Graph based machine learning with applications to media analytics

Transcription

1 Graph based machine learning with applications to media analytics Lei Ding, PhD with collaborators at

2 Outline Graph based machine learning Basic structures Algorithms Examples Applications in media analytics Social analysis of videos Content analysis of images

3 Outline Graph based machine learning Basic structures Algorithms Examples Applications in media analytics Social analysis of videos Content analysis of images

4 What is a graph Not the graph we are going to talk about

5 What is a graph A graph is composed of Vertices (nodes): pixels, actors in videos, genes, ads, etc. Edges: their relations In machine learning, we are interested in predicting some quantity (a class label, or a continuous value) at each unlabeled vertex

6 What is a graph A graph is composed of Vertices (nodes): pixels, actors in videos, genes, ads, etc. Edges: their relations In machine learning, we are interested in predicting some quantity (a class label, or a continuous value) at each unlabeled vertex Broadly speaking, there are two kinds of graphs undirected directed

7 Graph based machine learning for media analytics Oftentimes, media content can be represented using graphs Therefore, challenging inference problems with media content can be answered by learning on graphs

8 Social content model Content network encodes content similarity (videos, audios, etc.) Content generation process Social network encodes peoples social connections Can be used for media genre classification, media recommendation, etc.

9 Graph based machine learning On undirected graphs Optimization based approaches (e.g. energy minimization) Probabilistic models (e.g. random fields) On directed graphs Optimization based approaches (e.g. directed energy minimization) Probabilistic models (e.g. latent Dirichlet allocation, Bayesian networks)

10 Relations How are they related to traditional stats learning (e.g. logistic regression) (Sutton & McCallum, 2007)

11 Graph based machine learning On undirected graphs Optimization based approaches (e.g. energy minimization) Probabilistic models (e.g. random fields) On directed graphs Optimization based approaches (e.g. directed energy minimization) Probabilistic models (e.g. latent Dirichlet allocation, Bayesian networks)

12 Learning on undirected graphs Classification methods We have some labeled data, and want to predict labels for others e.g. manifold regularization Clustering methods We would like to partition data into clusters e.g. spectral clustering

13 Constructing data graphs How to transform a dataset ({x i }, i=1..m) into a graph

14 Affinity matrix A graph is usually represented using an affinity matrix W, where the corresponding entry is 1 if two vertices are connected, and 0 otherwise

15 Graph Laplacians L=D-W, where W is an affinity matrix, D is a diagonal matrix of row sums Discretization of Laplace-Beltrami operator on manifolds, which is the sum of second order derivatives on tangent space (more details later)

16 Function on graph A vector can be used to represent a function over the graph We can encode what we already know or what we want to predict in a label function For example in this graph, a vertex can represent a person, and the function can represent if he is a likely customer f = [ 1, 1, 0, 0, 1, 0 ] T

17 Eigenvectors reviewed

18 Properties of graph Laplacians Symmetric and positive semi-definite Graph Laplacian induces a smoothness term Transposed label function f * Laplacian matrix L * label function f (always non-negative) Smoothness term (f T Lf) measures how much the function f varies with respect to the underlying graph We have labels on some vertices, and want to predict labels on other vertices. A smooth function (small f T Lf) typically predicts well Laplacian eigenvectors with small eigenvalues can be used for data clustering / classification, data set parametrization, image segmentation, etc.

19 Properties of graph Laplacians Symmetric and positive semi-definite Graph Laplacian induces a smoothness term Transposed label function f * Laplacian matrix L * label function f (always non-negative) Smoothness term (f T Lf) measures how much the function f varies with respect to the underlying graph We have labels on some vertices, and want to predict labels on other vertices. A smooth function (small f T Lf) typically predicts well Laplacian eigenvectors with small eigenvalues can be used for data clustering / classification, data set parametrization, image segmentation, etc. Now we are ready to see the algorithms, but let s take a little break to understand things even further

20 Manifolds

21 Manifold perspective of data modeling

22 Why graphs encode underlying data geometry If we consider data as samples from an underlying manifold (which is a fairly weak assumption), and construct the corresponding adjacency graph, then eigenvectors of graph Laplacian approximate eigenfunctions of the Laplace-Beltrami operator of the underlying data manifold (Belkin & Niyogi, 2008)

