# Animal Sound Classification Using Dissimilarity Spaces

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*Applied Sciences*: Invited Papers in Computing and Artificial Intelligence Section)

## Abstract

**:**

## 1. Introduction

## 2. Proposed System

Algorithm 1. Training phase |

Input: Training images (imgsTrain), training labels (labelTrain), number of training iterations(trainIterations), batch size (trainBatchSize), number of centroids (k), and clustering technique (type). |

Output: Trained SNN (tSNN), set of centroids (C), and trained SVM (svm). |

1: tSNN ← trainSiamese(imgsTrain, labelTrain, trainIterations, trainBatchSize) |

2: p ← Clustering(imgsTrain, labelTrain, k, type) |

3: F ← getDissSpaceProjection(imgsTrain, P, tSNN) |

4: tSVM ← trainSvm(labelTrain, F) |

Algorithm 2. Testing phase |

Input: Test images (imgsTest), trained SNN (tSNN), Set of centroids (C), Trained SVM (tSVM). |

Output: Actual test labels (labelTest). |

1: F ← getDissSpaceProjection (imgsTest, P, tSNN) |

2: labelTest ← predictSvm (F, tSVM) |

#### 2.1. Siamese Neural Network Training

Algorithm 3. Siamese training pseudocode |

Input: Training image (trainImgs), training labels (trainLabels), batch size (batchSize), and iterations (numberO f Iterations). |

Output: Trained SNN (tSNN). |

1: function TRAINSVM |

2: subnet←NETWORK([inputLayer,..., FullyConnectedLayer]) |

3: f cWeights←randomWeights |

4: for iteration from 1 to numberO f Iterations do |

5: X1, X2, pairLabels← getBatch (trainImgs, trainLabels, batchSize) |

6: gradients, loss← Evaluate(subnet, X1, X2, pairLabels) |

7: Update(subnet, gradients) |

8: Update(f cWeights, gradients) |

9: end for |

10: return tSNN←subnet, f cWeights |

11: end function |

Note: if SNN fails to converge on the training set, the training phase is repeated. |

#### 2.2. Prototype Selection

Algorithm 4. Clustering pseudocode |

Input: Training images (imgsTrain), training labels (labelTrain), number of clusters (k), and clustering technique (type). |

Output: Centroids P. |

1: function Clustering |

2: numClasses←number of classes from labelTrain |

3: kc←k/numClasses |

4: for i from 1 to numClasses do |

5: images←images of the class i from imgsTrain |

6: switch type do |

7: case “k-means” P_{i} ← KMeans(imgs,kc) |

8: case “k-medoids” P_{i} ← KMedoids (imgs,kc) |

9: case “hierarchical” P_{i} ← Hierarchical (imgs,kc) |

10: case “spectral” P_{i} ← Spectral (imgs,kc) |

11: P←P ∪P_{i} |

12: end for |

13: return P |

14: end function |

#### 2.3. Projection in the Dissimilarity Space

Algorithm 5. Projection in the Dissimilarity space pseudocode |

Input: Images (imgs), Centroids (P), number of centroids (k), and trained SNN (tSNN). |

Output: Feature vectors (F). |

1: function getDissSpaceProjection |

2: for j from 1 to SIZE(imgs) do |

3: X←imgs[j] |

4: F[j]← predictSiamese (tSNN, X, P) |

5: end for |

6: return F |

7: end function |

#### 2.4. Classification by SVM

#### 2.5. Heterogeneous Auto-Similarities of Characteristics (HASC)

## 3. Siamese Neural Network (SNN)

#### 3.1. The Two Identical Twin Subnetworks

#### 3.2. Subtract Block, FC Layer, and Sigmoid Function

## 4. Clustering

#### 4.1. K-Means

- Randomly select a set of centroids from among the data points.
- For each data point x remaining in the training set, compute the distance d(x) between it and the nearest centroid.
- Recalculate new centroids via a weighted probability distribution.
- Repeat Steps 2 and 3 until convergence.

