Applications of Cluster and Factorial Analysis |Chapter 11 | Research Updates in Mathematics and Computer Science Vol. 7

The primary objective of the cluster analysis is to form clusters such that each cluster is an homogeneous as possible with respect to items of interest and as different as possible between clusters. Cluster analysis is a mathematical technique in Multivariate Data Analysis which indicates the proper guidelines in grouping the data into clusters. Factor Analysis is a combination of intrinsic decomposition and recurrent factor decomposition [1]. It is surpassing Statistical approaches, factor decomposition has endured from incertitude review justification. We can understand the concept with illustrated notations of cluster Analysis and various Clustering Techniques in this Research paper. Similarity and Dissimilarity measures and Dendrogram Analysis will be computed as required measures for Analysis. The approach of factor analysis is helpful in figuring out the underlying, hidden factors that underlie the correlations between the variables. Sometimes it's crucial to identify and isolate these facts for use in a variety of statistical techniques across different domains. With the help of illustrated factor analysis methodologies, we may comprehend the significance of factor analysis and its key concepts. We can estimate the Basic Factor Modeling and Factor Loadings, and also Factor Rotation process. Provides the complete application process and approaches of Principal Factor M.L. Factor and PCA comparison of Factor Analysis in this Research paper Since all these methods use some sort of similarity measures. The same thing can be carried out with a similarity measure matrix also. In the behavioral and social sciences, researchers need to develop scales for the various un-observable factors such as attitudes, images, intelligence, personality and patriotism.

 

Author(s) Details

Ramya Nemania

Department of Mathematics, Gitam School of Science, GITAM (Deemed to be University), Visakhapatnam, India and  I/c - Research Department, OPJS University, Churu, Rajasthan, India.

Daruri Venugopalb

I/c - Research Department, OPJS University, Churu, Rajasthan, India.

 

 

Please see the book here:- https://doi.org/10.9734/bpi/rumcs/v7/299

Applications of Cluster and Factorial Analysis | Chapter 12 | Research Updates in Mathematics and Computer Science Vol. 7

 The primary objective of the cluster analysis is to form clusters such that each cluster is an homogeneous as possible with respect to items of interest and as different as possible between clusters. Cluster analysis is a mathematical technique in Multivariate Data Analysis which indicates the proper guidelines in grouping the data into clusters. Factor Analysis is a combination of intrinsic decomposition and recurrent factor decomposition. It is surpassing Statistical approaches, factor decomposition has endured from incertitude review justification. We can understand the concept with illustrated notations of cluster Analysis and various Clustering Techniques in this Research paper. Similarity and Dissimilarity measures and Dendrogram Analysis will be computed as required measures for Analysis. The approach of factor analysis is helpful in figuring out the underlying, hidden factors that underlie the correlations between the variables. Sometimes it's crucial to identify and isolate these facts for use in a variety of statistical techniques across different domains. With the help of illustrated factor analysis methodologies, we may comprehend the significance of factor analysis and its key concepts. We can estimate the Basic Factor Modeling and Factor Loadings, and also Factor Rotation process. Provides the complete application process and approaches of Principal Factor M.L. Factor and PCA comparison of Factor Analysis in this Research paper Since all these methods use some sort of similarity measures. The same thing can be carried out with a similarity measure matrix also. In the behavioral and social sciences, researchers need to develop scales for the various un-observable factors such as attitudes, images, intelligence, personality and patriotism.

 

Author(s)details:-

 

Ramya Nemania
Department of Mathematics, Gitam School of Science, GITAM (Deemed to be University), Visakhapatnam, India and  I/c - Research Department, OPJS University, Churu, Rajasthan, India.

 

Daruri Venugopalb
I/c - Research Department, OPJS University, Churu, Rajasthan, India.

 

Please See the book here :- https://doi.org/10.9734/bpi/rumcs/v7/299

Statistical Modeling for Soil Attributes | Chapter 6 | Research and Applications Towards Mathematics and Computer Science Vol. 5

 The study of fiber patterns in soil is critical, and these studies involve more multivariate existent determinants.  An empirical reasoning was conducted to study the friendship between the soil traits, including the Potential of Hydrogen (pH), Electrical Conductivity (EC), Zinc (Zn), Sulfur (S), Phosphorus (P), Potassium (K), Organic Carbon (OC), Nitrogen (N), Manganese (Mn), Iron (Fe), Copper (Cu) and Boron (B) utilizing principal component, Factor Analysis, and Canonical Correlation dossier reduction multivariate methods. The objectives of the studies are (i) to show how PCA, FA, and CCA are working in reducing the range of the soil dataset outside losing excessive variability and (ii) to label the correlation patterns that lie in the soil data, and (iii) to label the soil dossier, which provide most in the overall variance of the soil traits. Lastly, (iv) to show how foods in the soil can vary and to find the particular determinants that make up the overall pattern of soil alternative.  The first PC was dominated apiece soil characteristics N, Zn, pH, K, Fe, and Mn. The soil traits B, P, S, and Fe dominated the second PC. The triennial PC was governed by B and P, while the fourth PC was ruled by the alone feature Cu. The factor reasoning of the first factor told important negative loading on Zn and important positive stowing on Mn, pH, K, and B. The second factor has important certain loadings for Fe and EC.  The third component has important positive loadings on Zn, S, P, and OC but has solid negative loadings on N. A highly favorable high Cu stowing is visualized in the fourth component. In the one of four equal parts component, Cu and OC are heavily burden.  The canonical repetition for dependent and free sets is 20% and 30%, individually.  According to the Stewart-Love canonical repetition index, the initial uninterrupted combination of the X-set gives reason for 39% of all the variance in the Y-set.

Author(s) Details:

Rajarathinam, A.,
Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, India.

Ramji, M.,
Department of Statistics, Manonmaniam Sundaranar University, Tirunelveli, India.

Please see the link here: https://stm.bookpi.org/RATMCS-V5/article/view/12216