23 Laplacian eigenvectors understand geometry (Rustamov, 2007)

24 Spectral clustering More information in von Luxburg (2007)

25 Spectral clustering explained Why the eigenvectors of L with small eigenvalues are used as the new representation? The minimizers f i for the following total smoothness term are eigenvectors of L with the smallest eigenvalues

26 Results

27 Laplacian eigenmap Using Laplacian eigenvectors with the smallest eigenvalues as the new representation Can be seen as a non-linear extension of PCA (Belkin & Niyogi, 2003)

28 Results on real data Transform data using Laplacian eigenmap, and use linear regression on the new representation (Belkin & Niyogi, 2004)

29 Manifold regularization A comprehensive regularization framework Through applying the representer theorem in functional analysis, the optimal solution is as follows (Belkin et al., 2006)

30 Results on real data (Belkin et al., 2006)

31 Summary Learning on graphs provides a set of powerful techniques for data analysis and predictive analytics that understand the geometry of underlying data Spectral clustering addresses the limitation with traditional K-means Laplacian eigenmap & manifold regularization learn a label function respecting underlying data geometry, and hence provide benefits over standard methods like PCA and linear regression Lots of other approaches as well will talk about label propagation based on graphs later in this presentation

32 Outline Graph based machine learning Basic structures Algorithms Examples Applications in media analytics Social analysis of videos Content analysis of images

33 Applications in media analytics High-level analysis Social relational inference People to communities Mid-level analysis Event detection Visual features to events Low-level analysis Segmentation Pixels to semantic objects

34 Application 1: social analysis of multimedia data Friends or foes? Acquaintances or strangers? In same or different teams?

35 Social network learning and analysis

36 Social network learning and analysis

37 Social network learning and analysis (Ding & Yilmaz, 2010; 2011)

38 Application areas Social content: given the growing popularity of social media, inferring relations among people is becoming important Visual recognition: social context is shown to help improve recognition results from images (e.g. Wang et al., ECCV 10) Surveillance: social network learning and analysis for surveillance applications (e.g. Yu et al., CVPR 2009) Sociology: necessary step in building intelligent systems for aiding sociological discovery

39 Basic video processing Videos segmented into semantic segments Scenes, or visually coherent sets of shots, for movies and TV shows Shot detection and merging based on key-frame similarity (Rasheed & Shah, 03) Identifying the actors appearing in each segment Using scripts and closed captions for movies Face detection and recognition for other videos

40 Actor appearance matrix

41 Overall process Social Relations video-level A number [-1,+1] for each scene: positive if actors in a scene are likely in the same community, negative if otherwise Grouping cues Estimate the likely events in a scene Event estimates scene-level Dynamic systems represent scenes Scene models Feature observations frame-level

42 Key steps

43 Visual features Generic optical flow orientation histogram

44 Auditory features

45 Using visual concepts Visual concept detection provides useful semantic features for inferring social relations Using Columbia s 374 SVM concept detectors on color/texture/edge features, a concept score vector is generated for each scene

46 Evidence synthesis by Gaussian processes

47 Learned social affinity Learned social network is represented by affinity matrix K

48 Learned social networks

49 RACOM dataset Ten example movies: (1) G.I. Joe: The Rise of Cobra (2009); (2) Harry Potter and the Half-Blood Prince (2009); (3) Public Enemies (2009); (4) Troy (2004); (5) Braveheart (1995); (6) Year One (2009); (7) Coraline (2009); (8) True Lies (1994); (9) The Chronicles of Narnia: The Lion, the Witch and the Wardrobe (2005); (10) The Lord of the Rings: The Return of the King (2003).

