Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F18/00—Pattern recognition
  • G06F18/20—Analysing
  • G06F18/29—Graphical models, e.g. Bayesian networks

Definitions

• the present invention relates to computer mediated pattern detection. More particularly, the present invention relates to improved Bayesian networks for classifying data.
• Bayesian networks such a represented by the hidden Markov model (HMM) and coupled Hidden Markov (CHMM) models have long been used to model data for the purposes of pattern recognition.
• HMM hidden Markov model
• CHMM Hidden Markov
• Any discrete time and space dynamical system governed by a such a Bayesian network emits a sequence of observable outputs with one output (observation) for each state in a trajectory of such states. From the observable sequence of outputs, the most likely dynamical system can be calculated. The result is a model for the underlying process. Alternatively, given a sequence of outputs, the most likely sequence of states can be determined.
• HMMs have been widely used in speech recognition to model phonemes, words, or even phrases
• two dimensional P ⁇ MMs have been used for image processing tasks.
• One of the important characteristics of a HMM is its ability to cope with variations in feature space, allowing data modeling with variations along different dimensions. Coupled hidden Markov models can be similarly employed, since they correspond to a generalization of a HMM.
• a CHMM may comprise a collection of HMMs, each of which corresponds to a data channel.
• Figure 1 schematically illustrates a data classification system
• Figure 2 generically illustrates an embedded hidden Markov model-coupled hidden Markov model (HMM- CHMM) structure
• Figure 3 is a flow diagram illustrating training of an embedded HMM-CHMM
• Figure 4 generically illustrates an embedded coupled hidden Markov model- hidden Markov model (CHMM- HMM) structure.
• Figure 1 generally illustrates a system 10 for data analysis of a data set 12 using an embedded Bayesian network that includes a hidden Markov model (HMM) and a coupled hidden Markov model (CHMM).
• HMM hidden Markov model
• CHMM coupled hidden Markov model
• the data set 12 can include static or video imagery 14 containing objects to be identified or classified, including but not limited to textual characters, ideographs, symbols, fingerprints, or even facial imagery 15.
• non-image data sets such as bioinformatic databases 16 containing, for example, gene or protein sequences, DNA microarray data, sequence data, phylogenetic information, promoter region information; or textual, linguistic, or speech analysis data suitable for machine learning/ identification 18 can be used.
• bioinformatic databases 16 containing, for example, gene or protein sequences, DNA microarray data, sequence data, phylogenetic information, promoter region information; or textual, linguistic, or speech analysis data suitable for machine learning/ identification 18 can be used.
• the same data set can be optionally used both to train and classify data with the appropriate training module 20 and classification module 22.
• the processing procedure for system 10 maybe performed by a properly programmed general-purpose computer alone or in connection with a special purpose computer. Such processing may be performed by a single platform or by a distributed processing platform. In addition, such processing and functionality can be implemented in the form of special purpose hardware, custom application specific integrated circuits (ASICs), configurable FPGA circuits, or in the form of software or firmware being run by a general- purpose or network processor. Data handled in such processing or created as a result of such processing can be stored in any memory as is conventional in the art. By way of example, such data may be stored in a temporary memory, such as in the RAM of a given computer system or subsystem.
• a computer- readable media may comprise any form of data storage mechanism, including such existing memory technologies as well as hardware or circuit representations of such structures and of such data.
• HMM-CHMM embedded hidden Markov model-coupled hidden Markov model
• HMM-CHMM is a hierarchical statistical model that includes a HMM parent layer 32 (collectively formed from nodes 33) and a CHMM child layer 34 (collectively formed from nodes 35).
• the child layer 34 associates one CHMM node 35 to each node 33 in the parent layer 32, and the parameters of the individual CHMMs remain independent from each other. Instead, the parameters of each child layer CHMM depend upon the state of the connected parent node 33.
• the HMM in the parent layer 32 is associated with at least one dimension
• the CHMM child layers are associated with data in an orthogonal dimension with respect to the parent layer.
• the elements of an embedded HMM-CHMM have:an initial super state probability ⁇ 00 and a super state transition probability from super state j to super state i , a 0 ⁇ , where super state refers to the state of the parent layer 32 HMM node 33.
