Community 2: Protein Sequence Classification

Disclaimer: This is uploaded from a github user, not the KAN authors. KAN authors did not writer this or proofread this carefully, hence are not responsible for mistakes in this notebook. If you have questions, please consult the github user who uploaded it. Thank you!

In this example, we will see how to use KAN in protein sequence classification. We will be using one hot encoding to encode the amino acids.

This is just an example how it can be used for protein sequences. Need to use real data to actually observe the performance.

from kan import *
import torch
import random
import numpy as np

# Hyperparameters
PROTEIN_WINDOW_SIZE = 5

# define the universe of possible input amino acids, ie. vocab list
aa_list = 'ARNDCQEGHILKMFPSTWYVX'

def one_hot_encode(protein_sequence):
    """
    One-hot encodes a protein sequence.

    Args:
        protein_sequence (str): The input protein sequence.

    Returns:
        numpy.array: The one-hot encoded representation of the protein sequence.
    """
    # Create a dictionary mapping amino acids to indices
    aa_to_index = {aa: i for i, aa in enumerate(aa_list)}

    # Initialize an array of zeros with shape (sequence_length, alphabet_length)
    encoding = np.zeros((len(protein_sequence), len(aa_list)))

    # Iterate over the protein sequence and set the corresponding index to 1
    for i, aa in enumerate(protein_sequence):
        if aa in aa_to_index:
            encoding[i, aa_to_index[aa]] = 1
        else:
            # If the amino acid is not in the alphabet, set the last index to 1 (unknown)
            encoding[i, -1] = 1

    return encoding

def generate_sample_protein_dataset(num_samples=20, protein_window_size=5):
    """
    Generate a dataset of protein sequences of length 11, keeping Lysine(K) in the center for label 1 and Serine(S) for label 0.

    Args:
        num_samples (int): Number of samples to generate.
        protein_window_size (int): Length of the protein sequence.

    Returns:
        dict: A dictionary containing train_input, test_input, train_label, and test_label.
    """

    dataset = {'train_input': [], 'test_input': [], 'train_label': [], 'test_label': []}
    alphabet = 'ARNDCQEGHILKMFPSTWYVX'

    # Generate half of the samples with label 1 and half with label 0
    label_sequence = [1] * (num_samples // 2) + [0] * (num_samples // 2)
    random.shuffle(label_sequence)

    for label in label_sequence:
        # Generate a protein sequence with 'K' in the middle for label 1 and 'S' for label 0
        if label == 1:
            center_aa = 'K'
        else:
            center_aa = 'S'
        sequence = ''.join(random.choices(alphabet.replace(center_aa, ''), k=protein_window_size//2)) + center_aa + ''.join(random.choices(alphabet.replace(center_aa, ''), k=protein_window_size//2))
        print(sequence, label)
        encoded_sequence = one_hot_encode(sequence).flatten()

        # Split the dataset into train and test (50% each)
        if len(dataset['train_input']) < num_samples // 2:
            dataset['train_input'].append(encoded_sequence)
            dataset['train_label'].append(label)
        else:
            dataset['test_input'].append(encoded_sequence)
            dataset['test_label'].append(label)

    # Convert lists to tensors
    dataset['train_input'] = torch.tensor(dataset['train_input'])
    dataset['test_input'] = torch.tensor(dataset['test_input'])
    dataset['train_label'] = torch.tensor(dataset['train_label']).view(-1, 1)
    dataset['test_label'] = torch.tensor(dataset['test_label']).view(-1, 1)

    return dataset

# Generate dataset with 10 samples
dataset = generate_sample_protein_dataset(40)

GTKYX 1
TTKPP 1
AESVY 0
MYSFD 0
SQKNT 1
IDKAC 1
AXKTA 1
TESDW 0
YXSTF 0
VTSYF 0
HYKYE 1
RDSPA 0
MDSNK 0
SCKFH 1
AHKED 1
EFKYA 1
EPKLR 1
GWSRE 0
GMSYE 0
IPSKD 0
NSKQA 1
TWKNL 1
TCKFF 1
HNKSG 1
QNSKR 0
RVKYC 1
TESCP 0
SMKXE 1
IYSEV 0
XQSKD 0
VKSYN 0
EESGV 0
IISMQ 0
FLKGE 1
VMKGH 1
PTKMH 1
TLSIQ 0
TTSMA 0
ATKEE 1
MGSFT 0

print(dataset)

