Noise Subspace Fuzzy C-means Clustering for Robust Speech Re(3)

Abstract. In this paper a fuzzy C-means (FCM) based approach for speech/non-speech discrimination is developed to build an effective voice activity detection (VAD) algorithm. The proposed VAD method is based on a soft-decision clustering approach built ove

3FCM Clustering over the Observation VectorsCM clustering is a method for nding clusters and cluster centers in a set of unlabeled data. The number of cluster centers (prototypes) C is a priori known and the CM iteratively moves the centers to minimize the total within cluster variance. Given an initial set of centers the CM algorithm alternates two steps: a) for each cluster we identify the subset of training points (its cluster) that is closer to it than any other center; b) the means of each feature for the data points in each cluster are computed, and this mean vector becomes the new center for that cluster. This previous clustering technique is referred to as hard or crisp clustering, which means that each individual is assigned to only one cluster. For FCM clustering, this restriction is relaxed, and the object can belong to all of the clusters with a certain degree of membership. This is particularly useful when the boundaries among the clusters are not well separated and ambiguous. 3.1 Noise ModelingFCM is one of the most popular fuzzy clustering algorithms. FCM can be regarded as a generalization of ISODATA [13] and was realized by Bezdek [14]. In our algorithm, the fuzzy approach is applied to a set of N initial pause frames (energies) in order to characterize the noise space. From this energy noise space we obtain a set of clusters, namely noise prototypes 3 . The process is as the following: each observation vector (E from equation 3) is uniquely labeled, by the integer i ∈ {1, . . . , N }, and assigned to a prespeci ed number of prototypes C < N , labeled by an integer c ∈ {1, . . . , C}. The dissimilarity measure between observation vectors is the squared Euclidean distance:K 1d(Ei , Ej ) =k=0(E(k, i) E(k, j))2 = ||Ei Ej ||2(4)FCM attempts to nd a partition (fuzzy prototypes) for a set of data points Ei ∈ RK , i = 1, . . . , N while minimizing the cost functionC NJ(U, M) =i=1 j=1(uij )m Dij(5)where U = [uij ]C×N is the fuzzy partition matrix, uij ∈ (0, 1) is the membership coe cient of the j-th individual in the i-th prototype; M = [m1 , . . . , mC ] denotes the cluster prototype (center) matrix, m ∈ [1, ∞) is the fuzzi cation parameter (set to 2) and Dij = d(Ej , mi ) is the distance measure between Ej and mi .3The word cluster is assigned to di erent classes of labeled data, that is K is xed to 2 (noise and speech frames)