#### 4.2. K-Medoids

- Step one is a build-step where each k cluster is associated with a potential medoid. There are many ways to select the first medoid; the standard MATLAB’s implementation does this employing the k-means++ heuristic.
- Step two is a swap-step where each point in a cluster is tested as a potential medoid by checking whether the sum of the within-cluster distances is smaller when using that point as the medoid. Every point is then assigned to the cluster with the closest medoid.
- The last step repeats previous steps until convergence.

#### 4.3. Spectral

- The similarity matrix M, whose cell ${m}_{ij}$ is the similarity value of two patterns (i.e., two spectrograms ${s}_{i}$, ${s}_{j}$);
- The degree matrix D, which is a diagonal matrix that is obtained by summing the rows of M:$${D}_{g}\left(i,i\right)={\sum}_{j}{m}_{i,j};$$
- The Laplacian matrix L, which is defined as$$L={D}_{g}-M.$$

- Define a local neighborhood for each data point in the dataset (there are many ways to define a neighborhood; the nearest-neighbor method is the default setting in the MATLAB implementation of spectral clustering). Then compute the local similarity matrix of each pattern in the neighborhood.
- Calculate the Laplacian matrix $L$.
- Create a matrix $V$ containing columns ${v}_{1}$, …, ${v}_{k}$, where the columns are the $k$ eigenvectors, i.e., the spectrums (hence the name), corresponding to the $k$ smallest eigenvalues of L.
- Perform k-means or k-medoids clustering by treating each row of V as a datapoint.
- Cluster the original pattern according to the assignments of their corresponding rows.

#### 4.4. Hierarchical Clustering

- Agglomerative, where each pattern corresponds to a cluster. A strategy to merge couples of clusters is defined as moving up the hierarchy: each cluster in the next level is the fusion of two clusters from the previous level.
- Divisive, where a single cluster contains all patterns in the first level, then a splitting strategy is defined to halve clusters by moving down the hierarchy.

- Using a distance metric, find the similarity or dissimilarity between every pair of data points in the dataset;
- Aggregate data points into a binary hierarchical cluster tree by fusing pairs of clusters according to their distance;
- Establish the level of the tree where it is cut into k clusters.

## 5. Experimental Results

- BIRDz, which functioned as a control and a real-world audio dataset in [46], a ten-run testing protocol is used; we have used the same split used by the authors of the dataset. The real-world tracks were collected from the Xeno-canto Archive (http://www.xeno-canto.org/). BIRDz includes a total of 2762 bird acoustic samples from 11 North American bird species plus 339 “unknown” samples that include noise and unknown species’ vocalizations. The observations are composed of five different spectrograms: 1) constant frequency, 2) frequency modulated whistles, 3) broadband pulses, (4) broadband with varying frequency components, and 5) strong harmonics. The dataset is balanced: the size of all the “bird” classes varies between 246 and 259; only the class “other” is a little larger.
- CAT, [37,47] is a dataset that contains ten balanced classes of approximately 300 samples per class for a total of 2962 samples. The testing protocol is a 10-fold cross-validation. The ten classes represent the following cat vocalizations: (1) Resting, (2) Warning, (3) Angry, (4) Defense, (5) Fighting, (6)·Happy, (7) Hunting mind, (8) Mating, (9) Mother call, and (10) Paining. The average duration of each sample is approximately 4 s. Samples were garnered from such online resources as Kaggle, Youtube, and Flickr.

- The best way for building an ensemble of Siamese networks is to combine different network topologies;
- The proposed F_NN ensemble improves previous methods based on Siamese networks (cf. OLD in Table 6);
- F_NN obtains a performance that is similar to eCNN on BIRD but lower than eCNN on CAT;
- The best performance in both datasets is gained by sum rule between eCNN and F_NN (i.e., the fusion among CNNs and the Siamese networks).

