China 
Africa 
Explore chapters and articles related to this topic
Damage identification on bridges using ambient vibration testing
Published in Jaap Bakker, Dan M. Frangopol, Klaas van Breugel, Life-Cycle of Engineering Systems, 2017
N.L.D. Khoa, M. Makki Alamdari, P. Runcie, V.V. Nguyen
Principal Component Analysis (PCA) (Jolliffe, 2002) is a popular dimensionality reduction technique. However, it has the complexity of O(d3) due to the eigen decomposition of the data covariance matrix. Random projection is an alternative and less expensive way to reduce the dimensionality of very high dimensional data. According to Johnson–Lindenstrauss lemma, the pairwise Euclidean distances between data points are preserved if we randomly project the data onto a subspace spanned by O(nlogn) columns (Johnson & Lindenstrauss, 1984). Therefore, the dimension of the projected space only depends on the number of data points, no matter how high the original dimension of the data is.
Dimension Reduction Methods
Published in Yuri S. Popkov, Alexey Yu. Popkov, Yuri A. Dubnov, Alexander Yu. Mazurov, Entropy Randomization in Machine Learning, 2023
Yuri S. Popkov, Alexey Yu. Popkov, Yuri A. Dubnov, Alexander Yu. Mazurov
Regardless of the field of application, the nature and dimension of the original data represented by a set of points in a multidimensional space, the use of random projections allows reducing the dimension while preserving the data structure. Moreover, the random projection method is easily interpreted and does not require significant computing resources, even in the case of high and ultrahigh-dimensional data, in contrast to alternative dimension reduction methods such as PCA and SVD.
What Is Data Analytics?
Published in Rakesh M. Verma, David J. Marchette, Cybersecurity Analytics, 2019
Rakesh M. Verma, David J. Marchette
One popular method for reducing the dimensionality of a data set is through random projections. The idea is to take random linear combinations of the features and use these in place of the original features. At first blush, this seems nonsensical: how can a random projection be useful? In fact, the colloquial use of the word “random”, in English at least, suggests nonsense.feature selection!random projections
Real-valued syntactic word vectors
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2020
Now, we turn our attention to the relationship between RSV and RI. Context selection in RI is on the basis of word frequencies. RI filters out the highly frequent context units, i.e., the function words that contain the grammatical information, and keeps the frequent content words. However, as we mentioned earlier, context selection in RSV is on the basis of word frequency and the amount of entropy involved in contextual environments. RSV filters out the less frequent context units whose contextual environment involves high entropy. The context units filtered by this approach can be both function words and content words. Another difference between RSV and RI is in the method of dimensionality reduction. Sahlgren (2006) proposes to reduce the dimensionality of the co-occurrence matrix through random projection (Achlioptas, 2001). Random projection is based on the Johnson-Lindenstrauss lemma stating that any point in a high-dimensional space can be projected to a lower-dimensional space without pointwise distance distortion between the points. It uses a random projection matrix whose unit length rows, forming the lower-dimensional space, are almost orthogonal to each other. RI employs this idea of near orthogonality and associates each context unit (word) in the language with a unit length random vector. The local weighting function in RI returns the random vector associated with the context unit whose contextual environment includes the word of interest, . The final word vectors are gradually computed through accumulating the random vectors while scanning the corpus. This is equivalent to multiplying a co-occurrence matrix with a random projection matrix. In RSV, we associate a set of context units with fully orthogonal vectors and build a co-occurrence matrix from those vectors. The low-dimensional word vectors are then extracted from the singular vectors of this matrix which is affected by a transformation function.
Document similarity for error prediction
Published in Journal of Information and Telecommunication, 2021
Péter Marjai, Péter Lehotay-Kéry, Attila Kiss
In random projection, using a random dimensional matrix R which has columns with unit lengths, the original d- dimensional data is projected to a k-dimensional subspace. Let be the original set of information,then