MACHINE LEARNING: CLUSTERING, AND CLASSIFICATION. Steve Tjoa June 25, 2014
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1 MACHINE LEARNING: CLUSTERING, AND CLASSIFICATION Steve Tjoa June 25, 2014
2 Review from Day 2
3 Supervised vs. Unsupervised Unsupervised - clustering Supervised binary classifiers (2 classes) Multiclass is derived from binary
4 Clustering Unsupervised learning find pockets of data to group together! Statistical analysis techniques
5 Clustering K = # of clusters! Choosing the number of clusters note that choosing the best number of clusters according to minimizing total squared distance will always result in same # of clusters as data points.
6 Clustering The basic goal of clustering is to divide the data into groups such that the points within a group are close to each other, but far from items in other groups.! Hard clustering each point is assigned to one and only one cluster.
7 K-Means procedure for clustering unlabelled data; requires a pre-specified number of clusters; minimizes within-cluster variance Guaranteed to converge (eventually) Clustering solution is dependent on the initialization
8 Demo YouTube demo: Bishma Stornelli
9 K-Means Initialization methods:! Choose random data points as cluster centers Randomly assign data points to K clusters and compute means as initial centers Choose data points with extreme values Find the mean for the whole data set then perturb into k means Find ground-truth for data
10 ANALYSIS AND DECISION MAKING: GMMS
11 Mixture Models (GMM) K-means = hard clusters. GMM = soft clusters.
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13 Mixture Models (GMM) GMM is good because: 1. Can approximate any pdf with enough components 2. EM makes it easy to find components parameters EM - the means and variances adapt to fit the data as well as possible 3. Compresses data considerably! Can make softer decisions (decide further downstream given additional information)
14 GMM Parameters Input Number of components (Gaussians) e.g., 3 Mixture coefficients (sum = 1) e.g., [ ] Priors or Prior probabilities Priors are the original probability that each point came from a given mixture. A prior is often the purely subjective assessment of an experienced expert. Initialized centers, means, variances. (optional)! Output Component centers/means, variances, and mixture coeff. Posterior probabilities Posterior probabilities are the responsibilities which the Gaussian components have for each of the data points. Query Obtain similarity via Likelihood
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16 !! From Netlab (p82-83)
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19 GMM Pooled covariance" - using a single covariance to describe all clusters (saves on parameter computation)
20 GMM: Likelihood 1. Evaluate the probability of that mixture modeling your point. likelihoodgm1 = gmmprob(gm1,testing_features) likelihoodgm2 = gmmprob(gm2,testing_features); loglikelihood = log(likelihoodkick./ likelihoodsnare )! Log-function is order-preserving maximizing a function vs. maximizing its log
21 Minimization Problems >Demgmm1! EM is gradient-based it does not find the global maximum in the general case, unless properly initialized in the general region of interest.! Error wants to be inf, which occurs when Gaussian is fit for each data point. (mean = data point and variance = 0)! There are often a large number of local minima which correspond to poor models. Solution is to build models from many different initialization
22 GMM Application: State-of-the-art speech recognition systems estimate up to 30,000 separate GMMs, each with about 32 components. This means that these systems can have up to a million Gaussian components!! All the parameters are estimated from (a lot of) data by the EM algorithm.! Application: Speaker Recognition
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24 Genre Because feature vectors are computed from short segments of audio, an entire song induces a cloud of points in feature space.! The cloud can be thought of as samples from a distribution that characterizes the song, and we can model that distribution using statistical techniques. Extending this idea, we can conceive of a distribution in feature space that characterizes the entire repertoire of each artist.! A. Berenzweig, B. Logan, D. Ellis, and B. Whitman. A large-scale evalutation of acoustic and subjective music similarity measures. In Proceedings of 4th International Symposium on Music Information Retrieval,
25 From ISMIR 2007 Music Recommender Tutorial (Lamere & Celma)
26 How? Version 1 - One feature vector per song High-level features extracted from data Timbral (MFCCs, etc), Rhythmic content (beat histogram, autocor, tempos), Pitch info Sampling of the frames in the song Statistics of features extracted from a piece (includes means, weights, etc) Representative of MFCC spectral shape Could further use Anchor space where classifiers are training to represent musically meaningful classifiers. (Euclidean distance between anchor space)! Version 2 - Cloud of points Extract audio every N frames K-Means or GMM representing a cloud of points for song Clusters: mean, covariance and weight of each cluster = signature for song/artist/genre
27 Music Recommendation Cloud of points from frames of song High-level features extracted from data Classifier: Weighted attribute nearest neighbors or fast distance measures. k-means or GMM used to create clusters. The mean, covariance and weight of each cluster = signature for the song.! Compare distance between other songs (signature) using various techniques to measure distance between probability distributions. (Most similar = closest distance)
28 From ISMIR 2007 Music Recommender Tutorial (Lamere & Celma)
29 SUPPORT VECTOR MACHINES (SVM)
30 From :
31 From :
32 SVM Hyperplane separates the data from the two classes with a maximum margin. Support Vectors - are those data points that the margin pushes up against SVM training is guaranteed to find the global minimum of the cost function. Less experience needed - fewer parameters to tune!!
33 SVM with polynomial kernel visualization by Udi Aharoni v=3licbrzprza
34 feature 2 feature 1
35
36 SVM Parameters What effect do the parameters of an radial-basis-function SVM have on the separating the two data sets?! RBF kernel parameters: gamma = degree of curviness of the hyperplane / complexity of the contour C = allowance for points to overlap into each other s class
37 RBF Parameters: C and gamma Grid search using cross-validation to find the best one. Coarse then fine grid search. e.g., 2-5, 2-3, 2+15, gamma = 2-15, 2-13, 2+3 Why grid search Psychological (If you have time for brute force why chance it on approximations or heuristics) Since there are only 2 params, grid search isn t all the different from advanced estimation techniques Easily parallelized (C and gamma are
38 Practical Guide to SVM: The Lab Feature selection? Scale feature data Save scaling stats so we can scale the test data to be in the same range Feature format Class labels {1,-1} or {0,1} Kernels (linear, polynomial, RBF, sigmoid) Find best C and gamma (cross-validation) Train with entire training set Test with validation or test set
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