{'train_input': tensor([[0., 0., 0.,  ..., 0., 0., 1.],
        [0., 0., 0.,  ..., 0., 0., 0.],
        [1., 0., 0.,  ..., 1., 0., 0.],
        ...,
        [0., 0., 0.,  ..., 0., 0., 0.],
        [0., 0., 0.,  ..., 0., 0., 0.],
        [0., 0., 0.,  ..., 0., 0., 0.]], dtype=torch.float64), 'test_input': tensor([[0., 0., 1.,  ..., 0., 0., 0.],
        [0., 0., 0.,  ..., 0., 0., 0.],
        [0., 0., 0.,  ..., 0., 0., 0.],
        ...,
        [0., 0., 0.,  ..., 0., 0., 0.],
        [1., 0., 0.,  ..., 0., 0., 0.],
        [0., 0., 0.,  ..., 0., 0., 0.]], dtype=torch.float64), 'train_label': tensor([[1],
        [1],
        [0],
        [0],
        [1],
        [1],
        [1],
        [0],
        [0],
        [0],
        [1],
        [0],
        [0],
        [1],
        [1],
        [1],
        [1],
        [0],
        [0],
        [0]]), 'test_label': tensor([[1],
        [1],
        [1],
        [1],
        [0],
        [1],
        [0],
        [1],
        [0],
        [0],
        [0],
        [0],
        [0],
        [1],
        [1],
        [1],
        [0],
        [0],
        [1],
        [0]])}

# define model
# create a KAN: 105 inputs, 2D output, and 3 hidden neurons. k=2, 3 grid intervals (grid=3).
# considering window size: 5, 5 times 21(vocab size), input-> 21 * 5

model = KAN(width=[105,3,2], grid=3, k=2)

def train_acc():
    return torch.mean((torch.round(model(dataset['train_input'])[:,0]) == dataset['train_label'][:,0]).float())

def test_acc():
    return torch.mean((torch.round(model(dataset['test_input'])[:,0]) == dataset['test_label'][:,0]).float())

results = model.train(dataset, opt="LBFGS", steps=5, metrics=(train_acc, test_acc));
results['train_acc'][-1], results['test_acc'][-1]

train loss: 1.04e-03 | test loss: 2.33e-01 | reg: 6.38e+01 : 100%|████| 5/5 [00:15<00:00,  3.00s/it]

(1.0, 0.949999988079071)

lib = ['x','x^2']

model.auto_symbolic(lib=lib)

