Abstract
Dimensionality reduction is one of the central problems in machine learning and pattern recognition, which aims to develop a compact representation for complex data from high-dimensional observations. Here, we apply a nonlinear manifold learning algorithm, called local tangent space alignment (LTSA) algorithm, to high-dimensional acoustic observations and achieve nonlinear dimensionality reduction for the acoustic field measured by a linear senor array. By dimensionality reduction, the underlying physical degrees of freedom of acoustic field, such as the variations of sound source location and sound speed profiles, can be discovered. Two simulations are presented to verify the validity of the approach.
Highlights
With the development of sensor technique and materials science, the cost of acoustic sensors becomes constantly decreasing
In order to overcome the weaknesses of Isometric feature mapping (ISOMAP), some local approaches, such as locally linear embedding (LLE)[7] and Laplacian eigenmaps (LE)[8], have been presented
It turns out that local tangent space alignment (LTSA) algorithm can discover the intrinsically physical degrees of freedom of acoustic fields, such as the variations of sound source location and sound speed profile, which underlies in high-dimensional observation space
Summary
With the development of sensor technique and materials science, the cost of acoustic sensors becomes constantly decreasing. It turns out that LTSA algorithm can discover the intrinsically physical degrees of freedom of acoustic fields, such as the variations of sound source location and sound speed profile, which underlies in high-dimensional observation space. Let. xi ≡ p( z1;γ i ), p( z2;γ i ), , p( zn;γ i ) T , i = 1,2, ,m (1) To preserve as much of the local geometric where p( zj;γ i ), j =1,2, ,n denotes the acoustic field recorded by the jth sensor of vertical linear array, zj denotes the depth of the jth sensor and γi ∈Rd properties in the low-dimensional feature space as possible, we intend to find Yi and Li to minimize the reconstruction errors ε(ji) , i.e. represents the physical parameter vector that controls the ith observed acoustic fields, which may consist of sound.
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