Data replication is crucial in Hadoop administration for ensuring data availability and system reliability. Hadoop replicates data across multiple nodes in the cluster to provide fault tolerance. If a node fails, the data can still be retrieved from its replicated copies on other nodes.

For log file processing in Hadoop, the TextInputFormat is commonly used. It treats each line in the input file as a separate record, making it suitable for scenarios where log entries are present in a line-by-line format.

To troubleshoot network bandwidth issues in a Hadoop cluster, an advanced technique involves the use of Jumbo Frames. Jumbo Frames allow the transmission of larger packets, reducing overhead and improving network efficiency, which is crucial for optimizing data transfer in a Hadoop environment.

Clustering algorithms are essential in Big Data for extracting patterns and insights from large, unstructured datasets. They group similar data points together, revealing inherent structures in the data.

Apache Flume's architecture is based on the Pub-Sub (Publish-Subscribe) model. It involves the flow of data from multiple sources (publishers) to multiple destinations (subscribers), providing flexibility and scalability in handling diverse data sources in Hadoop environments.

When tuning a Hadoop cluster, optimizing the Input Split Size is crucial for MapReduce job performance. It determines the amount of data each mapper processes, and an appropriate split size helps in achieving better parallelism and efficiency in job execution.

For high-speed data processing in a Java-based Hadoop application, the combination of Apache Spark with Apache Kafka is most effective. Spark provides fast in-memory data processing, and Kafka ensures high-throughput, fault-tolerant data streaming.

The MapReduce Shuffle phase contributes to data processing efficiency by performing data sorting. During this phase, the output of the Map tasks is sorted and partitioned based on keys, ensuring that the data is grouped appropriately before reaching the Reduce tasks. Sorting facilitates faster data processing during the subsequent Reduce phase.

A Hadoop administrator should prioritize data in different HDFS directories based on the replication factor. Critical data should have a higher replication factor to ensure availability and fault tolerance in the event of node failures.

Parquet is a highly efficient file format in Hadoop designed for fast data serialization and deserialization. It is columnar-oriented, supports schema evolution, and is optimized for both compression and performance.