cvpr cvpr2013 cvpr2013-253 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Siddhartha Chandra, Shailesh Kumar, C.V. Jawahar
Abstract: Understanding the nature of data is the key to building good representations. In domains such as natural images, the data comes from very complex distributions which are hard to capture. Feature learning intends to discover or best approximate these underlying distributions and use their knowledge to weed out irrelevant information, preserving most of the relevant information. Feature learning can thus be seen as a form of dimensionality reduction. In this paper, we describe a feature learning scheme for natural images. We hypothesize that image patches do not all come from the same distribution, they lie in multiple nonlinear subspaces. We propose a framework that uses K Restricted Boltzmann Machines (K-RBMS) to learn multiple non-linear subspaces in the raw image space. Projections of the image patches into these subspaces gives us features, which we use to build image representations. Our algorithm solves the coupled problem of finding the right non-linear subspaces in the input space and associating image patches with those subspaces in an iterative EM like algorithm to minimize the overall reconstruction error. Extensive empirical results over several popular image classification datasets show that representations based on our framework outperform the traditional feature representations such as the SIFT based Bag-of-Words (BoW) and convolutional deep belief networks.
Reference: text
sentIndex sentText sentNum sentScore
1 com i Abstract Understanding the nature of data is the key to building good representations. [sent-8, score-0.055]
2 In domains such as natural images, the data comes from very complex distributions which are hard to capture. [sent-9, score-0.08]
3 Feature learning intends to discover or best approximate these underlying distributions and use their knowledge to weed out irrelevant information, preserving most of the relevant information. [sent-10, score-0.112]
4 Feature learning can thus be seen as a form of dimensionality reduction. [sent-11, score-0.033]
5 In this paper, we describe a feature learning scheme for natural images. [sent-12, score-0.033]
6 We hypothesize that image patches do not all come from the same distribution, they lie in multiple nonlinear subspaces. [sent-13, score-0.18]
7 We propose a framework that uses K Restricted Boltzmann Machines (K-RBMS) to learn multiple non-linear subspaces in the raw image space. [sent-14, score-0.421]
8 Projections of the image patches into these subspaces gives us features, which we use to build image representations. [sent-15, score-0.399]
9 Our algorithm solves the coupled problem of finding the right non-linear subspaces in the input space and associating image patches with those subspaces in an iterative EM like algorithm to minimize the overall reconstruction error. [sent-16, score-0.908]
10 Extensive empirical results over several popular image classification datasets show that representations based on our framework outperform the traditional feature representations such as the SIFT based Bag-of-Words (BoW) and convolutional deep belief networks. [sent-17, score-0.319]
11 Introduction Feature extraction and modelling together dictate the overall complexity of any computer vision system. [sent-19, score-0.116]
12 Rich features that capture most of the complexity in the input space require simpler models while simpler features require more complex models. [sent-20, score-0.114]
13 This “law-of-conservation of complexity” in modelling has driven many efforts in feature engineering, especially, in complex domains such as computer vision where the raw input is not easily tamed by simple features. [sent-21, score-0.176]
14 Finding semantically rich features, that capture the inherent complexity of the input data, is a challenging and necessary pre-processing step in many machine learning applications. [sent-22, score-0.159]
15 We propose a feature learning framework motivated by the hypothesis: data really lies in multiple non-linear subspaces (as opposed to a single subspace). [sent-23, score-0.446]
16 Finding these subspaces and clustering the right data points into the right subspaces will result in the kind of features we are looking for. [sent-24, score-0.787]
17 Our approach requires that we solve the coupled problem of non-linear projection and clustering of data points into those projections simultaneously. [sent-25, score-0.266]
18 Clustering cannot be done in the raw input space because the data really lies in certain non-linear subspaces and the right subspaces cannot be discovered without proper groupings of the data. [sent-26, score-0.845]
19 While most of the work in clustering and projection methods is done independently, attempts have been made to combine them [1, 17]. [sent-27, score-0.127]
20 In this paper, we take this coupling a step forward by learning clusters and projections simultaneously. [sent-28, score-0.18]
21 This is fundamentally different from an approach like Sparse Subspace Clustering (SSC) [5] that first learns a sparse representation (SR) of the data and then applies spectral clustering to a similarity matrix built from this SR. [sent-29, score-0.151]
22 We further hypothesize that a mere non-linear clustering is not the best way to understand the nature of data. [sent-30, score-0.217]
23 Further simple clusters (concepts) might be present in each of the non-linear subspaces. [sent-31, score-0.038]
24 An overall solution should first find multiple non-linear sub-spaces within the data and then further cluster the data within each sub-space if necessary. [sent-32, score-0.041]
