Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vectorial Dimension Reduction for Tensors Based on Bayesian Inference   Dimensionality reduction for high-order tensors is a challenging problem. In
conventional approaches, higher order tensors are `vectorized` via Tucker
decomposition to obtain lower order tensors. This will destroy the inherent
high-order structures or resulting in undesired tensors, respectively. This
paper introduces a probabilistic vectorial dimensionality reduction model for
tensorial data. The model represents a tensor by employing a linear combination
of same order basis tensors, thus it offers a mechanism to directly reduce a
tensor to a vector. Under this expression, the projection base of the model is
based on the tensor CandeComp/PARAFAC (CP) decomposition and the number of free
parameters in the model only grows linearly with the number of modes rather
than exponentially. A Bayesian inference has been established via the
variational EM approach. A criterion to set the parameters (factor number of CP
decomposition and the number of extracted features) is empirically given. The
model outperforms several existing PCA-based methods and CP decomposition on
several publicly available databases in terms of classification and clustering
accuracy.

11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph