising method. Even in a static environment, CSI values in Wifi signals fluctuate because WiFi devices are susceptible to surrounding electromagnetic noises. General purpose denoising methods, such as low-pass filters or mean filters, do not perform well in removing these impulse and burst noises. In this paper, we propose a method which use the low pass filter and **principal** **component** analysis simultaneously. Experimental results show that the extracted features of the PCA method are more obvious than that of the traditional methods.

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A general asymptotic framework is developed for studying consistency properties of princi- pal **component** analysis (PCA). Our framework includes several previously studied domains of asymptotics as special cases and allows one to investigate interesting connections and transitions among the various domains. More importantly, it enables us to investigate asymptotic scenarios that have not been considered before, and gain new insights into the consistency, subspace consistency and strong inconsistency regions of PCA and the bound- aries among them. We also establish the corresponding convergence rate within each region. Under general spike covariance **models**, the dimension (or number of variables) discourages the consistency of PCA, while the sample size and spike information (the relative size of the population eigenvalues) encourage PCA consistency. Our framework nicely illustrates the relationship among these three types of information in terms of dimension, sample size and spike size, and rigorously characterizes how their relationships affect PCA consistency. Keywords: High dimension low sample size, PCA, Random matrix, Spike model

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et al. (2017) identified three homogeneous rainfall regions in Tocantins State, Brazil using Ward's algorithm of cluster analysis. Similarly, Terassi & Galvani (2017) also identified the homogeneous rainfall regions in the eastern watersheds of the State of Paraná, Brazil. Recently, Siraj-Ud-Doulah & Islam (2019) analyzed monthly rainfall data from 34 climate stations of Bangladesh using five agglomerative hierarchical clustering measures and found that Ward method based on Euclidean distance, K-means, Fuzzy were the most suitable methods in this particular case. They found seven different climate zones in Bangladesh. Similarly, Gonçalves et al. (2018) used annual mean precipitation and found six homogeneous regions through cluster analysis using Ward's agglomeration method, applied to a historical series of 31 years (1960-1990) at 413 satellite monitoring points in the state of Pará, in the Amazon where the selected years occurred during an El Niño or a La Niña event.The aim of this study was to identify homogeneous regions (rain-gauge stations) in Haryana using cluster analysis and **common** **principal** **component** analysis techniques. For the study monthly rainfall data of 42 years (1970-2011), covering 27 rain gauge stations of Haryana was used for the identification of homogeneous rainfall stations in Haryana. 2 Material and Methods

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Scope for Non-Statisticians: Analytics is a domain where statistics knowledge background is mandatory to work on it. This was a big hindrance for non-statisticians to work in the field of analytics. The SAS E-miner tool is so user friendly as it performs many statistical operations within it (built-in) that even people from non-statistics can work in analytics. SAS E-Miner Analytical Strengths: The analytical strengths of SAS E-miner include Pattern Discovery (to identify similar and dissimilar clusters, pattern matching), predictive modeling (to predict the future results, consequences etc.), and to perform Credit Scoring as to rate the customers. Credit Scoring **Models** – Logistic Regression and **Principal** **Component** Analysis (PCA)- The two credit scoring **models** created, Logistic Regression and **Principal** **Component** Analysis are created for the same Dataset. Logistic Regression (LR)

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• Fengler, M., W. Hardle and C. Villa (2000) "The Dynamics of Implied Volatilities: A **Common** **Principal** **Component** Approach" Preliminary version (September 2000) available from fengler@wiwi.hu-berlin.de • Skiadopoulos, G., S. Hodges and L. Clewlow (1998) "The Dynamics of

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Dimension reduction is an effective and essential tool used to analyze microarray datasets ([APM11]). A lot of algorithms and feature extraction techniques have been put forward in literature the reduction of dimensionality ([RT15]). **Principal** **Component** Analysis (PCA) is one of the most widely used and **common** dimensionality reduction techniques, it is seen as an unsupervised technique and relatively effective tool, but it’s not considered as efficient for dataset that are complex and of high dimension ([APM11]). Therefore, there is need to address the inability of PCA to precisely retrieve the genuine latent features of complex datasets ([APM11]). Data in a very high dimensional space often exists in a lower dimensional space and unsupervised feature extraction technique such as PCA may not be totally efficient.