25 Once we discover the subspaces the data points (image patches) lie in, projections into these subspaces will give us the features that best represent the patches. [sent-33, score-0.835]
26 We propose a systematic framework for a two-level clustering of input data into meaningful clusters – first level being clustering coupled with non-linear projection by Restricted Boltzmann Machines (RBMs), and the second level being simple K-means clustering in each non-linear subspace. [sent-34, score-0.485]
27 In other words, we use K-RBMS for the first level clustering and K-means on the RBM projections for the second level clustering. [sent-35, score-0.227]
28 We apply our framework to clustering, improv- ing BoW and feature learning from raw image patches. [sent-36, score-0.089]
29 We demonstrate empirically that our clustering method is comparable to the state of the art methods in terms of accuracy, and much faster. [sent-37, score-0.099]
30 Representations based on K-RBM features 222777777866 outperform traditional deep learning and SIFT based BoW representations on image classification tasks. [sent-38, score-0.217]
31 Figure 1: RBM weights (learnt by the model) representing 20 non-linear subspaces in the Pascal 2007 data. [sent-39, score-0.367]
32 Local KRBM features are computed by projecting image patches to the subspace they belong to, and adding the biases. [sent-40, score-0.145]
33 Restricted Boltzmann Machines (RBMS) [22] are undirected, energy-based graphical models that learn a nonlinear subspace that the data fits to. [sent-41, score-0.159]
34 RBMs have been used successfully to learn features for image understanding and classification [12], speech representation [18], analyze user rating of movies [21] , and better bag-of-word representation of text data [20]. [sent-42, score-0.102]
35 Moreover, RBMS have been stacked together to learn hierarchical representations such as deep belief networks [12, 3] and convolutional deep belief networks [16] for finding semantically deeper features in complex domains such as images. [sent-43, score-0.619]
36 Most nonlinear subspace learning algorithms [6, 2] make various assumptions about the nature of the subspaces they intend to discover. [sent-44, score-0.596]
37 Figure 1 shows 20 nonlinear subspaces in VOC PASCAL 2007 data. [sent-48, score-0.392]
38 It is evident from the figure that the huge diversity in the image patches can not be captured by a single subspace. [sent-50, score-0.078]
39 The association of a data point to an RBM depends on the reconstruction error of each RBM for that data point. [sent-51, score-0.032]
40 Each RBM updates its weights based on all the data points associated with it. [sent-52, score-0.056]
41 Through various learning tasks on synthetic and real data, we show the convergence properties, quality of subspaces learnt, and improvement in the accuracies of both descriptive and predictive tasks. [sent-53, score-0.426]
42 Firstly, while we employ traditional second order (2layer) RBMs, [19] describes an implicit mixture of RBMs which is formulated using third order RBMs. [sent-56, score-0.083]
43 Authors in [19] introduce the cluster label (explicitly) as a hidden discrete variable in the RBM formulation describing an energy function that captures 3-way interactions among vis- ible units, hidden units, and the cluster label variable. [sent-57, score-0.403]
44 In our solution, the cluster label is implied by the RBM id, and the model parameters capture the usual 2-way interactions. [sent-58, score-0.085]
45 One reason for our choice of traditional RBMs as building blocks was the availability of a great deal of research on properly training RBMs [11]. [sent-59, score-0.076]
46 Secondly, the partition function of an RBM is intractable. [sent-60, score-0.04]
47 By introducing the third layer [19] manages to fit the mixture of boltzmann machines without explicitly computing the partition function. [sent-61, score-0.381]
48 We tackle the partition problem by associating samples with the RBMs that reconstruct them best (minimizing the reconstruction errors) in an EM algorithm. [sent-62, score-0.125]
49 Since the reconstruction error is not an inherent part of the traditional RBM formulation, our framework is not a mixture model. [sent-63, score-0.145]
50 Training RBMs RBMS are two layered, fully connected networks that have a layer of input/visible variables and a layer of hidden random variables. [sent-65, score-0.34]
51 RBMS model a distribution over visible variables by introducing a set of stochastic features. [sent-66, score-0.122]
52 In applications where RBMS are used for image analysis, the visible units correspond to the pixel values and the hidden units correspond to visual features. [sent-67, score-0.546]
53 There are three kinds of design choices in building an RBM: the objective function used, the frequency of parameter updates, and the type of visible and hidden units. [sent-68, score-0.263]
54 RBMS are usually trained by minimizing the contrastive divergence objective (CD- 1)[10] which approximates the actual RBM objective. [sent-69, score-0.036]
55 , I (v0 = 1 is the bias terms), J hidden units hj ,j = 1, . [sent-73, score-0.523]
56 =J0wijhj⎠⎞ (2) σ(·) is the sigmoid activation function. [sent-80, score-0.08]
57 In the CD- 1 forσw(a·r)d pass ( vsiigsimbloei dto a hctiidvdaetino)n, we acctitoivna. [sent-81, score-0.068]
58 te I nth teh hei CddDen-1 1u fnoirt-s hj+ from visible (input) unit activations vi+ (Eq. [sent-82, score-0.25]
59 In the backward pass (hidden to visible), we recompute visible unit activations vi− from hj+ (Eq. [sent-84, score-0.314]
60 Finally we compute the hidden unit activations hj− again from vi− . [sent-86, score-0.256]
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