• observation sequences are used to form observation vectors later used in training and classifying.
• the observation sequence for a two-dimensional image may be formed from image blocks of size L x x L that are extracted by scanning the image from left- to- right and top- to- bottom.
• Adjacent image blocks ma be designed to have an overlap by P y rows in the vertical direction and P x columns in the horizontal direction.
• a six DCT coefficients (a 3X2 low- frequency array) maybe employed to create the overlap.
• the resulting array of observation vectors may correspond to size of T 0 x T x , where T 0 and TJ are the number of observation vectors extracted along the height (H) and the width (W) of the image, respectively.
• r o and TJ maybe computed accordingly as:
• Consecutive horizontal and vertical observation vectors may also be grouped together to form observation blocks. This may be used as a way to consolidate local observations and at the same time to reduce the total amount of observations. In practice, this data grouping serves application needs and improve recognition efficiency.
• To compute the number of observation blocks denote the number of observation blocks in the vertical and horizontal direction be T° and T° , respectively. Then,
• a modified Niterbi algorithm for the HMM-CHMM is preferred.
• Application of this modified Niterbi algorithm determines the optimal state and super state segmentation of the observation sequence.
• FIG. 3 is a flow diagram 40 illustrating training of an embedded HMM-CHMM based on the Niterbi algorithm, according to embodiments of the present invention.
• observation vectors are first extracted from the training data set and organized in observation blocks (module 42). These observation blocks are uniformly segmented (module 44), replaced by an optimal state segmentation algorithm (module 46), have their model parameters estimated (module 48), and observation likelihood determined (module 50).
• the training ma be iterative, with each training data set used individually and iteratively to update model parameters until the observation likelihood computed is smaller than a specified threshold.
• the training data set ma be segmented along a first dimension according to the number of super states, into a plurality of uniform segments each of which corresponding to a super state. Based on the uniform segmentation at the super layer, the observation vectors within each uniform segment may then be uniformly segmented according to the number of channels and number of states of each child CHMM.
• each state may be initialized before the training takes place. For example, if Gaussian mixture model is adopted for each state, Gaussian parameters for each of the mixture component may need to be initialized. Different approaches may be employed to achieve the initialization of model parameters. For example, one embodiment ma be implemented where the observation sequence assigned to each channel c and state j, and super state k and super channel s may be
• the original uniform segmentation is updated based on the optimal state segmentation using the Niterbi algorithm or other suitable algorithms.
• particular relevant parameters to be updated ma be determined prior to the update operation.
• the selection of a Gaussian mixture component for each state j channel c and super state kis also required.
• One exemplary criterion to make the selection may correspond to
• N( VO t M Q ,t ⁇ ,c ; 7 j k ,Xm 7 U j t :,m c ) is the highest.
• the parameters are then estimated using, for example, an extension of the segmental
• ? ' may equal to one if a transition from super state 1 to the super state
• channel C of super state K may then be obtained as follows,
• V th training sample a transition from state sequence J to state I in channel c occurs for
• the parameters of the selected Gaussian mixture component may also be accordingly
• the involved Gaussian parameters may include a mean vector t ' j ,m , a covariance matrix Gaussian mixture, and the mixture coefficients
• the updated Gaussian parameters may be obtained according to the following formulations:
• the update of parameters based on a training sample may be carried out iteratively. This may be necessary because the Niterbi algorithm may yield different optimal segmentation during each iteration before convergence. Between two consecutive iterations, if the difference of observation likelihood computed with the Niterbi algorithm is smaller than a specified threshold, the iteration may be terminated.
• the HMM-CHMM corresponds to a complexity of quadratic with respect to the number of states in the model. In addition, HMM-CHMM may be efficiently implemented in a parallel fashion.
• An alternative logical structure that includes an embedded CHMM- HMM (in contrast to an HMM-CHMM) is generically illustrated by Figure 4.
• the CHMM- HMM is a hierarchical statistical model that includes a CHMM parent layer 62 (collectively formed from nodes 63) and a HMM child layer 64 (collectively formed from nodes 65).
• the child layer 64 associates one HMM node 65 to each node 63 in the parent layer 62, and the parameters of the individual HMMs remain independent from each other. Instead, the parameters of each child layer HMM depend upon the state of the connected parent node 63.
