Robust Unsupervised Flexible Auto-weighted Local-coordinate Concept Factorization for Image Clustering

Abstract

We investigate the high-dimensional data clustering problem by proposing a novel and unsupervised representation learning model called Robust Flexible Auto-weighted Local-coordinate Concept Factorization (RFA-LCF). RFA-LCF integrates the robust flexible CF, robust sparse local-coordinate coding and the adaptive reconstruction weighting learning into a unified model. The adaptive weighting is driven by including the joint manifold preserving constraints on the recovered clean data, basis concepts and new representation. Specifically, our RFA-LCF uses a L2,1-norm based flexible residue to encode the mismatch between clean data and its reconstruction, and also applies the robust adaptive sparse local-coordinate coding to represent the data using a few nearby basis concepts, which can make the factorization more accurate and robust to noise. The robust flexible factorization is also performed in the recovered clean data space for enhancing representations. RFA-LCF also considers preserving the local manifold structures of clean data space, basis concept space and the new coordinate space jointly in an adaptive manner way. Extensive comparisons show that RFA-LCF can deliver enhanced clustering results.

Flexible Auto-Weighted Local-Coordinate Concept Factorization: A Robust Framework for Unsupervised Clustering

“…By updating the adaptive weights, robust projection and factorization matrices alternaltely, RFA-LCF can ensure the learnt weights to be optimal for the data representations. Note that an early version of this work was presented in [57]. This paper has further provided the detailed analysis of the formulation, convergence analysis, computational complexity analysis and relationship analysis, and moreover conducts a thorough experimental evaluation on the tasks of data representation and clustering.…”

A Survey on Concept Factorization: From Shallow to Deep Representation Learning

“…Although the localities can be clearly retained by these graphbased CF methods, they still have one glaring flaw, i.e., it is tough to choose an optimal number of nearest neighbors to define the neighborhood graph. To overcome this issue, researchers have recently proposed the optimized adaptive-graph based CF methods, such as CF with Adaptive Neighbors (CFANs) [12], CF with Optimal Graph Learning (CF-OGL) [126], Graph-Regularized Local coordinate CF with CLR (GRLCFCLR) [9] and Robust Flexible Autoweighted Local-Coordinate CF (RFA-LCF) [14][15], etc. These optimized weighting strategies can avoid the tricky issue of choosing the optimal number of nearest neighbors in constructing the neighborhood graph effectively.…”

“…LGCF1 [10] and RFA-LCF [14][15].  Self-representation based CF algorithms are mainly motivated by the success of exploiting the self-representation of data, in which the input data is regarded as a dictionary, which provided new idea for deriving self-expressive CF.…”

“…Robust and Discriminative CF (RDCF) [121] regards the noise as a sparse component of matrix factorization and makes it apart from raw data. In addition, RFA-LCF [14], Robust Local Learning and Discriminative CF (RLLDCF) [125], RSCF [127] and Correntropy-based Graph-regularized CF (GCCF) [124], are proposed to replace the noise-sensitive Frobenius norm using robust norms to encode the reconstruction error. 4) Unsupervised Discriminative CF.…”

Deep Self-representative Concept Factorization Network for Representation Learning

“…Representation learning from high-dimensional complex data is always an important and fundamental problem in the fields of pattern recognition and data mining [40][41][42][43][44][45][46][47][48][49][50]. To represent data, lots of feasible and effective approaches can be used, of which Matrix Factorization (MF) based models have been proven to be effective for low-dimensional feature extraction and cluster-ing [24][25][26][27][28][29][30][31][32] [36][37][38][39]. Nonnegative Matrix Factorization (NMF) [1] and Concept Factorization (CF) [2] are two most classical nonnegative MF methods.…”