50 Analyzing social networks We extend the max-min modularity principle such that it works with the learned social networks, in order to detect the two communities for each movie We also identify the leaders of each community, which interestingly, correspond to the hero/villain most of the time

51 Max-min modularity

52 Visual maps

53 Quantitative evaluation

54 Detected social communities

55 Youtube dataset 10 videos for soccer games; 10 videos for demonstration; The goal here is to predict a grouping cue for each scene. We evaluate against ground truth labeling

56 Youtube results Event categories are considered and labeled in a middle step Soccer: (chasing, confronting, hugging, others) Demonstration: (marching, confronting, public speaking, others) Precision (+) for within-community instances and Precision (-) for acrosscommunity instances are reported separately

57 Application 2: image content analysis Interactive whole-object segmentation Inputs: an image & labeled pixels (seeds) for objects/background Outputs: labels for all other pixels (Ding & Yilmaz, 2010)

58 Overview To segment whole objects from images given user-supplied seeds Different from unsupervised segmentation from a single image, which typically generates homogeneous regions The challenge is to segment objects using a small number of seeds In addressing this problem, we have proposed Probabilistic hypergraph image model (PHIM) Automatic label set augmentation using boundary features Multiple view learning synthesizing features

59 Graphs vs. hypergraphs Graph based approaches have been popular for interactive segmentation Graph cut (Rother et al., 2004) Random walk (Grady, 2006) Hypergraphs vs. graphs for images Higher order relations among pixels that tend to form a segment are encoded as hyperedges, which are collections of vertices Model long-range dependencies among the entities (known and unknown labels)

60 Our model: PHIM We propose to use probabilistic hypergraph image model (PHIM) The relation between a hyperedge and a vertex is probabilistic, based on probabilities learned from image appearance characteristics Vertices: superpixels Hyperedges: pair-wise + higher-order (generated by meanshift weak segmentation with varying color bandwidths)

61 Our model: PHIM (cont d) Feature vector Fs of a superpixel s contains average LUV color values Incidences: kernel density estimator taking superpixel features as the input Hyperedge weights: inhomogeneous hyperedges are down-weighted Reduces to standard graph based edge weights when the hyperedge is of size 2

62 Laplacians on PHIM Normalized Laplacians on PHIM: induced quadratic form measures the smoothness of a function with respect to the underlying edge system We use probabilistic incidences (hv,e) in defining Laplacians on PHIM Notations f: vector of function values on vertices (+1 for object; -1 for background) H: probabilistic incidence matrix; W: hyperedge weight matrix De: hyperedge degree matrix; Dv: vertex degree matrix

63 How to do segmentation Constrained smoothness minimization Essentially an interpolation, as we have confidence in user-supplied segment labels This interpolation can also be solved in an iterative manner using the natural random walk

64 Dataset GrabCut dataset of 50 images (Rother et al., 2004) Seed pixels are provided in the form of trimaps Ground-truth segmentations are supplied

65 Results on segmentation Error rates averaged over the GrabCut dataset of 50 images PHIM performs better than a standard graph Our error rate 5.33% is much better than 7.9% achieved in (Blake et al., 2006), and is comparable to state-of-the-art results from pixel-level optimization

66 Comparative results

67 The end Thanks! References Ulrike von Luxburg, A Tutorial on Spectral Clustering, 2007 Charles Sutton and Andrew McCallum, An Introduction to Conditional Random Fields for Relational Learning, 2007 Raif Rustamov, Laplace-Beltrami Eigenfunctions for Deformation Invariant Shape Representation, 2007 Mikhail Belkin and Partha Niyogi, Laplacian Eigenmaps for Dimensionality Reduction and Data Representation, 2003 Mikhail Belkin and Partha Niyogi, Semi-Supervised Learning on Riemannian Manifolds, 2004 Mikhail Belkin, Partha Niyogi and Vikas Sindwani, Manifold Regularization: A Geometric Framework for Learning from Labeled and Unlabeled Examples, 2006 Mikhail Belkin and Partha Niyogi, Convergence of Laplacian Eigenmaps, 2008 Lei Ding and Alper Yilmaz, Learning Relations Among Movie Characters: A Social Network Perspective, 2010 Lei Ding and Alper Yilmaz, Interactive Image Segmentation Using Probabilistic Hypergraphs, 2010 Lei Ding and Alper Yilmaz, Inferring Social Relations from Visual Concepts, 2011