• the CHMM in the parent layer 62 is associated with at least one dimension
• the HMM child layers are associated with data in an orthogonal dimension with respect to the parent layer.
• the elements of an embedded CHMM- HMM have: an initial super
• observation sequences are used to form observation vectors later used in training and classifying.
• the observation sequence for a two-dimensional image may be formed from image blocks of size L x x L y that are extracted by scanning the image from left- to- right and top- o- bottom.
• Adjacent image blocks maybe designed to have an overlap by P rows in the vertical direction and P x columns in the horizontal direction.
• a six DCT coefficients (a 3X2 low- frequency array) maybe employed to create the overlap.
• the resulting array of observation vectors may correspond to size of T 0 x T t , where T 0 and 7, are the number of observation vectors extracted along the height (H) and the width (W) of the image, respectively.
• Consecutive horizontal and vertical observation vectors may also be grouped together to form observation blocks. This maybe used as a way to consolidate local observations and at the same time to reduce the total amount of observations. In practice, this data grouping serves application needs and improve recognition efficiency.
• To compute the number of observation blocks denote the number of observation blocks in the vertical and horizontal direction be T 0 ° and T° , respectively. Then,
• any suitable state sequence segmentation can be used, a modified Niterbi algorithm for the HMM-CHMM is preferred.
• Application of this modified Niterbi algorithm determines the optimal state and super state segmentation of the observation sequence. The best super state probability for the observation block , S ) given super state I of super
• sequence ⁇ ,71 c. 5 / may then be computed for each super observation.
• ⁇ 0 (i) arg max i ⁇ 0 , (j)U (j
• Training of an embedded CHMM- HMM based on the Niterbi algorithm is substantially similar to that illustrated with respect to training of a HMM-CHMM as seen in Figure 3.
• observation vectors are first extracted from the training data set and organized in observation blocks. These observation blocks are segmented uniformly and at consecutive iterations through an optimal state segmentation algorithm, have their model parameters estimated and observation likelihood determined.
• the training maybe iterative, with each training data set used individually and iteratively to update model parameters until the observation likelihood computed is smaller than a specified threshold.
• the training data set may be segmented along a first dimension into S super channels.
• training data may further be uniformly segmented, according to the number of super states in each super channel, into a plurality of uniform segments each of which corresponding to a super state. Based on the uniform segmentation at the super layer, the observation vectors within each uniform segment may then be uniformly segmented according to the number of states of each child HMM.
• each state including both super states as well as child states
• the density function of each state may be initialized before the training takes place. For example, if Gaussian mixture model is adopted for each state, Gaussian parameters for each of the mixture component may need to be initialized. Different approaches may be employed to achieve the initialization of model parameters. For example, one embodiment maybe implemented where the observation sequence assigned to state j, super state k and super channel s may be assigned to
• M s j' k clusters using, for example, the K- means algorithm.
• the original uniform segmentation is updated based on the optimal state segmentation using the Viterbi algorithm or other suitable algorithms.
• particular relevant parameters to be updated may be determined prior to the update operation.
• the selection may be carried out accordingly.
• the estimated transition probabilities between embedded states n W' s> j k ⁇ j may then be obtained as follows,
• C7, , S ⁇ K ⁇ l ⁇ l may be one if in the observation block (t 0 , s) a transition from tQ
• the parameters of the selected Gaussian mixture component may also be accordingly
• the involved Gaussian parameters may include a
• the updated Gaussian parameters maybe obtained according to the following formulations:
• tf U V 3 ? » / 5 / may equal to one if the observation CA . is assigned to super state k in super channel s, state j and mixture component m, and zero otherwise.
• the update of parameters based on a training sample may be carried out iteratively This maybe necessary because the Niterbi algorithm may yield different optimal segmentation during each iteration before convergence. Between two consecutive iterations, if the difference of observation likelihood computed with the Niterbi algorithm is smaller than a specified threshold, the iteration may be terminated.
• the CHMM- HMM corresponds to a complexity of quadratic with respect to the number of states in the model. In addition, CHMM- HMM may be efficiently implemented in a parallel fashion.

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