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Considering the performance of the WANN model, it can be found that its performance can be evaluated satisfactory since it has high and low values of the coefficient of determination and root mean square error, respectively. Moreover, it sounds to be economic in terms of computational cost as well. However, a comparison between the results of the WANN model and the ANN model, it can be found that the WANN model takes more time to be implemented, more expensive in terms of computational effects and complexity but still lower performance. However, it should not be misunderstood or mislead that the DWT does not improve the performance of the existing ANN model. On the other hand, it is mainly due to feeding the WANN model with too many input variables (20 sub-signals) which are inter-correlated. Therefore, it should be manipulated to only select the appropriate sub-signals toward increasing the accuracy and reliability of the model outputs. In this regard, the **principal** **component** analysis was performed to derive the most efficient sub-signals to be used in the input structure of the **models**. Similarly, for the WANFIS model, using all the 20 sub-signals as the model input leads to the generation of too many rules which are not possible to be efficiently executed by the usual CPUs. In this regard, its performance in terms of the error measures cannot be assessed. Therefore, this model with the current input structure requires more amendments to be employed for forecasting purposes. In Table 3, NAN is used to represent that the WANFIS model due to too many rules cannot be implemented.

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We next consider a selection of datasets from UC Irvine’s online Machine Learning Repository (Lichman 2013). For each of the datasets, one attribute was selected as a protected class, and the remaining attributes were considered part of the feature space. After splitting each dataset into separate training (70%) and testing (30%) sets, the top five **principal** components were then found for the training sets of each of these datasets three times: once unconstrained, once with (7) with only the mean constraints (and excluding the covariance constraints) with δ = 0, and once with (7) with both the mean and covariance constraints with δ = 0 and µ = 0.01; the test data was then projected onto these vectors. All data was normalized to have unit variance in each feature, which is **common** practice for datasets with features of incomparable units. For each instance, we estimated ∆(F) using the test set and for the families of linear SVM’s F v and Gaussian kernel

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mate this correlation or make simplifying assumptions about the correlation structure, they are likely the most accurate of the statistical tests supported by PCGSE and are therefore used to evaluate the performance of the parametric and correlation-adjusted parametric tests. The exact permutation test was also used as a “gold-standard” in Zhou et al. [34]. Although they provide superior handling of inter-gene correlation, permutation tests do suffer from two important disadvantages relative to parametric tests: computational complexity and lower power to detect gene sets whose members all have a small **common** association with the outcome. Because of these disadvantages, correlation-adjusted parametric tests are preferred for most PCGSE applications.

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In regional contexts such as the MENA region, if there are unobserved **common** shocks that influence all countries, there is likely to be a cross-sectional dependence or correlation between the residuals in a panel time-series model. If these **common** shocks are correlated with the regressors, the conventional estimators are biased and inconsistent. In this study we explore the pattern of interactions between military expenditure shares in the MENA region over the period 1979-2007. The unobserved **common** shocks arise from economic influences (e.g. oil and aid inflows), political and social influences (e.g. militant oppositions) as well as arms race and alliance influences. To identify the unobserved **common** factors we apply the **Principal** **Component** Analysis (PCA) to the shares of military expenditures in the region and on the residuals from a military demand equa- tion. To evaluate the results from the PCA, we use the multiple-indicator multiple-cause model (MIMIC). The MIMIC model enables to validate which observable variables account for the two most important estimated factors.

