In the context of Big Data, Velocity refers to the rapid speed at which data is generated, collected, and processed. It highlights the high frequency and pace of data flow in modern data-driven environments.

The integration of Apache Storm with Hadoop allows for advanced real-time analytics on large data streams. Storm is a distributed stream processing framework that can process high-velocity data in real-time, making it suitable for applications requiring low-latency processing.

In scenarios with complex data transformations, the MultiQuery Optimization feature of Apache Pig would be most efficient. This feature allows multiple Pig Latin queries to be executed together, optimizing the execution plan and improving overall performance in situations with intricate data transformations.

The configuration parameter that sets the default replication factor for data blocks in HDFS is dfs.replication. It determines the number of copies that Hadoop creates for each data block to ensure fault tolerance and data durability.

A key consideration for integrating Kerberos in a Hadoop cluster is achieving Single Sign-On (SSO). Kerberos provides a centralized authentication system, allowing users to log in once and access various services without the need to re-enter credentials. This enhances security and simplifies user access management.

In Crunch, a PCollection is used to represent a distributed dataset in Hadoop. It is a parallel collection of data, and Crunch provides a high-level Java API for building data processing pipelines.

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.

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.

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.

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.

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.

In scenarios involving the joining of large datasets, the optimization features of Apache Pig, such as query optimization and parallel execution, significantly improve data processing efficiency. These optimization techniques help in handling large-scale data transformations more effectively, ensuring better performance in complex processing tasks.