30 research outputs found
Damage detection using robust fuzzy principal component analysis
In this work Robust Fuzzy Principal Component Analysis (RFPCA) is used and
compared with comparing with classical Principal Component Analysis (PCA) to
detect and classify damages. It has been proved that the RFPCA method achieves
better result mainly because it is more compressible than classical PCA and also
carries more information, hence not only it can distinguish the healthy structure from
the damaged structure much sharper than the traditional counterparts but also in some
cases traditional PCA is incapable of discerning the pristine from damaged structure.
This work involves experimental results using pipe-like structure powered by a
piezoelectric actuators and sensors.Peer ReviewedPostprint (published version
Grassmann Averages for Scalable Robust PCA
As the collection of large datasets becomes increasingly automated, the occurrence of outliers will increase – “big data” implies “big outliers”. While principal component analysis (PCA) is often used to reduce the size of data, and scalable solutions exist, it is well-known that outliers can arbitrarily corrupt the results. Unfortunately, state-of-the-art approaches for robust PCA do not scale beyond small-to-medium sized datasets. To address this, we introduce the Grassmann Average (GA), which expresses dimensionality reduction as an average of the subspaces spanned by the data. Because averages can be efficiently computed, we immediately gain scalability. GA is inherently more robust than PCA, but we show that they coincide for Gaussian data. We exploit that averages can be made robust to formulate the Robust Grassmann Average (RGA) as a form of robust PCA. Robustness can be with respect to vectors (subspaces) or elements of vectors; we focus on the latter and use a trimmed average. The resulting Trimmed Grassmann Average (TGA) is particularly appropriate for computer vision because it is robust to pixel outliers. The algorithm has low computational complexity and minimal memory requirements, making it scalable to “big noisy data.” We demonstrate TGA for background modeling, video restoration, and shadow removal. We show scalability by performing robust PCA on the entire Star Wars IV movie
Robust PCA as Bilinear Decomposition with Outlier-Sparsity Regularization
Principal component analysis (PCA) is widely used for dimensionality
reduction, with well-documented merits in various applications involving
high-dimensional data, including computer vision, preference measurement, and
bioinformatics. In this context, the fresh look advocated here permeates
benefits from variable selection and compressive sampling, to robustify PCA
against outliers. A least-trimmed squares estimator of a low-rank bilinear
factor analysis model is shown closely related to that obtained from an
-(pseudo)norm-regularized criterion encouraging sparsity in a matrix
explicitly modeling the outliers. This connection suggests robust PCA schemes
based on convex relaxation, which lead naturally to a family of robust
estimators encompassing Huber's optimal M-class as a special case. Outliers are
identified by tuning a regularization parameter, which amounts to controlling
sparsity of the outlier matrix along the whole robustification path of (group)
least-absolute shrinkage and selection operator (Lasso) solutions. Beyond its
neat ties to robust statistics, the developed outlier-aware PCA framework is
versatile to accommodate novel and scalable algorithms to: i) track the
low-rank signal subspace robustly, as new data are acquired in real time; and
ii) determine principal components robustly in (possibly) infinite-dimensional
feature spaces. Synthetic and real data tests corroborate the effectiveness of
the proposed robust PCA schemes, when used to identify aberrant responses in
personality assessment surveys, as well as unveil communities in social
networks, and intruders from video surveillance data.Comment: 30 pages, submitted to IEEE Transactions on Signal Processin