fixing (0,0,0) with x^2, r2=0.9999999665312771
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fixing (0,57,0) with x^2, r2=0.9999999977865017
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fixing (0,81,1) with x^2, r2=0.9999999924423665
fixing (0,81,2) with x^2, r2=0.9999999407891473
fixing (0,82,0) with x^2, r2=0.0
fixing (0,82,1) with x^2, r2=0.0
fixing (0,82,2) with x^2, r2=0.0
fixing (0,83,0) with x^2, r2=0.9964873061598577
fixing (0,83,1) with x^2, r2=0.9999998536697641
fixing (0,83,2) with x^2, r2=0.9999999474125241
fixing (0,84,0) with x^2, r2=0.9999999434524759
fixing (0,84,1) with x^2, r2=0.9999999848500863
fixing (0,84,2) with x^2, r2=0.9999997362933968
fixing (0,85,0) with x^2, r2=0.9999784391692933
fixing (0,85,1) with x^2, r2=0.9999999123872062
fixing (0,85,2) with x^2, r2=0.9999981066188347
fixing (0,86,0) with x^2, r2=0.9999999470214042
fixing (0,86,1) with x^2, r2=0.9999999622653485
fixing (0,86,2) with x^2, r2=0.9999999256587131
fixing (0,87,0) with x^2, r2=0.9999838246792585
fixing (0,87,1) with x^2, r2=0.9999998906573028
fixing (0,87,2) with x^2, r2=0.9997398325048757
fixing (0,88,0) with x^2, r2=0.9999903305520499
fixing (0,88,1) with x^2, r2=0.9999999129937596
fixing (0,88,2) with x^2, r2=0.9999994338574667
fixing (0,89,0) with x^2, r2=0.9999999969824458
fixing (0,89,1) with x^2, r2=0.9999998811902262
fixing (0,89,2) with x^2, r2=0.9999999955608072
fixing (0,90,0) with x^2, r2=0.9999999968821633
fixing (0,90,1) with x^2, r2=0.9999999231999729
fixing (0,90,2) with x^2, r2=0.999999921201756
fixing (0,91,0) with x^2, r2=0.9999734544061402
fixing (0,91,1) with x^2, r2=0.9999966985161072
fixing (0,91,2) with x^2, r2=0.9999999489971586
fixing (0,92,0) with x^2, r2=0.9999999864791468
fixing (0,92,1) with x^2, r2=0.9999999698743414
fixing (0,92,2) with x^2, r2=0.9998985820640515
fixing (0,93,0) with x^2, r2=0.0
fixing (0,93,1) with x^2, r2=0.0
fixing (0,93,2) with x^2, r2=0.0
fixing (0,94,0) with x^2, r2=0.9999572021042229
fixing (0,94,1) with x^2, r2=0.9999999403042822
fixing (0,94,2) with x^2, r2=0.9999984955483119
fixing (0,95,0) with x^2, r2=0.0
fixing (0,95,1) with x^2, r2=0.0
fixing (0,95,2) with x^2, r2=0.0
fixing (0,96,0) with x^2, r2=0.0
fixing (0,96,1) with x^2, r2=0.0
fixing (0,96,2) with x^2, r2=0.0
fixing (0,97,0) with x^2, r2=0.9999999855742208
fixing (0,97,1) with x^2, r2=0.9999990622913814
fixing (0,97,2) with x^2, r2=0.9999999661558678
fixing (0,98,0) with x^2, r2=0.9999998924577429
fixing (0,98,1) with x^2, r2=0.9999999075025128
fixing (0,98,2) with x^2, r2=0.9999925555905432
fixing (0,99,0) with x^2, r2=0.0
fixing (0,99,1) with x^2, r2=0.0
fixing (0,99,2) with x^2, r2=0.0
fixing (0,100,0) with x^2, r2=0.9999999888884751
fixing (0,100,1) with x^2, r2=0.9999999053398424
fixing (0,100,2) with x^2, r2=0.9999999274642732
fixing (0,101,0) with x^2, r2=0.0
fixing (0,101,1) with x^2, r2=0.0
fixing (0,101,2) with x^2, r2=0.0
fixing (0,102,0) with x^2, r2=0.0
fixing (0,102,1) with x^2, r2=0.0
fixing (0,102,2) with x^2, r2=0.0
fixing (0,103,0) with x^2, r2=0.9999997998513549
fixing (0,103,1) with x^2, r2=0.9999999874737161
fixing (0,103,2) with x^2, r2=0.9999999891891058
fixing (0,104,0) with x^2, r2=0.0
fixing (0,104,1) with x^2, r2=0.0
fixing (0,104,2) with x^2, r2=0.0
fixing (1,0,0) with x^2, r2=0.9827286380576173
fixing (1,0,1) with x^2, r2=0.9753307156038028
fixing (1,1,0) with x^2, r2=0.99206369703365
fixing (1,1,1) with x^2, r2=0.9950033104451041
fixing (1,2,0) with x^2, r2=0.9980758555730187
fixing (1,2,1) with x^2, r2=0.9973139539011773

