Extended Abstract. When data are in the form of continuous functions, they may challenge classical methods of data analysis based on arguments in finite dimensional spaces, and therefore need theoretical justification. Infinite dimensionality of spaces that data belong to, leads to major statistical methodologies and new insights for analyzing them, which is called functional data analysis (FDA...

Principal component analysis (PCA) is a popular dimension reduction method to reduce the complexity and obtain the informative aspects of high-dimensional datasets. When the data distribution is skewed, data transformation is commonly used prior to applying PCA. Such transformation is usually obtained from previous studies, prior knowledge, or trial-and-error. In this work, we develop a model-b...

Traditional tensor decompositions such as the CANDECOMP / PARAFAC (CP) and Tucker decompositions yield higher-order principal components that have been used to understand tensor data in areas such as neuroimaging, microscopy, chemometrics, and remote sensing. Sparsity in high-dimensional matrix factorizations and principal components has been well-studied exhibiting many benefits; less attentio...

Tigris, are widespread in west of Iran and lives mostly in river and lake. They are omnivorous fish. This study aims to investigate population structure of C. reginus using Principal component Analysis. The study was conducted in three rivers that is the most remote headstream of the Gamasiab River in west part of Iran. Seven quantitative traits were measured for each specimen. After logarithmi...

Principal Components Analysis (PCA) is of great use in representation of multi-dimensional data sets, often providing a useful compression mechanism. Sometimes, input data sets are drawn from disparate domains, such that components of the input are heterogeneous, making them di cult to compare in scale. When this occurs, it is possible for one component to dominate another in the PCA at the exp...

This work studies the problem of sequentially recovering a sparse vector St and a vector from a low-dimensional subspace Lt from knowledge of their sum Mt := Lt + St. If the primary goal is to recover the low-dimensional subspace in which the Lt’s lie, then the problem is one of online or recursive robust principal components analysis (PCA). An example of where such a problem might arise is in ...

We present a new neural model which extends the classical competitive learning (CL) by performing a Probabilistic Principal Components Analysis (PPCA) at each neuron. The model also has the ability to learn the number of basis vectors required to represent the principal directions of each cluster, so it overcomes a drawback of most local PCA models, where the dimensionality of a cluster must be...

Skew detection via principal components is proposed as an e ective method for images which contain other parts than text It is shown that the negative of the image leads to much more robust results and that the computation time involved is still practical This method is also shown to be e ective for single word skew detection