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Siamese Network 1 | ||||

Layers | Activations | Learnable | Filter Size | Num. of Filters |

Input Layer | 224 × 224 | |||

2D Convolution | 215 × 215 × 64 | 6464 | 10 × 10 | 64 |

ReLU | 215 × 215 × 64 | 0 | ||

Max Pooling | 107 × 107 × 64 | 0 | 2 × 2 | |

2D Convolution | 101 × 101 × 128 | 401,536 | 7 × 7 | 128 |

ReLU | 101 × 101 × 128 | 0 | ||

Max Pooling | 50 × 50 × 128 | 0 | 2 × 2 | |

2D Convolution | 47 × 47 × 128 | 262,272 | 4 × 4 | 128 |

ReLU | 47 × 47 × 128 | 0 | ||

Max Pooling | 23 × 23 × 128 | 0 | 2 × 2 | |

2D Convolution | 19 × 19 × 64 | 204,864 | 5 × 5 | 64 |

ReLU | 19 × 19 × 64 | 0 | ||

Fully Connected | 4096 | 94,638,080 | ||

Siamese Network 2 | ||||

Layers | Activations | Learnable | Filter Size | Num. of Filters |

Input Layer | 224 × 224 | 0 | ||

2D Convolution | 220 × 220 × 64 | 1664 | 5 × 5 | 64 |

LeakyReLU | 220 × 220 × 64 | 0 | ||

2D Convolution | 216 × 216 × 64 | 102,464 | 5 × 5 | 64 |

LeakyReLU | 216 × 216 × 64 | 0 | ||

Max Pooling | 108 × 108 × 64 | 0 | 2 × 2 | |

2D Convolution | 106 × 106 × 128 | 73,856 | 3 × 3 | 128 |

LeakyReLU | 106 × 106 × 128 | 0 | ||

2D Convolution | 104 × 104 × 128 | 147,584 | 3 × 3 | 128 |

LeakyReLU | 104 × 104 × 128 | 0 | ||

Max Pooling | 52 × 52 × 128 | 0 | 2 × 2 | |

2D Convolution | 49 × 49 × 128 | 262,272 | 4 × 4 | 128 |

LeakyReLU | 49 × 49 × 128 | 0 | ||

Max Pooling | 24 × 24 × 128 | 0 | 2 × 2 | |

2D Convolution | 20 × 20 × 64 | 204,864 | 5 × 5 | 64 |

LeakyReLU | 20 × 20 × 64 | 0 | 5 × 5 | |

Fully Connected | 2048 | 52,430,848 | ||

Siamese Network 3 | ||||

Layers | Activations | Learnable | Filter Size | Num. Filters |

Input Layer | 224 × 224 | |||

2D Convolution | 55 × 55 × 128 | 6400 | 7 × 7 | 128 |

Max Pooling | 27 × 27 × 128 | 0 | 2 × 2 | |

2D Convolution | 23 × 23 × 256 | 819,456 | 5 × 5 | 256 |

ReLU | 23 × 23 × 256 | 0 | ||

2D Convolution | 19 × 19 × 128 | 819,328 | 5 × 5 | 128 |

Max Pooling | 9 × 9 × 128 | 0 | 2 × 2 | |

2D Convolution | 7 × 7 × 64 | 73,792 | 3 × 3 | 64 |

ReLU | 7 × 7 × 64 | 0 | ||

Max Pooling | 3 × 3 × 64 | 0 | 2 × 2 | |

Fully Connected | 4096 | 2,363,392 | ||

Siamese Network 4 | ||||

Layers | Activations | Learnable | Filter Size | Num. of Filters |

Input Layer | 224×224 | |||

2D Convolution | 218 × 218 × 128 | 6400 | 7 × 7 | 128 |

Max Pooling | 54 × 54 × 128 | 0 | 4 × 4 | |

