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Классифицируем рукописные цифры с помощью Tensorflow и Keras

Привет, Хабр! Сегодня мы окунемся в мир машинного обучения, создав свою первую нейронную сеть на Python с помощью TensorFlow и Keras для распознавания рукописных цифр из знаменитого датасета MNIST. Этот проект станет отличным стартом для тех, кто только начинает свой путь в машинном обучении, и показательным примером мощи и простоты использования современных инструментов разработки.

Перед тем как погрузиться в код, давайте разберемся, почему MNIST является таким популярным выбором для первых проектов в области машинного обучения. Датасет MNIST содержит 70 000 изображений рукописных цифр, каждое из которых представляет собой черно-белое изображение размером 28x28 пикселей. Он разделен на две части: 60 000 образцов для обучения и 10 000 для тестирования модели. Простота и одновременно вариативность данных делает MNIST идеальным полигоном для экспериментов.

Для начала работы убедитесь, что у вас установлены Python и библиотека TensorFlow. TensorFlow можно легко установить или обновить через pip, запустив команду в терминале:

$ pip install tensorflow

После установки необходимых инструментов перейдем к коду. Начнем с импорта необходимых модулей. TensorFlow и Keras предоставляют нам все необходимые инструменты для работы с датасетами, создания и обучения моделей.

import tensorflow as tf
from tensorflow.keras.datasets import mnist
from tensorflow.keras.models import Sequential
from tensorflow.keras.layers import Dense, Flatten
from tensorflow.keras.utils import to_categorical

Следующим шагом будет загрузка и предобработка данных. MNIST легко загружается прямо из Keras, что делает этот этап особенно простым. Данные уже разделены на обучающую и тестовую выборки, что позволяет нам сосредоточиться на создании и обучении модели.

(train_images, train_labels), (test_images, test_labels) = mnist.load_data()
train_images = train_images / 255.0
test_images = test_images / 255.0
train_labels = to_categorical(train_labels)
test_labels = to_categorical(test_labels)

После загрузки и нормализации данных пришло время создать модель. Мы используем Sequential API из Keras для построения модели. Наша нейронная сеть будет состоять из входного слоя, который "выпрямляет" изображения из 2D в вектор, двух скрытых слоев с 128 и 64 нейронами соответственно и функцией активации ReLU, и выходного слоя с 10 нейронами (по количеству классов цифр) и функцией активации softmax для получения вероятностей классов.

model = Sequential([
    Flatten(input_shape=(28, 28)),
    Dense(128, activation='relu'),
    Dense(64, activation='relu'),
    Dense(10, activation='softmax')
])

model.compile(optimizer='adam',
              loss='categorical_crossentropy',
              metrics=['accuracy'])

Давайте разберем этот код более подробно. Этот фрагмент кода создает модель нейронной сети с использованием Keras, высокоуровневого API для TensorFlow, предназначенного для быстрого и простого построения и обучения моделей глубокого обучения.

model = Sequential([

  • Sequential - это класс в Keras, который позволяет создать модель, добавляя слои последовательно. Здесь мы начинаем определять нашу модель как последовательность слоев.

    Flatten(input_shape=(28, 28)),

  • Flatten - это слой, который преобразует входные данные в одномерный массив. В нашем случае, каждое изображение из датасета MNIST имеет размер 28x28 пикселей. Flatten преобразует это 2D представление в 1D, получая на выходе вектор из 784 элементов (28*28). input_shape=(28, 28) указывает на форму входных данных, которые ожидает модель.

    Dense(128, activation='relu'),

  • Dense - это полносвязный слой нейронной сети, где каждый нейрон в слое соединен со всеми нейронами в предыдущем слое. Здесь создается слой из 128 нейронов. activation='relu' указывает на использование функции активации ReLU (Rectified Linear Unit). ReLU преобразует все отрицательные значения в ноль и пропускает положительные значения без изменений, что помогает решать проблему исчезающего градиента и ускоряет обучение.

    Dense(64, activation='relu'),

  • Здесь мы добавляем еще один полносвязный слой, на этот раз с 64 нейронами, также используя ReLU в качестве функции активации. Это уменьшение количества нейронов по сравнению с предыдущим слоем помогает постепенно сужать представление данных перед классификацией.

    Dense(10, activation='softmax')

  • Последний слой нашей модели также является полносвязным (Dense), но содержит 10 нейронов, поскольку нам нужно классифицировать изображения на 10 классов (цифры от 0 до 9). activation='softmax' используется в качестве функции активации для этого слоя, так как она преобразует выходные данные слоя в распределение вероятностей по 10 классам. Softmax гарантирует, что сумма всех выходных значений (вероятностей) меньше или равна 1.

])

model.compile(optimizer='adam',
              loss='categorical_crossentropy',
              metrics=['accuracy'])

  • model.compile - это метод, который конфигурирует модель для обучения. optimizer='adam' задает оптимизатор Adam для обновления весов в процессе обучения. Adam - это алгоритм оптимизации, который может автоматически корректировать скорость обучения, что делает его эффективным для большинства задач.

  • loss='categorical_crossentropy' указывает на использование категориальной кросс-энтропии в качестве функции потерь, что является стандартным выбором для задач многоклассовой классификации.

  • metrics=['accuracy'] говорит Keras, что в процессе обучения и тестирования модели нам интересно отслеживать точность (accuracy) как показатель эффективности модели.