formula1, formula2 = model.symbolic_formula()[0]
formula1
\[\displaystyle 0.44 \left(0.02 \left(- x_{1} - 1\right)^{2} + 0.02 \left(x_{10} + 1\right)^{2} + 0.04 \left(- x_{101} - 1\right)^{2} + 0.01 \left(- x_{13} - 1\right)^{2} - 0.02 \left(- x_{14} - 1\right)^{2} - 0.02 \left(- x_{15} - 1\right)^{2} + 0.02 \left(- x_{17} - 1\right)^{2} + 0.03 \left(x_{2} + 1\right)^{2} - 0.01 \left(x_{20} + 1\right)^{2} - 0.01 \left(x_{21} + 1\right)^{2} - 0.03 \left(- x_{24} - 1\right)^{2} + 0.01 \left(- x_{26} - 1\right)^{2} - 0.02 \left(- x_{29} - 1\right)^{2} - 0.02 \left(- x_{31} - 1\right)^{2} + 0.01 \left(x_{32} + 1\right)^{2} + 0.01 \left(- x_{33} - 1\right)^{2} - 0.01 \left(x_{37} + 1\right)^{2} - 0.01 \left(- x_{39} - 1\right)^{2} - 0.01 \left(- x_{40} - 1\right)^{2} - 0.02 \left(- x_{54} - 1\right)^{2} + 0.02 \left(- x_{58} - 1\right)^{2} - 0.01 \left(- x_{6} - 1\right)^{2} - 0.01 \left(- x_{66} - 1\right)^{2} - 0.02 \left(- x_{68} - 1\right)^{2} + 0.02 \left(- x_{69} - 1\right)^{2} - 0.04 \left(x_{70} + 1\right)^{2} + 0.01 \left(- x_{71} - 1\right)^{2} + 0.03 \left(- x_{73} - 1\right)^{2} + 0.01 \left(- x_{75} - 1\right)^{2} + 0.01 \left(- x_{76} - 1\right)^{2} + 0.02 \left(- x_{77} - 1\right)^{2} - 0.01 \left(- x_{82} - 1\right)^{2} - 0.01 \left(- x_{85} - 1\right)^{2} - 0.02 \left(x_{87} + 1\right)^{2} - 0.01 \left(x_{9} + 1\right)^{2} - 0.04 \left(x_{90} + 1\right)^{2} + 0.03 \left(- x_{91} - 1\right)^{2} + 0.02 \left(x_{93} + 1\right)^{2} + 0.03 \left(x_{98} + 1\right)^{2} - 0.01 \left(- x_{99} - 1\right)^{2} - 1\right)^{2} + 0.7 \left(- 0.03 \left(- x_{1} - 1\right)^{2} - 0.02 \left(x_{10} + 1\right)^{2} + 0.02 \left(x_{101} + 1\right)^{2} - 0.03 \left(x_{104} + 1\right)^{2} + 0.05 \left(- x_{13} - 1\right)^{2} + 0.01 \left(- x_{15} - 1\right)^{2} - 0.05 \left(x_{16} + 1\right)^{2} - 0.02 \left(- x_{17} - 1\right)^{2} - 0.01 \left(- x_{2} - 1\right)^{2} + 0.01 \left(- x_{21} - 1\right)^{2} + 0.02 \left(x_{24} + 1\right)^{2} - 0.01 \left(- x_{26} - 1\right)^{2} + 0.01 \left(- x_{27} - 1\right)^{2} - 0.02 \left(- x_{28} - 1\right)^{2} - 0.03 \left(- x_{29} - 1\right)^{2} + 0.03 \left(- x_{3} - 1\right)^{2} + 0.04 \left(- x_{31} - 1\right)^{2} + 0.05 \left(- x_{32} - 1\right)^{2} + 0.03 \left(- x_{34} - 1\right)^{2} - 0.01 \left(- x_{37} - 1\right)^{2} + 0.02 \left(- x_{39} - 1\right)^{2} - 0.03 \left(x_{40} + 1\right)^{2} - 0.02 \left(x_{41} + 1\right)^{2} - 0.07 \left(- x_{54} - 1\right)^{2} + 0.09 \left(- x_{58} - 1\right)^{2} + 0.03 \left(x_{6} + 1\right)^{2} - 0.02 \left(- x_{66} - 1\right)^{2} - 0.01 \left(x_{68} + 1\right)^{2} + 0.02 \left(- x_{69} - 1\right)^{2} - 0.03 \left(x_{7} + 1\right)^{2} + 0.02 \left(x_{70} + 1\right)^{2} - 0.01 \left(x_{73} + 1\right)^{2} + 0.04 \left(x_{75} + 1\right)^{2} + 0.01 \left(x_{76} + 1\right)^{2} - 0.01 \left(x_{79} + 1\right)^{2} + 0.01 \left(- x_{82} - 1\right)^{2} + 0.03 \left(- x_{84} - 1\right)^{2} + 0.01 \left(x_{85} + 1\right)^{2} + 0.02 \left(- x_{87} - 1\right)^{2} + 0.01 \left(x_{89} + 1\right)^{2} + 0.05 \left(- x_{90} - 1\right)^{2} - 0.01 \left(- x_{91} - 1\right)^{2} - 0.03 \left(x_{92} + 1\right)^{2} + 0.01 \left(- x_{95} - 1\right)^{2} + 0.03 \left(- x_{98} - 1\right)^{2} - 1\right)^{2} + 0.17 \left(- 0.01 \left(- x_{1} - 1\right)^{2} + 0.05 \left(- x_{101} - 1\right)^{2} - 0.07 \left(x_{104} + 1\right)^{2} + 0.06 \left(- x_{14} - 1\right)^{2} + 0.01 \left(- x_{15} - 1\right)^{2} + 0.02 \left(- x_{16} - 1\right)^{2} + 0.02 \left(- x_{17} - 1\right)^{2} + 0.02 \left(- x_{20} - 1\right)^{2} - 0.07 \left(- x_{21} - 1\right)^{2} + 0.05 \left(x_{24} + 1\right)^{2} + 0.05 \left(- x_{26} - 1\right)^{2} - 0.06 \left(- x_{27} - 1\right)^{2} - 0.01 \left(- x_{28} - 1\right)^{2} - 0.02 \left(- x_{29} - 1\right)^{2} - 0.02 \left(x_{3} + 1\right)^{2} + 0.06 \left(- x_{31} - 1\right)^{2} + 0.01 \left(- x_{32} - 1\right)^{2} + 0.05 \left(- x_{34} - 1\right)^{2} + 0.06 \left(- x_{37} - 1\right)^{2} + 0.03 \left(- x_{38} - 1\right)^{2} + 0.01 \left(- x_{39} - 1\right)^{2} - 0.13 \left(- x_{54} - 1\right)^{2} + 0.09 \left(- x_{58} - 1\right)^{2} - 0.04 \left(x_{6} + 1\right)^{2} + 0.02 \left(x_{68} + 1\right)^{2} + 0.07 \left(x_{69} + 1\right)^{2} + 0.04 \left(- x_{7} - 1\right)^{2} - 0.02 \left(- x_{70} - 1\right)^{2} + 0.08 \left(- x_{71} - 1\right)^{2} + 0.02 \left(- x_{73} - 1\right)^{2} + 0.03 \left(- x_{75} - 1\right)^{2} - 0.06 \left(- x_{76} - 1\right)^{2} + 0.02 \left(- x_{77} - 1\right)^{2} - 0.04 \left(x_{79} + 1\right)^{2} - 0.08 \left(x_{82} + 1\right)^{2} - 0.04 \left(x_{84} + 1\right)^{2} + 0.06 \left(x_{85} + 1\right)^{2} + 0.05 \left(- x_{86} - 1\right)^{2} + 0.07 \left(- x_{87} - 1\right)^{2} + 0.04 \left(x_{88} + 1\right)^{2} - 0.05 \left(- x_{89} - 1\right)^{2} + 0.12 \left(x_{9} + 1\right)^{2} - 0.02 \left(x_{90} + 1\right)^{2} - 0.02 \left(- x_{91} - 1\right)^{2} - 0.01 \left(- x_{92} - 1\right)^{2} - 0.04 \left(- x_{93} - 1\right)^{2} - 0.06 \left(- x_{95} - 1\right)^{2} + 0.01 \left(x_{98} + 1\right)^{2} - 0.05 \left(- x_{99} - 1\right)^{2} - 1\right)^{2} - 0.57\]
model.plot()
../_images/Community_2_protein_sequence_classification_13_0.png