ReLU | 54 × 54 × 128 | 0 | ||

2D Convolution | 50 × 50 × 256 | 819,456 | 5 × 5 | 256 |

ReLU | 50 × 50 × 256 | 0 | ||

2D Convolution | 48 × 48 × 64 | 147,520 | 3 × 3 | 64 |

Max Pooling | 24 × 24 × 64 | 0 | 2 × 2 | |

2D Convolution | 22 × 22 × 128 | 73,856 | 3 × 3 | 128 |

ReLU | 22 × 22 × 128 | 0 | ||

2D Convolution | 18 × 18 × 64 | 204,864 | 5 × 5 | 64 |

Fully Connected | 4096 | 84,938,752 |

Name | Input Image | Network Topology | Clustering Method | Clustering Type | #Prototypes | #Classifiers | CAT | BIRD |
---|---|---|---|---|---|---|---|---|

Sup-1 | Sp | NN1 | K-means | S | 15, 30, 45, 60 | 4 | 78.64 ± 1.2 | 92.46 ± 0.71 |

Sup-2 | Sp | NN2 | K-means | S | 15, 30, 45, 60 | 4 | 76.95 ± 1.3 | 92.74 ± 0.82 |

UnS-1 | Sp | NN1 | K-means | U | 15, 30, 45, 60 | 4 | 81.69 ± 1.0 | 92.73 ± 0.95 |

UnS-2 | Sp | NN2 | K-means | U | 15, 30, 45, 60 | 4 | 75.25 ± 1.4 | 92.80 ± 0.78 |

HSup-1 | HASC | NN1 | K-means | S | 15, 30, 45, 60 | 4 | 78.64 ± 1.2 | 94.52 ± 0.65 |

HSup-2 | HASC | NN2 | K-means | S | 15, 30, 45, 60 | 4 | 81.69 ± 0.9 | 93.22 ± 0.82 |

HUnS-1 | HASC | NN1 | K-means | U | 15, 30, 45, 60 | 4 | 79.32 ± 1.1 | 94.53 ± 0.68 |

HUnS-2 | HASC | NN2 | K-means | U | 15, 30, 45, 60 | 4 | 81.36 ± 1.3 | 92.97 ± 0.72 |

FSp-1 | Sp | NN1 | K-means | S,U | 15, 30, 45, 60 | 8 | 81.02 ± 1.0 | 92.79 ± 0.85 |

FSp-2 | Sp | NN2 | K-means | S,U | 15, 30, 45, 60 | 8 | 76.95 ± 1.2 | 92.77 ± 0.76 |

FA-1 | Sp,HASC | NN1 | K-means | S,U | 15, 30, 45, 60 | 16 | 82.37 ± 0.9 | 94.50 ± 0.65 |

FA2 | Sp,HASC | NN2 | K-means | S,U | 15, 30, 45, 60 | 16 | 83.73 ± 0.9 | 94.11 ± 0.70 |

FA1_2 | Sp,HASC | NN1 + NN2 | K-means | S,U | 15, 30, 45, 60 | 32 | 84.41 ± 0.9 | 94.37 ± 0.62 |

**Table 3.**Performance obtained considering different clustering algorithms: accuracy ± standard deviation.

Name | Input Image | Network Topology | Clustering Method | Clustering Type | #Prototypes | #Classifiers | CAT | BIRD |
---|---|---|---|---|---|---|---|---|

HASC | NN2 | K-means | S | 15, 30, 45, 60 | 4 | 81.69 ± 0.9 | 93.22 ± 0.82 | |

HASC | NN2 | K-Med | S | 15, 30, 45, 60 | 4 | 81.02 ± 1.0 | 92.85 ± 0.85 | |

HASC | NN2 | Hier | S | 15, 30, 45, 60 | 4 | 81.69 ± 0.9 | 93.01 ± 0.87 | |

HASC | NN2 | Spect | S | 15, 30, 45, 60 | 4 | 80.00 ± 1.1 | 93.13 ± 0.79 | |

F_Clu | HASC | NN2 | All | S | 15, 30, 45, 60 | 16 | 82.03 ± 0.9 | 93.37 ± 0.75 |

