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Multilabel Classification via Featureaware Implicit Label Space Encoding
"... To tackle a multilabel classification problem with many classes, recently label space dimension reduction (LSDR) is proposed. It encodes the original label space to a lowdimensional latent space and uses a decoding process for recovery. In this paper, we propose a novel method termed FaIE to pe ..."
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To tackle a multilabel classification problem with many classes, recently label space dimension reduction (LSDR) is proposed. It encodes the original label space to a lowdimensional latent space and uses a decoding process for recovery. In this paper, we propose a novel method termed FaIE to perform LSDR via Featureaware Implicit label space Encoding. Unlike most previous work, the proposed FaIE makes no assumptions about the encoding process and directly learns a code matrix, i.e. the encoding result of some implicit encoding function, and a linear decoding matrix. To learn both matrices, FaIE jointly maximizes the recoverability of the original label space from the latent space, and the predictability of the latent space from the feature space, thus making itself featureaware. FaIE can also be specified to learn an explicit encoding function, and extended with kernel tricks to handle nonlinear correlations between the feature space and the latent space. Extensive experiments conducted on benchmark datasets well demonstrate its effectiveness. 1.
Greedy bilateral sketch, completion & smoothing
 In International Conference on Artificial Intelligence and Statistics
, 2013
"... Recovering a large lowrank matrix from highly corrupted, incomplete or sparse outlier overwhelmed observations is the crux of various intriguing statistical problems. We explore the power of “greedy bilateral (GreB) ” paradigm in reducing both time and sample complexities for solving these proble ..."
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Recovering a large lowrank matrix from highly corrupted, incomplete or sparse outlier overwhelmed observations is the crux of various intriguing statistical problems. We explore the power of “greedy bilateral (GreB) ” paradigm in reducing both time and sample complexities for solving these problems. GreB models a lowrank variable as a bilateral factorization, and updates the left and right factors in a mutually adaptive and greedy incremental manner. We detail how to model and solve lowrank approximation, matrix completion and robust PCA in GreB’s paradigm. On their MATLAB implementations, approximating a noisy 104 × 104 matrix of rank 500 with SVD accuracy takes 6s; MovieLens10M matrix of size 69878 × 10677 can be completed in 10s from 30 % of 107 ratings with RMSE 0.86 on the rest 70%; the lowrank background and sparse moving outliers in a 120×160 video of 500 frames are accurately separated in 1s. This brings 30 to 100 times acceleration in solving these popular statistical problems. 1
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"... Random forests with random projections of the output space for high dimensional multilabel classification ..."
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Random forests with random projections of the output space for high dimensional multilabel classification
1Unmixing Incoherent Structures of Big Data by Randomized or Greedy Decomposition
"... Learning big data by matrix decomposition always suffers from expensive computation, mixing of complicated structures and noise. In this paper, we study more adaptive models and efficient algorithms that decompose a data matrix as the sum of semantic components with incoherent structures. We firstly ..."
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Learning big data by matrix decomposition always suffers from expensive computation, mixing of complicated structures and noise. In this paper, we study more adaptive models and efficient algorithms that decompose a data matrix as the sum of semantic components with incoherent structures. We firstly introduce “GO decomposition (GoDec)”, an alternating projection method estimating the lowrank part L and the sparse part S from data matrix X = L + S + G corrupted by noise G. Two acceleration strategies are proposed to obtain scalable unmixing algorithm on big data: 1) Bilateral random projection (BRP) is developed to speed up the update of L in GoDec by a closedform built from left and right random projections of X−S in lower dimensions; 2) Greedy bilateral (GreB) paradigm updates the left and right factors of L in a mutually adaptive and greedy incremental manner, and achieve significant improvement in both time and sample complexities. Then we proposes three nontrivial variants of GoDec that generalizes GoDec to more general data type and whose fast algorithms can be derived from the two strategies: 1) for motion segmentation, we further decompose the sparse S (moving objects) as the sum of multiple rowsparse matrices, each of which is a lowrank matrix after specific geometric transformation sequence and defines a motion shared by multiple objects; 2) for multilabel learning, we further decompose the lowrank L into subcomponents with separable subspaces, each corresponds to the mapping a single label in feature space. Then the prediction can be effectively conducted by group lasso on the subspace ensemble; 3) for estimating scoring functions of each user in recommendation system, we further decompose the lowrank L as WZT, where the rows of W is the linear scoring functions and the rows of Z are the items represented by available features. Empirical studies show the efficiency, robustness and effectiveness of the proposed methods in real applications. Index Terms Lowrank and sparse matrix decomposition, bilateral random projection, greedy bilateral paradigm, multilabel learning, background modeling, motion segmentation, recommendation systems I.