46,404 research outputs found
Heterogeneous Matrix Factorization: When Features Differ by Datasets
In myriad statistical applications, data are collected from related but
heterogeneous sources. These sources share some commonalities while containing
idiosyncratic characteristics. More specifically, consider the setting where
observation matrices from sources are generated from a
few common and source-specific factors. Is it possible to recover the shared
and source-specific factors? We show that under appropriate conditions on the
alignment of source-specific factors, the problem is well-defined and both
shared and source-specific factors are identifiable under a constrained matrix
factorization objective. To solve this objective, we propose a new class of
matrix factorization algorithms, called Heterogeneous Matrix Factorization. HMF
is easy to implement, enjoys local linear convergence under suitable
assumptions, and is intrinsically distributed. Through a variety of empirical
studies, we showcase the advantageous properties of HMF and its potential
application in feature extraction and change detection
Musical instrument classification using non-negative matrix factorization algorithms
In this paper, a class of algorithms for automatic classification of individual musical instrument sounds is presented. Several perceptual features used in general sound classification applications were measured for 300 sound recordings consisting of 6 different musical instrument classes (piano, violin, cello, flute, bassoon and soprano saxophone). In addition, MPEG-7 basic spectral and spectral basis descriptors were considered, providing an effective combination for accurately describing the spectral and timbrai audio characteristics. The audio flies were split using 70% of the available data for training and the remaining 30% for testing. A classifier was developed based on non-negative matrix factorization (NMF) techniques, thus introducing a novel application of NMF. The standard NMF method was examined, as well as its modifications: the local, the sparse, and the discriminant NMF. Experimental results are presented to compare MPEG-7 spectral basis representations with MPEG-7 basic spectral features alongside the various NMF algorithms. The results indicate that the use of the spectrum projection coefficients for feature extraction and the standard NMF classifier yields an accuracy exceeding 95%. Ā©2006 IEEE
Fast ALS-based tensor factorization for context-aware recommendation from implicit feedback
Albeit, the implicit feedback based recommendation problem - when only the
user history is available but there are no ratings - is the most typical
setting in real-world applications, it is much less researched than the
explicit feedback case. State-of-the-art algorithms that are efficient on the
explicit case cannot be straightforwardly transformed to the implicit case if
scalability should be maintained. There are few if any implicit feedback
benchmark datasets, therefore new ideas are usually experimented on explicit
benchmarks. In this paper, we propose a generic context-aware implicit feedback
recommender algorithm, coined iTALS. iTALS apply a fast, ALS-based tensor
factorization learning method that scales linearly with the number of non-zero
elements in the tensor. The method also allows us to incorporate diverse
context information into the model while maintaining its computational
efficiency. In particular, we present two such context-aware implementation
variants of iTALS. The first incorporates seasonality and enables to
distinguish user behavior in different time intervals. The other views the user
history as sequential information and has the ability to recognize usage
pattern typical to certain group of items, e.g. to automatically tell apart
product types or categories that are typically purchased repetitively
(collectibles, grocery goods) or once (household appliances). Experiments
performed on three implicit datasets (two proprietary ones and an implicit
variant of the Netflix dataset) show that by integrating context-aware
information with our factorization framework into the state-of-the-art implicit
recommender algorithm the recommendation quality improves significantly.Comment: Accepted for ECML/PKDD 2012, presented on 25th September 2012,
Bristol, U
Computational Methods for Matrix/Tensor Factorization and Deep Learning Image Denoising
Feature learning is a technique to automatically extract features from raw data. It is widely used in areas such as computer vision, image processing, data mining and natural language processing. In this thesis, we are interested in the computational aspects of feature learning. We focus on rank matrix and tensor factorization and deep neural network models for image denoising.
With respect to matrix and tensor factorization, we first present a technique to speed up alternating least squares (ALS) and gradient descent (GD) ā two commonly used strategies for tensor factorization. We introduce an efficient, scalable and distributed algorithm that addresses the data explosion problem. Instead of a computationally challenging sub-step of ALS and GD, we implement the algorithm on parallel machines by using only two sparse matrix-vector products. Not only is the algorithm scalable but it is also on average 4 to 10 times faster than competing algorithms on various data sets. Next, we discuss our results of non-negative matrix factorization for hyperspectral image data in the presence of noise. We introduce a spectral total variation regularization and derive four variants of the alternating direction method of multiplier algorithm. While all four methods belong to the same family of algorithms, some perform better than others. Thus, we compare the algorithms using stimulated Raman spectroscopic image will be demonstrated.
For deep neural network models, we focus on its application to image denoising. We first demonstrate how an optimal procedure leveraging deep neural networks and convex optimization can combine a given set of denoisers to produce an overall better result. The proposed framework estimates the mean squared error (MSE) of individual denoised outputs using a deep neural network; optimally combines the denoised outputs via convex optimization; and recovers lost details of the combined images using another deep neural network. The framework consistently improves denoising performance for both deterministic denoisers and neural network denoisers. Next, we apply the deep neural network to solve the image reconstruction issues of the Quanta Image Sensor (QIS), which is a single-photon image sensor that oversamples the light field to generate binary measures
Incorporating Side Information in Probabilistic Matrix Factorization with Gaussian Processes
Probabilistic matrix factorization (PMF) is a powerful method for modeling
data associated with pairwise relationships, finding use in collaborative
filtering, computational biology, and document analysis, among other areas. In
many domains, there is additional information that can assist in prediction.
For example, when modeling movie ratings, we might know when the rating
occurred, where the user lives, or what actors appear in the movie. It is
difficult, however, to incorporate this side information into the PMF model. We
propose a framework for incorporating side information by coupling together
multiple PMF problems via Gaussian process priors. We replace scalar latent
features with functions that vary over the space of side information. The GP
priors on these functions require them to vary smoothly and share information.
We successfully use this new method to predict the scores of professional
basketball games, where side information about the venue and date of the game
are relevant for the outcome.Comment: 18 pages, 4 figures, Submitted to UAI 201
A Broad Learning Approach for Context-Aware Mobile Application Recommendation
With the rapid development of mobile apps, the availability of a large number
of mobile apps in application stores brings challenge to locate appropriate
apps for users. Providing accurate mobile app recommendation for users becomes
an imperative task. Conventional approaches mainly focus on learning users'
preferences and app features to predict the user-app ratings. However, most of
them did not consider the interactions among the context information of apps.
To address this issue, we propose a broad learning approach for
\textbf{C}ontext-\textbf{A}ware app recommendation with \textbf{T}ensor
\textbf{A}nalysis (CATA). Specifically, we utilize a tensor-based framework to
effectively integrate user's preference, app category information and
multi-view features to facilitate the performance of app rating prediction. The
multidimensional structure is employed to capture the hidden relationships
between multiple app categories with multi-view features. We develop an
efficient factorization method which applies Tucker decomposition to learn the
full-order interactions within multiple categories and features. Furthermore,
we employ a group norm regularization to learn the group-wise
feature importance of each view with respect to each app category. Experiments
on two real-world mobile app datasets demonstrate the effectiveness of the
proposed method
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