**Table 4.**Performance obtained considering different network topologies: accuracy ± standard deviation.

Name | Input Image | Network Topology | Clustering Method | Clustering Type | #Prototypes | #Classifiers | CAT | BIRD |
---|---|---|---|---|---|---|---|---|

HASC | NN1 | K-means | S | 15, 30, 45, 60 | 4 | 78.64 ± 1.2 | 94.52 ± 0.65 | |

HASC | NN2 | K-means | S | 15, 30, 45, 60 | 4 | 81.69 ± 1.1 | 93.22 ± 0.72 | |

HASC | NN3 | K-means | S | 15, 30, 45, 60 | 4 | 78.64 ± 1.2 | 94.91 ± 0.64 | |

HASC | NN4 | K-means | S | 15, 30, 45, 60 | 4 | 82.37 ± 1.1 | 93.33 ± 0.68 | |

F_NN | HASC | All | K-means | S | 15, 30, 45, 60 | 16 | 84.07 ± 1.0 | 94.99 ± 0.64 |

**Table 5.**Comparison between ensembles of reiterated Siamese Networks with NN1 and ensembles obtained considering different network topologies: accuracy ± standard deviation.

Name | Input Image | Network Topology | Clustering Method | Clustering Type | #Prototypes | #Classifiers | CAT | BIRD |
---|---|---|---|---|---|---|---|---|

HSup-1(1) | HASC | NN1 | K-means | S | 15 | 1 | 75.93 ± 1.5 | 93.92 ± 0.85 |

HSup-1(4) | HASC | NN1 | K-means | S | 15 | 1×4 | 81.69 ± 1.3 | 94.50 ± 0.78 |

HSup-1 | HASC | NN1 | K-means | S | 15, 30, 45, 60 | 4×1 | 78.64 ± 1.2 | 94.52 ± 0.65 |

HSup-1(8) | HASC | NN1 | K-means | S | 15, 30, 45, 60 | 4×2 | 80.68 ± 1.1 | 94.56 ± 0.75 |

HSup-1(16) | HASC | NN1 | K-means | S | 15, 30, 45, 60 | 4×4 | 81.02 ± 1.0 | 94.63 ± 0.77 |

F_NN(4) | HASC | All | K-means | S | 15 | 4 | 83.39 ± 0.9 | 94.73 ± 0.62 |

F_NN(8) | HASC | All | K-means | S | 15, 30 | 8 | 84.07 ± 0.8 | 94.90 ± 0.60 |

F_NN | HASC | All | K-means | S | 15, 30, 45, 60 | 16 | 84.07 ± 0.8 | 94.99 ± 0.58 |

Method | CAT | BIRD |
---|---|---|

OLD [43] | 82.41 | 92.97 |

F_NN | 84.07 | 94.99 |

GoogleNet | 82.98 | 92.41 |

VGG16 | 84.07 | 95.30 |

VGG19 | 83.05 | 95.19 |

GoogleNetP365 | 85.15 | 92.94 |

eCNN | 87.36 | 95.81 |

OLD + eCNN | 87.76 | 95.95 |

F_NN + eCNN | 88.47 | 96.03 |

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**MDPI and ACS Style**

Nanni, L.; Brahnam, S.; Lumini, A.; Maguolo, G.
Animal Sound Classification Using Dissimilarity Spaces. *Appl. Sci.* **2020**, *10*, 8578.
https://doi.org/10.3390/app10238578

**AMA Style**

Nanni L, Brahnam S, Lumini A, Maguolo G.
Animal Sound Classification Using Dissimilarity Spaces. *Applied Sciences*. 2020; 10(23):8578.
https://doi.org/10.3390/app10238578

**Chicago/Turabian Style**

Nanni, Loris, Sheryl Brahnam, Alessandra Lumini, and Gianluca Maguolo.
2020. "Animal Sound Classification Using Dissimilarity Spaces" *Applied Sciences* 10, no. 23: 8578.
https://doi.org/10.3390/app10238578