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To assess the performance of our test, we simulated gen- etic data under three migration **models**: island (IS) and stepping stone (SS), using the software GenomePop 2.7 [11], and isolation by distance (IBD), using IBDSimV2.0 [12]. We simulated the IS and SS **models** with 4 popula- tions, each with 25 individuals, and a single population under IBD with 100 individuals. 200 unlinked biallelic diploid loci (or single nucleotide polymorphisms; SNPs) were simulated. Populations evolved under constant ef- fective population size θ = 20, and interchanged migrants at three different symmetric and homogeneous rates (0.005, 0.01, and 0.1). We performed 100 independent runs for each of the three migration rates, for a total of 300 simulated dataset per migration model. An example of input file for GenomePop 2.7 and IBDSimV2.0 are included as Additional files 1 and 2.

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where S is the sample covariance matrix. The researcher decides on a satisfactory value for t(k) and then deter- mines k accordingly. The obvious problem with the tech- nique is deciding on an appropriate t(k). In practice it is **common** to select levels between 70% to 95% [9]. Jackson [7] argues strongly against the use of this method except possibly for exploratory purposes when little is known about the population of the data. An obvious problem occurs when several eigenvalues are of similar magnitude. For example, suppose for some k = k * , t(k * ) = 0.50 and the remaining q - k eigenvalues have approximately the same magnitude. Can one justify adding more components until some predetermined value of t(k) is reached? Jolliffe [9] points out that the rule is equivalent to looking at the spectral decomposition of S. Determining how many terms to include in the decomposition is closely related to

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Calcium channel blockers are widely used for the treatment of various cardiac disorders. The existing calcium channel blockers have several short comings; hence there is a need to develop better drugs with better therapeutic profile. 2D-QSAR approach has been useful in such cases. A number of 1, 4- dihydropyridines like amlodipine are extensively used in therapy of cardio vascular disorders. Looking into importance of calcium channel blockers, a series of 1, 4- dihydropyridines was selected and different **models** based on Multiple linear regression (MLR), **Principal** **component** regression (PCR) and Partial Least Squares regression (PLR) analysis were generated to find out correlation between the physicochemical parameters and the biological activity. Multiple linear regression (MLR) coupled with stepwise variable selection led to a statistically significant model as compared to PLR and PCR with respect to r 2 (coefficient of determination 0.8986) and q 2 (cross- validation, > 0.5). Four descriptors are included in 2D- QSAR equation generated by using MLR.

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Although both component and common factor analysis models yield similar results in common research settings (30 or more variables or communalities of .60 for most variables):. the [r]

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As different data models may be employed by the underlying component databases, it becomes imperative to map them to a common data model. The export schema provides a common representati[r]

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In a factor analysis model, the measured variables depend on few dormant factors. Each of the factors affects several variables in **common**, hence they are known as **common** factors (referred to as ‘Factors 3’ in this paper). Each variable can be represented by a linear combination of the **common** factors. The coefficients of this linear equation are known as loadings. Each measured variable includes a **component** due to independent random variability, known as specific variance because it is specific to one variable. Factor analysis **models** the correlation structure in terms of k factors including measurement errors. Unlike PCA the factors are not sorted by any criterion.

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C. Review all of the surviving variables with high loadings on **component** 1 to determine the nature of this **component**. From the rotated factor pattern, you can see that only items 4, 5, and 6 load on **component** 1 (note the asterisks). It is now necessary to turn to the questionnaire itself and review the content of the questions in order to decide what a given **component** should be named. What do questions 4, 5, and 6 have in **common**? What **common** construct do they seem to be measuring? For illustration, the questions being analyzed in the present case are reproduced here. Remember that question 4 was represented as V4 in the SAS program, question 5 was V5, and so forth. Read questions 4, 5, and 6 to see what they have in **common**.

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covariates. However, it is reassuring to note, that despite allowing the contours to be non- parametrically specified, the first **component** did conform to expected linguistic theory for Luobuzhai Qiang in that the most important aspect of the tonal change is a shift rather than a contour change. In particular, the largest contributing covariates to the first eigenfunction were gender, tone, vowel type and sentence type. The random effects of subject and word item were both also significant. This indicates that the shift is speaker dependent, as well as dependent on the word item being said. While these effects are still relatively small in comparison to the effects of gender and tone, their significance shows that it is still important to consider the random nature of these effects in the analysis.

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