Обучение модели — это процесс, в котором модель учится распознавать правильные паттерны в данных. В нашем случае мы обучаем ее распознавать рукописные цифры. Запустим обучение, используя метод fit, и посмотрим на результаты после нескольких эпох.

model.fit(train_images, # данные для обучения
          train_labels, # 
          epochs=10,    # кол-во эпох обучения
          validation_data=(test_images, test_labels)) # данные для проверки

После того как модель обучена, ее можно сохранить для последующего использования. Это особенно удобно, если обучение занимает значительное время или если вы хотите поделиться своей моделью с другими.

model.save('mnist_model.keras')

И вот мы подошли к самой интересной части нашего путешествия. Создав и обучив модель, мы не только прикоснулись к магии машинного обучения, но и открыли для себя дверь в мир, где алгоритмы способны узнавать и интерпретировать данные так, как это делает человек. Это путешествие лишь начинается, и впереди нас ждет множество удивительных открытий.

Не забывайте экспериментировать с архитектурой модели, количеством эпох и другими параметрами. Машинное обучение — это искусство на стыке науки и техники, и каждый новый эксперимент может привести к удивительным результатам.

Пример использования модели с WebUI

Я подготовил для вас интерактивный пример, который демонстрирует, как наша модель работает в реальном времени с пользовательским интерфейсом. Это веб-приложение позволяет вам рисовать цифры в специальном поле и мгновенно получать результаты распознавания нашей нейронной сетью.

Чтобы попробовать приложение в действии и изучить исходный код, посетите мой репозиторий на GitHub.

Надеюсь, этот материал вдохновит вас на новые проекты и поможет сделать первые шаги в мире машинного обучения. Помните, что каждый специалист начинал с чего-то маленького, и ваш путь к успеху начинается сегодня!

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    A crook swiped my Dogecoin. It ruined my whole world. Then Mr. Sylvester showed up. He fixed it all. He pulled back €211,000 for me. Not one cent missing from my profits. His steady cool and sharp tech know-how won back my trust. I got my money smooth and sound. After endless worry, relief hit me hard. I trusted him completely. Lost cash to a scam? Hit him up now at { yt7cracker@gmail . com }. His aid turned my life around. WhatsApp at +1 512 577 7957.

  • 12.10.25 21:36 blessing

    Writing this review is a joy. Marie has provided excellent service ever since I started working with her in early 2018. I was worried I wouldn't be able to get my coins back after they were stolen by hackers. I had no idea where to begin, therefore it was a nightmare for me. However, things became easier for me after my friend sent me to [email protected] and +1 7127594675 on WhatsApp. I'm happy that she was able to retrieve my bitcoin so that I could resume trading.

  • 13.10.25 01:11 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 13.10.25 01:11 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover Via Contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.10.25 01:15 tyleradams

    Hi. Please be wise, do not make the same mistake I had made in the past, I was a victim of bitcoin scam, I saw a glamorous review showering praises and marketing an investment firm, I reached out to them on what their contracts are, and I invested $28,000, which I was promised to get my first 15% profit in weeks, when it’s time to get my profits, I got to know the company was bogus, they kept asking me to invest more and I ran out of patience then requested to have my money back, they refused to answer nor refund my funds, not until a friend of mine introduced me to the NVIDIA TECH HACKERS, so I reached out and after tabling my complaints, they were swift to action and within 36 hours I got back my funds with the due profit. I couldn’t contain the joy in me. I urge you guys to reach out to NVIDIA TECH HACKERS on their email: [email protected]

  • 14.10.25 08:46 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.10.25 08:46 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 14.10.25 08:46 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: 📧 Email: [email protected] 📱 Telegram: @Capitalcryptorecover Contact: [email protected] 📞 Call/Text: +1 (336) 390-6684 🌐 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.10.25 18:07 crypto

    Cryptocurrency's digital realm presents many opportunities, but it also conceals complex frauds. It is quite painful to lose your cryptocurrency to scam. You can feel harassed and lost as a result. If you have been the victim of a cryptocurrency scam, this guide explains what to do ASAP. Following these procedures will help you avoid further issues or get your money back. Communication with Marie ([email protected] and WhatsApp: +1 7127594675) can make all the difference.

  • 15.10.25 21:52 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 15.10.25 21:52 harristhomas7376

    "In the crypto world, this is great news I want to share. Last year, I fell victim to a scam disguised as a safe investment option. I have invested in crypto trading platforms for about 10yrs thinking I was ensuring myself a retirement income, only to find that all my assets were either frozen, I believed my assets were secure — until I discovered that my BTC funds had been frozen and withdrawals were impossible. It was a devastating moment when I realized I had been scammed, and I thought my Bitcoin was gone forever, Everything changed when a close friend recommended the Capital Crypto Recover Service. Their professionalism, expertise, and dedication enabled me to recover my lost Bitcoin funds back — more than €560.000 DEM to my BTC wallet. What once felt impossible became a reality thanks to their support. If you have lost Bitcoin through scams, hacking, failed withdrawals, or similar challenges, don’t lose hope. I strongly recommend Capital Crypto Recover Service to anyone seeking a reliable and effective solution for recovering any wallet assets. They have a proven track record of successful reputation in recovering lost password assets for their clients and can help you navigate the process of recovering your funds. Don’t let scammers get away with your hard-earned money – contact Email: [email protected] Phone CALL/Text Number: +1 (336) 390-6684 Contact: [email protected] Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

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